Design of a Motion Control IC
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i 中文摘要 本論文旨在研究線性X-Y平台上之運動控制晶片。此線性X-Y平台採用兩 支永磁式同步線性馬達來驅動。第一、先定義X-Y平台及馬達驅動系統之數學模 式。第二、本文將推導類神經網路控制器並用在X-Y平台各軸之位置控制迴路上 以提升X-Y平台之控制性能。第三、應用有限狀態機器來實現上述控制器電路， 並以VHDL語言來描述此有限狀態機器及以FPGA晶片來實現。FPGA 晶片採用 ALTERA Stratix II EP2S60F672C5 。此晶片具有48,352 ALUTs ，最多492 I/O 接 腳，36 DSP方塊功能與總共2,544,192 RAM位元。另外、有一顆Nios II 處理器能 嵌入FPGA 晶片內。故此FPGA 晶片相當適合發展X-Y平台之運動控制器。第四、 X-Y平台運動軌跡規劃將在Nios II 處理器內以軟體實現。步級響應及圓形、窗 形、星形、波浪形運動軌跡響應等將用來評估運動控制性能。最後，透過Matlab 及FPGA模擬系統來分析並證實本論文提出類神經模糊控制器在X-Y平台上的有效 性及正確性。
Transcript of Design of a Motion Control IC
i
中文摘要
本論文旨在研究線性X-Y平台上之運動控制晶片。此線性X-Y平台採用兩
支永磁式同步線性馬達來驅動。第一、先定義X-Y平台及馬達驅動系統之數學模
式。第二、本文將推導類神經網路控制器並用在X-Y平台各軸之位置控制迴路上
以提升X-Y平台之控制性能。第三、應用有限狀態機器來實現上述控制器電路，
並以VHDL語言來描述此有限狀態機器及以FPGA晶片來實現。FPGA 晶片採用
ALTERA Stratix II EP2S60F672C5。此晶片具有48,352 ALUTs，最多492 I/O 接
腳，36 DSP方塊功能與總共2,544,192 RAM位元。另外、有一顆Nios II 處理器能
嵌入FPGA 晶片內。故此FPGA 晶片相當適合發展X-Y平台之運動控制器。第四、
X-Y平台運動軌跡規劃將在Nios II 處理器內以軟體實現。步級響應及圓形、窗
形、星形、波浪形運動軌跡響應等將用來評估運動控制性能。最後，透過Matlab
及FPGA模擬系統來分析並證實本論文提出類神經模糊控制器在X-Y平台上的有效
性及正確性。
ii
Abstract
The aim of this thesis is to study the principles of a motion control IC for a
linear X-Y table which is driven by two Permanent Magnet Linear Synchronous Motors
(PMLSMs). Firstly, a mathematical model of PMLSM drive is defined. And for
increasing the performance of the PMLSM drive system, a NFC (Neural Fuzzy
Controller) is derived and applied to the position control loop of PMLSM drive.
Secondly, the FPGA by using FSM (Finite State Machine) method is presented to
realize the aforementioned controllers, and the VHDL (VHSIC Hardware Description
Language) is adopted to describe the circuit of the FSM. However, a mathematical X-Y
table constructed by two NFCs and two PMLSM models is described and set up in
FPGA. Thirdly, the motion trajectory planning for X-Y table is implemented by
software using Nios II processor. The motion trajectory evaluated in this thesis includes
the step response, sinusoid response, circular trajectory tracking, window trajectory
tracking, star trajectory tracking and flexuous trajectory tracking, etc. The program in
Nios II processor is coded using C language. Fourthly, the simulation is carried out by
using MATLAB package and FPGA (Field Programmable Gate Array) developed
environment-QUARTUS II, respectively. The FPGA chip adopts ALTERA Stratix II
EP2S60F672C5 and a Nios II processor can be embedded into this FPGA chip. Finally,
the simulation results verified the effectiveness of the proposed motion control IC for
linear X-Y table under different motion trajectories.
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Acknowledgments
The work was carried out at Southern Taiwan University (STU) during the
period from 2008 to 2010. I would like to thank all of my teachers in Department of
Electrical Engineering.
I wish to express my deepest appreciation to my advisor professor Ying-Shieh
Kung for his guidance and support throughout my research.
I want to thank my labmates: Yang Chih Yuan, Hsieh Nan Hui, Yang Feng
Ming, Sarah, Blanca and Bui Thi Hai Linh for their help and advice. And I also thank
all friends who make have unforgettable time and sweet memories in Taiwan.
I also wish to express my gratitude to my family and my wife’s family for their
support.
Finally, I am grateful to my parents and my wife Catarina for their constant love,
support, encouragement. And special send my love to my son.
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Contents 摘要 ................................................................................................................................... i
Abstract ............................................................................................................................ ii
Acknowledgments ......................................................................................................... iiii
Contents .......................................................................................................................... iv
List of tables .................................................................................................................... v
List of figures .................................................................................................................. vi
Chapter 1 Introduction .................................................................................................... 1
1.1 Research background & Literature review ............................................................... 1
1.2 Chapter outline ......................................................................................................... 4
Chapter 2 Mathematical model of PMLSM drive and neural fuzzy controller design ... 5
2.1 Mathematical model of PMLSM .............................................................................. 5
2.1.1 The structure of PMLSM ................................................................................. 6
2.1.2 Modelling of PMLSM ..................................................................................... 8
2.2 Neural Fuzzy Controller (NFC) design .................................................................. 10
2.2.1 PI type Fuzzy Controller (FC) ....................................................................... 10
2.2.2 Reference Model (RM) .................................................................................. 12
2.2.3 Radial Basic Function Neural Network (RBFNN) ........................................ 12
2.4 Fuzzy parameters adjusting mechanism ................................................................. 14
Chapter 3 Hardware and software co-design of the servo control system using SoPC
technology ....................................................................................................................... 16
3.1 Description of SoPC builder design ....................................................................... 16
3.1.1 Stratix II EP2S60F672C5 .............................................................................. 16
3.1.2 Nios II embedded processor .......................................................................... 18
3.2 Hardware and software co-design for a closed-loop servo control system ............ 20
Chapter 4 Hardware realization of the neural fuzzy controller for X-Y table .............. 33
4.1 Plant IP ................................................................................................................... 33
4.2 Speed controller IP ................................................................................................. 35
4.3 Position controller IP .............................................................................................. 36
4.3.1 Reference model ............................................................................................ 39
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4.3.2 PI type fuzzy controller.................................................................................. 41
4.3.3 Radial basis function neural network............................................................. 42
4.3.4 Adjusting mechanism .................................................................................... 47
Chapter 5 Software realization of the motion trajectory for linear X-Y table .............. 48
5.1 The Nios II software ............................................................................................... 49
5.2 Motion trajectory .................................................................................................... 52
5.2.1 Point to point motion trajectory ..................................................................... 52
5.2.2 Circular motion trajectory .............................................................................. 54
5.2.3 Star motion trajectory .................................................................................... 55
5.2.4 Window motion trajectory ............................................................................. 56
5.2.5 Flexuous motion trajectory ............................................................................ 57
5.3 Perfomance measures ............................................................................................. 59
Chapter 6 Simulation results of the motion controller .................................................. 60
6.1 Simulation in MATLAB......................................................................................... 60
6.1.1 One dimensional motion trajectory................................................................ 60
6.1.2 Two dimensional motion trajectory ............................................................... 65
6.2 Simulation in FPGA ............................................................................................... 76
6.2.1 One dimensional motion trajectory.............................................................. 76
6.2.2 Two dimensional motion trajectory ............................................................. 79
Chapter 7 Conclusion and future works ........................................................................ 89
7.1 Overview ................................................................................................................ 89
7.2 Future works ........................................................................................................... 89
REFERENCES .............................................................................................................. 90
BIOGRAPHY ................................................................................................................ 95
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List of tables
Table 3.1: Stratix II EP2S60F672C5 device features ..................................................... 17
Table 3.2: The simulation results using method 1 .......................................................... 29
Table 3.3: The simulation results using method 1 and 2 ................................................ 32
Table 5.1: Utility evaluation of motion control IC for Linear X-Y table in FPGA ........ 49
Table 6.1: The tracking error of trajectory response in case using FC(MATLAB) ....... 68
Table 6.2: The rule table after adjusted in the circular simulation case(MATLAB) ...... 70
Table 6.3: The rule table after adjusted in the star simulation case(MATLAB) ............ 71
Table 6.4: The rule table after adjusted in the window simulation case ......................... 72
Table 6.5: The rule table after adjusted in the flexuous simulation case ........................ 73
Table 6.6: The tracking error of trajectory response in case using NFC ........................ 74
Table 6.7: The tracking error of trajectory response in the case using FC(FPGA) ........ 82
Table 6.8: The tracking error of trajectory response in the case using NFC(FPGA) ..... 87
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List of figures
Figure 2.1: The block diagram of the motion controller system for PMLSM .................. 5
Figure 2.2: Unrolling a rotary electric machine ................................................................ 9
Figure 2.3: Halving and squashing a rotary electric machine ......................................... 10
Figure 2.4: The structure of PMLSM ............................................................................... 7
Figure 2.5: Motor Axis d & q Mode ................................................................................. 8
Figure 2.6: Simplified control block diagram for PMLSM .............................................. 9
Figure 2.7: The architecture of a neural-fuzzy controller system for PMLSM .............. 10
Figure 2.8: Fuzzification and fuzzy rule table ................................................................ 11
Figure 2.9: RBF neural network ..................................................................................... 13
Figure 3.1: FPGA development board ............................................................................ 17
Figure 3.2: The Nios Embedded Processor .................................................................... 19
Figure 3.3: The Nios Development Tool Flow ............................................................... 20
Figure 3.4: Closed-loop control system .......................................................................... 21
Figure 3.5: Circuit and the separate block diagram of overall control system ............... 22
Figure 3.6: VHDL code of overall closed-loop control system ...................................... 22
Figure 3.7: The circuit design of plant using Finite State Machine (FSM) .................... 23
Figure 3.8: VHDL code of Plant ..................................................................................... 24
Figure 3.9: The circuit design of PID controller using Finite State Machine ................. 24
Figure 3.10: VHDL code of PID controller .................................................................... 26
Figure 3.11: Simulation results in QUARTUS II (case 1) .............................................. 27
Figure 3.12: Simulation results in MATLAB (case 1) ................................................... 28
Figure 3.13: Simulation result in Quartus II (case 2) ..................................................... 28
Figure 3.14: Simulation result in MATLAB (case 2) ..................................................... 29
Figure 3.15: Hardware and software co-design of closed-loop servo control system .... 30
Figure 3.16: The C languages for PID controller ........................................................... 31
Figure 3.17: Simulation results when using hardware and software co-design .............. 32
Figure 4.1: FPGA-realization of single axis position controller .........................................
based on neural fuzzy control ...................................................................... 33
Figure 4.2: State diagram of FSM for describing the Plant ............................................ 34
Figure 4.3: The block of Plant ........................................................................................ 35
Figure 4.4: State diagram of FSM for describing the Speed P controller ....................... 35
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Figure 4.5: The block of Speed controller ...................................................................... 36
Figure 4.6: The block diagram of neural fuzzy controller .............................................. 36
Figure 4.7: State diagram of FSM for describing the overall position controller IP ...... 37
Figure 4.8: The function block of neural fuzzy Controller ............................................. 39
Figure 4.9: State diagram of FSM for describing the reference model .......................... 41
Figure 4.10: State diagram of FSM for describing the Fuzzy + PI controller ................ 42
Figure 4.11: Structure of the proposed RBF NN ............................................................ 42
Figure 4.12: State diagram of FSM for describing the RBF NN .................................... 43
Figure 4.13: State diagram of FSM for describing the radial-basic function ................. 43
Figure 4.14: State diagram of FSM for describing the norm .......................................... 44
Figure 4.15: State diagram of FSM for describing the exponential function ................. 45
Figure 4.16: The block of exponential function ............................................................. 45
Figure 4.17: State diagram of FSM for describing the training RBF NN ...................... 46
Figure 4.18: State diagram of FSM for describing jacobian ........................................... 47
Figure 4.19: State diagram of FSM for describing jacobian ........................................... 47
Figure 5.1: The architecture of a motion controller for X-Y table ................................. 48
Figure 5.2: Nios II IDE development system diagram ................................................... 50
Figure 5.3: Exception handling process .......................................................................... 51
Figure 5.4: Typical initialization settings 2 kHz interrupts ............................................ 51
Figure 5.5: Flow chart of main and ISR program ........................................................... 52
Figure 5.6: Point-to-point trapezoidal velocity profile ................................................... 54
Figure 5.7: Circular motion trajectory ............................................................................ 54
Figure 5.8: Star motion trajectory ................................................................................... 55
Figure 5.9: Window motion trajectory ........................................................................... 57
Figure 5.10 Flexuous motion trajectory .......................................................................... 58
Figure 6.1: Diagram of fuzzy control for PMLSM drive ............................................... 60
Figure 6.2: Diagram of Neural fuzzy control for PMLSM drive .................................... 61
Figure 6.3: Membership functions, fuzzy rule table and control effort surface ............. 61
Figure 6.4: Radial basis function neural network ........................................................... 63
Figure 6.5: Position response and control effort when using .............................................
Fuzzy controller (MATLAB) ....................................................................... 64
Figure 6.6: Position response and control effort when using .............................................
Neural-Fuzzy controller (MATLAB) .......................................................... 64
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Figure 6.7: Rule table after adjusted and the control effort surface for ..............................
Step response with neuron fuzzy controller (MATLAB) ............................ 65
Figure 6.8: Diagram of fuzzy control for linear X-Y table ............................................. 66
Figure 6.9: FC using circular trajectory tracking response (MATLAB) ........................ 66
Figure 6.10: FC using star trajectory tracking response (MATLAB) ............................. 67
Figure 6.11: FC using window trajectory tracking response (MATLAB) ..................... 67
Figure 6.12: FC using flexuous trajectory tracking response (MATLAB) ..................... 68
Figure 6.13: Diagram of neural fuzzy control for linear X-Y table ................................ 69
Figure 6.14: NFC using circular trajectory tracking response (MATLAB) ................... 70
Figure 6.15: NFC using star trajectory tracking response (MATLAB) .......................... 71
Figure 6.16: NFC using window trajectory tracking response (MATLAB) ................... 72
Figure 6.17: NFC using flexuous trajectory tracking response (MATLAB) .................. 73
Figure 6.18: Average of the tracking error (MATLAB) ................................................. 75
Figure 6.19: Standard deviation of the tracking error (MATLAB) ................................ 75
Figure 6.20: Rule table and the control effort surface (FPGA) ...................................... 76
Figure 6.21: Step response and control effort when using FC (FPGA) .......................... 78
Figure 6.22: Step response and control effort when using NFC (FPGA) ....................... 78
Figure 6.23: Rule table after adjusted and the control effort surface for ............................
Step response (simulation in FPGA) ......................................................... 79
Figure 6.24: FC using circular trajectory tracking response (FPGA) ............................. 80
Figure 6.25: FC using star trajectory tracking response (FPGA) ................................... 80
Figure 6.26: FC using window trajectory tracking response (FPGA) ............................ 81
Figure 6.27: FC using flexuous trajectory tracking response (FPGA) ........................... 81
Figure 6.28: NFC using circular trajectory tracking response (FPGA) .......................... 83
Figure 6.29: Rule table after adjusted and the control effort surface for ............................
Circular motion trajectory .......................................................................... 83
Figure 6.30: NFC using star trajectory tracking response (FPGA) ................................ 84
Figure 6.31: Rule table after adjusted and the control effort surface for ............................
star motion trajectory ................................................................................. 84
Figure 6.32: NFC using circular trajectory tracking response (FPGA) .......................... 85
Figure 6.33: Rule table after adjusted and the control effort surface for ............................
Window motion trajectory ......................................................................... 85
Figure 6.34: NFC using flexuous trajectory tracking response (FPGA) ........................ 86
x
Figure 6.35: Rule table after adjusted and the control effort surface for ............................
Flexuous motion trajectory ........................................................................ 86
Figure 6.36: The average tracking error (FPGA) ........................................................... 88
Figure 6.37: Standard deviation of the tracking error (FPGA) ....................................... 88
1
Chapter 1
Introduction
1.1 Research background & Literature review
Nowadays, modern control systems, such as semiconductor manufacturing
equipment, transportation, X-Y driving devices and robots have become important
systems which usually require high speed and high accuracy linear motions [1]. These
systems can be divided into two parts includes the mechanical parts with servo drive
systems and the servo controllers that control the multi axis motion of the mechanical
parts. In general, the system is composed of an X-Y table, where each motion axis is
driven by an individual actuator system, such as DC or AC motors [2]. DC motors used
to be popular in the industry because of their simple control; you only need to control
the armature voltage to vary the motor’s speed. Because the motor’s carbon brush and
convertor were mechanical components, they would produce sparks and cause damage
when the motor was running, which was one major shortcoming of the DC motor. In
addition, the DC motor posed a threat to the environment, had a short life cycle, and
was expensive to maintain. And AC motors can be classified into three different types:
the synchronous motor, the induction motor, and the reluctance motor. The stator and
rotor of an AC motor are the only contact bearing components. The spinning of the rotor
is caused by the stator’s magnetic field, and needs more complicated control technology
(such as the magnetic field guide control) to implement different movements. With the
development of semiconductor control devices, the computation required for AC motor
control is met easily. Because of this advantage, AC motors are very popular today [3].
The motion mechanisms using motor drives usually lead to the existence of
unknown dynamics, coupled interferences, unmeasured friction, and disturbance among
each other, which often significantly deteriorates the system performance in machining
processes [4]. Therefore, in order to improve the tracking performance in machining
processes, many studies have been presented [5]–[7]. First, the stability of CNC
machines with output time delay and the measurement error are studied in [5]. Phase
margin and frequency response analyses are used for controller design to determine
regions of system stability. However, cross-coupled dynamics, disturbance load torque,
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and uncertainties among each axis mechanism were not considered in the stability
analysis. Second, the dead zone nonlinearity due to the mechanical motion system was
compensated using an adaptive fuzzy controller with the estimation of the dead zone
nonlinearity [6]. From the results shown in [6], it is obvious that the dead zone
nonlinearity can be effectively compensated, but the linear state feedback control used
in [5] for position tracking control was designed without robustness consideration. Then,
due to the cross-coupled effect of the X-Y table, the nonlinear friction compensation
based on single axis motion dynamics was presented in [7]. The nonlinear friction with
integrated disturbance load torque was represented by an approximated nonlinear
function. Moreover, the compensator design was presented using the input/output
relations of the nonlinear function. Unfortunately, robustness to variations of system
parameters was not considered simultaneously in the design of the compensator. In
modern manufacturing, the design of a two axis motion control with high performance
and high precision machining is required. Therefore, the motion control of an X-Y table,
which is composed of two permanent-magnet linear synchronous motors (PMLSMs), is
considered in this thesis. Such a system can be found in many applications, e.g.,
machine tools and integrated circuit (IC) manufacturing equipment. Moreover, The
advantages of superior power density, high performance motion control with fast speed
as well as better accuracy, are such that permanent magnet linear synchronous motors
(PMLSMs) are being increasingly used [8-10]. At the same time, the end effect of
PMLSM can be controlled more easily than linear induction motor. Therefore, PMLSM
is suitable for high-performance servo applications and has been used widely for
industrial robots, machine tools, semiconductor manufacturing systems, X-Y driving
devices, etc. [11]–[14]. However, the PMLSM does not use conventional gears or ball
screws, so uncertainties, such as parameter variations, external load disturbance, friction
force and unknown dynamics, in the drive system greatly affect servo performance and
diminish the performance of the pre-designed PMLSM driving system [5]. In addition,
since the operation of PMLSM involves two contacting bodies, nonlinear friction force
is inevitable among the forces of motion. The friction characteristic may be easily
varied due to the change of normal forces in contact, temperature, and humidity [15],
[16]. In addition, in a closed-loop control system, the nonlinear friction force often
results in steady state error, limit cycle, and low bandwidth [15], [16]. Furthermore,
friction is a natural phenomenon that is quite difficult to model and is not completely
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understood. Therefore, in order to obtain high performance motion control system, the
compensation of the mentioned uncertainties and nonlinear friction force, which directly
impose on the mover of the PMLSM, quickly and directly is very important. Recently,
many researchers have focused on this area and have employed different control
algorithms for PMLSM drives to improve their performance. For instance, some
researchers have proposed a robust control for the PMLSM. The robust control design is
based on the parameters and model of the PMLSM. However, measuring the parameters
of the PMLSM is very difficult [17]. Some researchers have used conventional adaptive
control [1, 18, and 19] for the PMLSM. Conventional adaptive control method does not
depend on accurate knowledge of the parameters. In recent years, intelligent control
techniques [20-21,22-26] such as fuzzy control, neural networks control, adaptive fuzzy
control, and neural fuzzy controller have been developed and applied to the position
control of servo motor drives to yield high operating performance. A high performance
motor control system should have a fast dynamic response to adjustments in its control
parameters, so the motor outputs influenced by the disturbances can recover to their
original status as soon as possible [28]. Specially, neural fuzzy systems have been
largely considered by researchers as they employ the learning ability of the neural
network with the advantage of the rule base structure of fuzzy logic [29]. For example,
if the domain knowledge or human expert knowledge of the controller is only partially
available, such integration can automatically be incorporated into the adaptive system in
which the remaining unknown control knowledge can then be acquired through the
learning process by the neural network. Other advantages include fine-tuning and
automatic setting of the fuzzy controller parameters, which are often obtained
heuristically rather than analytically and as such can eliminate laborious and time
consuming procedures [30-31].
In many neural-control paradigms, the back-propagation algorithm has been
popularly used. However, being a gradient descent method, such algorithm has many
drawbacks which include slow convergence, local minimum, etc [32]. In this study, the
Radial Basis Function neural network (RBF) [33-34] is implemented as a neural-fuzzy
controller (NFC) and identifies PMLSM to tune parameters of fuzzy controller.
Nevertheless, the execution of the intelligent control techniques requires a lot of
computations, so implementation of these highly complex control algorithms depend on
the PC systems in most studies [35-36]. Nowadays, owing to the progress of VLSI
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technology, the FPGA provides a compromise between the special purpose application
specific integrated circuit hardware and general purpose processors. Therefore, using an
FPGA to form a compact, low cost, and high performance servo system for precision
machine has become an important issue. However, in many research works, the FPGA
is merely used to realize the hardware part of the overall control system [38], [39]. In
recent years, an embedded processor Intellectual Property (IP) and an application IP can
now be developed and downloaded into the FPGA to construct a System-on-a-
Programmable-Chip (SoPC) environment [37].
The FPGA chip employed herein is an Altera Stratix II EP2S60F672C5 with
48,352 ALUTs, maximum 492 user I/O pins, 36 DSP blocks, 2,544,192 bits of RAM,
and a Nios II embedded processor. Therefore, it is suitable for the development of the
servo motion controller of the X-Y table. Finally, the simulation results verified the
correctness and effectiveness of the controllers show that the neural fuzzy controller for
XY table was the best.
1.2 Chapter outline
The thesis is divided into seven chapters. The outlines of chapters are as follow:
Chapter 1: Gives research background and review the literatures.
Chapter 2: Introduces to mathematic model of PMLSM and neural fuzzy controller
design.
Chapter 3: Shows the SoPC design methodology of servo control system
Chapter 4: Presents hardware design of the neural fuzzy controller for linear X-Y table
in FPGA
Chapter 5: Presents software realization of the motion trajectory for linear X-Y table in
FPGA
Chapter 6: Simulates the control system in MATLAB and in FPGA
Chapter 7: Gives a conclusion which gives the summary and some future work.
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Chapter 2
Mathematical model of PMLSM drive and neural
fuzzy controller design
The overall architecture of the control system for PMLSM is shown in Figure 2.1
which includes two control loops:
- Speed loop: P controller is presented.
- Position loop: neural fuzzy controller is adopted.
Figure 2.1: The block diagram of the motion controller system for PMLSM
2.1 Mathematical model of PMLSM [43-44]
Linear motors (LMs) fall into two main types: linear synchronous motors (LSM)
and linear induction motors (LIM). In linear induction motors the rotor magnetic field is
produced by the induced current, when in linear synchronous motors rotor field is
produced by the permanent magnets or by the independently generated current. Linear
motors could be applied in many areas. Industrial automation systems are the main field
of application of the linear motors. Linear induction motors have found applications in
the following areas: conveyor systems; liquid metal pumping; material handling; low
and medium speed trains. Linear synchronous motors are successfully utilized in any
application where high precision motion control is required: machining tools; welding
robots; laser scribing systems; industrial laser cutting systems; industrial robots. Linear
motors are used for high-speed ground transportation as propulsion and levitation
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systems. Also extensive use of LMs could be found in building and factory
transportation systems. LMs are applied as elevator hoisting machines, ropeless
elevators in ultra-high buildings, horizontal transportation systems at factories. There
are several types of LSMs which are classified according to the following items:
• Short primary / short secondary
• Ironcore / ironless
• Moving primary / moving secondary
• Tubular / flat
• Permanent magnet excitation / electromagnetic excitation
• Single sided / double sided
• Transverse flux / longitudinal flux
Nowadays flat brushless permanent magnet (PM) linear synchronous motors are
dominating. The main reasons for the PM-machine popularity are higher force density,
efficiency and faster response due to existing magnetic field than in LIMs.
2.1.1 The structure of PMLSM
Linear Motors (LMs) develop directly magnetic forces between a stator and a
translator, or mover, acting upon a linear prime mover (for generating) or on a mover
machine (for actuation). No mechanical transmission is required between the translator
and the prime mover. Since there is a linear counterpart for every rotary electromagnetic
machine, we expect to encounter numerous conventional or easy to visualize LMs.
Figure 2.2 illustrates the now classic birth of the linear counterpart of a rotary induction
machine by simply unrolling it. A flat single sided topology is thus obtained.
Alternatively, if the stator and rotor of a rotary machine are halved and "squashed"
subsequently, a flat double sided configuration results, as shown in Figure 2.3.
Figure 2.2: Unrolling a rotary electric machine
(a) Profile of motor rotation (b) Single sided-type linear motor
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Figure 2.3: Halving and squashing a rotary electric machine
(a) Profile of motor rotation (b) Double sided-type linear motor
Analysis of LMs, one traditional way to describe the construction of PMLSM is
to cut and unroll a PM rotary synchronous motor to produce a flattened configuration as
shown in Figure 2.4. So we have a lying plate with permanent magnets and a stator
winding which slides in a straight line. The slider which consists of a slotted armature
and three-phase windings is termed moving primary, or mover, or slide, while the fixed
magnet plate could be named as secondary, or exciter, or, somewhat confusingly, stator.
The primary and the secondary are separated by a flat air gap. The constant value of the
air gap is maintained by guide rail and bearings.
Figure 2.4: The construction of a PMLSM
When the coils of the mover are excited by 3-phase alternating current and armature
magnetic field is generated. This field produces a travelling flux wave along the main
axis of the linear motor. This flux wave interacts with the flux produced by the
permanent magnets of the stationary fixed magnet plate. Interaction results in an
electromagnetic force which moves the primary in positive or negative direction in
dependence of the alignment of the permanent magnets along the magnet plate. In this
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case such a force is called thrust, or traction force, or propulsion force. The linear
motion is obtained directly by electromagnetic force.
2.1.2 Modelling of PMLSM [3]
The equivalent electric circuit of the permanent magnet synchronous motor is
shown in Figure 3, where the voltage equation’s reference coordinates are settled on the
synchronous rotation coordinates.
(a) Axis d mode
(b) Axis q mode
Figure 2.5: Motor Axis d & q mode
According to Figure 2.4, the axis d-q voltage can be shown as:
0
fe
ds
qs
dssqse
dseqss
ds
qs
i
i
sLrL
LsLr
v
v
(2.1)
The voltage is calculated to:
ds
ds
qs
feqs
ds
qs
ds
s
ds
qs
e
qs
ds
e
qs
s
ds
qs
L
v
L
v
i
i
L
r
L
L
L
L
L
r
i
i
dt
d
(2.2)
9
From (2.2), the mathematical model of a typical PMLSM is described as following
ds
d
qsp
ds
qs
d
d
sdsv
Lix
L
Li
L
r
dt
di 1.
(2.3)
qs
qs
p
qs
f
qs
qs
s
dsp
qs
dsqsv
Lx
Li
L
rix
L
L
dt
di 1..
(2.4)
Where vds, vqs are the d and q axis voltages; ids, iqs, are the d and q axis currents, rs is the
phase winding resistance; Lds, Lqs are the d and q axis inductance; p
x is the translator
speed; f
is the permanent magnet flux linkage; is the pole pitch. The developed
electromagnetic thrust force is given by [3]
qsfdsqsdseiiLLF ))((
2
3
(2.5)
The current control of a PMLSM drive is based on a vector control approach. That is, if
we control ids to 0, the PMLSM will be decoupled, so that control a PMLSM will
become easy as to control a DC linear motor. After simplification and considering the
mechanical load, the model of a PMLSM can be written as the following equations,
qstqfeiKiF
2
3 (2.6)
with
ftK
2
3 (2.7)
and the mechanical dynamic equation of PMLSM is
dt
dxB
dt
xdMFF
p
m
p
mLe
2
2
(2.8)
wheree
F is the motor thrust force,t
K is force constant, m
M is the total mass of the
moving element,m
B is viscous friction coefficient and L
F is the external force. And the
control block diagram in current loop can be simplified as the Figure 2.6.
*i q
K t
F L
F e+-
BsM mm
1
s
1 X P
Figure 2.6: Simplified control block diagram for PMLSM
10
2.2 Neural Fuzzy Controller (NFC) design
The solid rectangular area in Figure 2.7 presents the structure of a fuzzy
controller based on RBFNN identification for PMLSM drive. It consists of a fuzzy
controller, a reference model, a radial basis function neural networks and an adjusting
mechanism. Neural fuzzy control is similar to conventional adaptive control, but they
differ in some ways. The main differences are that (i) the fuzzy controller has a special
nonlinear structure that is suitable for various plant conditions, and (ii) engineer
experience about motor dynamics and control knowledge can be incorporated into an
NFC based on RBFNN identification. Detailed description of a neural fuzzy controller
is as follows.
Inference
Mechanism DFIFI
Reference model
1-Z-1
1-Z-1
Z-1
neural fuzzy controller
Radial Basis Function Neural Networks
PI
cmd_speed
u
xe
info_position
xe
xm
+
X*e
-
e
de
uf
yrbf
+-
Jacobian transformationcmd_speed
info_position
Adjusting Mechanism
Kv kt
FL
Fe
+-
+-
Xp
PMLSM drive
mm BSM
1
S
1KeKe
Xe
1/Ke
11 Z
Figure 2.7: The architecture of a neural fuzzy controller system for PMLSM
2.2.1 PI type Fuzzy Controller (FC)
In Figure 2.8, the tracking error and the change of the error, e , e are defined as
)()()( kxkxkeem
(2.9)
)1()()( kekeke (2.10)
and e, de and uf are input and output variables of FC, respectively.
The design procedure of the FC is as follows:
(a) Take e, de as the input variables of FC, and define their linguist variables as E
and dE. The linguist value of E and dE are {A0, A1, A2, A3, A4, A5, A6} and {B0,
B1, B2, B3, B4, B5, B6}, respectively. Each linguist value of E and dE is based on
11
the symmetrical triangular membership function which is shown in Figure 2.4.
(b) Compute the membership degree of e and de. Figure 2.8 shows that the only two
linguistic values are excited (resulting in a non-zero membership) in any input
value, and it’s the membership degree )( eAi
and )( deB j
can be straightforward
derived from Figure 2.8.
(c) Select the initial fuzzy control rules by referring to the dynamic response
characteristics , such as
ij,jic is THEN B is e and A is IF
fue (2.11)
where i and j = 0~6, Ai and Bj are fuzzy number, and cj,i is real number. The graph of
fuzzification and fuzzy rule table is also shown in Figure 2.4.
Figure 2.8: Fuzzification and fuzzy rule table
(d) Construct the fuzzy system uf(e,de) by using the singleton fuzzifier, product-
inference rule, and central average defuzzifier method. Although there are totally 49
fuzzy rules in Figure 2.4 will be inferred, actually only 4 fuzzy rules can be
effectively excited to generate a non-zero output. Therefore, the output of FC can be
expressed as follows:
12
*
)(*)(
)](*)([
),(,
1 1
,1 1
1 1
,
mn
i
in
j
jmnmi
in
j
jmBA
i
in
j
jmBAnm
fdc
dee
deec
deeu
mn
mn
(2.12)
where )(*)( ,
deedmn BAmn
. And thosen,m
c are adjustable parameters. In addition, it
is straightforward to obtain 1 1 1
,
i
in
j
jmmn
d in (2.10).
The output of FC is:
)(*)()1()( kukkkukufipi
(2.13)
)1()()( kukuku (2.14)
2.2.2 Reference Model (RM)
Second order system with natural frequency, n and damping ratio, is usually as
the RM in the neural fuzzy control system and as follow
22
2
*2)(
)(
nn
n
r
r
ss
s
(2.15)
Applying the bilinear transformation, the second order system can be transformed to a
discrete model by
2
2
1
1
2
2
1
10
1*
1
1)(
)(
zbzb
zazaa
zx
zx
r
r (2.16)
Furthermore, the difference equation is written as:
)2()1()()2()1()(*
2
*
1
*
021 kxakxakxakxbkxbkx
rrrrrr (2.17)
2.2.3 Radial Basic Function Neural Network (RBFNN)
2.2.3.1 RBF network architecture
The architecture of the RBFNN is presented in Figure 2.9. The network consists of
three layers: an input layer, a hidden layer and an output layer.
Input layer: An input vector x, are applied to all neurons in the hidden layer.
T
nxxxx ,...,
21 (2.18)
In Figure 2.10, input of RBF neural network is
13
Tkxkxkux 1,, (2.19)
Hidden layer: The hidden layer is composed of number n RBFs that are
connected directly to all the elements in the output layer. A node in the hidden
layer will produce a greater output when the input pattern presented is close to
its center. The basis function for the jth
hidden node is often defined by a
Gaussian exponential function shown as follows:
mjx
b
cx
hj
j
j....,4,3,2,1,
2exp
2
2
(2.20)
Where b jthe width of the j
th neuron is, cccc jnjj
T
j,...,, 21 is the center of j
th
RBF unit.
Output layer: The network output yrbf
is formed by a linearly weighted sum of
the number of basic functions in the hidden layer. The values for the output
nodes can be calculated as
h jw jx
m
j
rbf
1
(2.21)
Where w jis the weight from the j
th hidden layer neuron to the output layer
neuron and hj is the output of the jth
node in the hidden layer.
Figure 2.9: RBF neural network
14
2.2.3.2 Training algorithm in RBFNN
The instantaneous cost function is defined as
22
2
1)(
2
1nnprbf
exxJ (2.22)
Then according to the gradient descent method, the learning algorithm of weights, node
center and variance are adjusted by following equations:
)()()()1( khkekwkwjnnjj
(2.23)
k
kkkkkekk
b
cxhwcc
j
jii
jjjiji 21
(2.24)
kkkkekk
b
kckxhwbb
j
jjjj
jii
3
2
1
(2.25)
Where j=1,2,..m, i=1,2,3 and is a learning rate. Further, the u
xp
is Jacobian
transformation and can be derived from Figure 2.3:
b
chw
xx
j
jm
j
jj
rbfpku
uu2
1
1
(2.26)
2.4 Fuzzy parameters adjusting mechanism
The gradient descent method is used to derive the FC control law in Figure 2.3.
The adjusting of fuzzy controller parameters is to minimize the square error between the
mover position and the output of the RM. The instantaneous cost function is defined by
22)
2
1
2
1pme
xxeJ (2.27)
and the parameters of nmc , are adjusted according to
c
Jc
nm
e
nm
,
,
(2.28)
with m = j, j+1, n = i,i+1 and where represents learning rate. The chain rule is used
and the partial differential equation for e
J in (2.25) can be written as
nm
f
f
p
nm
e
c
u
u
xe
c
J
,,
(2.29)
From (2.10), we can get
15
mn
nm
fd
kc
ku
,
,)(
)(
(2.30)
and using Jacobian formulation from (2.24)
b
chw
xx
j
jm
j
jjip
rbf
ip
f
pu
KKu
KKu
2
1
1
)()(
(2.31)
Therefore, (2.28) is substituted into (2.27), and then the parameters nmc ,
of fuzzy
controller described by (2.10) can be adjusted using the following expression.
2
1
1
,,
)())(()(
j
j
j
m
j
jmnipnmb
kuchwdkkkekc
(2.32)
with m = j, j+1 and n = i, i+1.
16
Chapter 3
Hardware and software co-design of the servo
control system using SoPC technology
In this chapter, the SoPC design methodology for closed-loop servo control
system is presented. The Altera System-on-a-Programmable-Chip (SoPC) Builder
provides the capability to rapidly define and generate complex SoPC architectures. And
a simple GUI driven interface allows component selection, customization, and
integration. Further, the SoPC enables to integrate an embedded processor IP (Nios II
processor) and a user application IP into an FPGA. Therefore, in this section, a closed-
loop servo control system design will be emulated and discussed based on the SoPC
environment.
3.1 Description of SoPC builder design
SoPC Builder is an automated system development tool that dramatically
simplifies the task of creating high performance SoPC designs. The tool accelerates
time-to-market by automating the system definition and integration phases of SoPC
development. Using SoPC Builder, system designers can define a complete system,
from hardware to software, within one tool and in a fraction of the time of traditional
system-on-a-chip (SoC) design. SoPC Builder is integrated within the Altera Quartus II
software to give Programmable Logic Device (PLD) designers immediate access to a
revolutionary new development tool.
3.1.1 Stratix II EP2S60F672C5
With a size range of from about 10K to 180K gates, the Stratix II is one of the
biggest, fastest chips in FPGA chip’s family. With this device, it can be implement a
high density logic design and get high performance and great signal integrity in the most
efficient device possible. Table 3.1 lists the Stratix II P2S60F672C5 device features [10]:
17
Table 3.1: Stratix II EP2S60F672C5 device features
Figure 3.1: FPGA development board
18
3.1.2 Nios II embedded processor
The Nios processor is the soft-core IP. Its can configure some parameters by
software. Following that, users can embed this processor into Altera’s FPGA to
construct a SoPC environment. The Novel FPGA technology provides users with
flexible design of methodology. In this section, we will describe the features and
functionality of the Nios embedded processor development board which included the
Excalibur
Development Kit [21], [22].
3.1.2.1 Development Board Features
The Nios development board with Stratix II Edition provides a hardware
platform for developing embedded systems. This board provides the following features:
A Stratix II FPGA with more than 13,500 Adaptive Logic Modules (ALM)
and 1.3 million bits of on-chip memory
16 Mbytes of flash memory
1 Mbyte of static RAM
16 Mbytes of SDRAM
On board logic for configuring the Stratix II device from flash memory
On-board Ethernet MAC/PHY device
Two 5V-tolerant expansion/prototype headers each with access to 41 Stratix
II user I/O pins
CompactFlashTM connector for Type I CompactFlash cards
Mictor connector for hardware and software debug
Two RS-232 DB9 serial ports
Four push-button switches connected to Stratix II user I/O pins
Eight LEDs connected to Stratix II user I/O pins
Dual 7-segment LED display
JTAG connectors to Altera® devices via Altera download cables
50 MHz oscillator and zero-skew clock distribution circuitry
Power-on reset circuitry
19
3.1.2.2 The Nios Development Tool Flow
The Excalibur
Development Kit (EDK) provides rapidly design flow in Nios
development system. The Nios development system can be builded up rapidly and
easily by software. The Nios is configurable soft core embedded processor. The
embedded processor can be customized rapidly some peripherals as the Figure 3.2
shown. Figure 3.3 shows the design flow of Nios development tool. The embedded
processor and peripherals can configure easily by System Builder. Therefore, the
hardware and software design can be separated and paralleled work in the same time.
Figure 3.2: The Nios Embedded Processor
20
Figure 3.3: The Nios Development Tool Flow
3.2 Hardware and software co-design for a closed-loop
servo control system
Based on the SoPC technology, a closed-loop servo control system by mixing
hardware and software implementation in FPGA chip will be discussed. The circuits
requiring fast processing but simple computation are suitable to be implemented by
hardware in the FPGA, and the complicated control algorithm with heavy computation
can be realized by software in the FPGA [16][17]. The results of the software/hardware
co-design increase the programmability and the flexibility of the designed digital system,
enhance the system performance by parallel processing, and reduce development time.
To exploit the features, a plant with first-order system and a PID controller to form a
closed loop control system is taken as a design example and shown in Figure 3.4. The
sampling time frequency using in plant system is 500 Hz but in digital controller is 1
kHz. The plant and the PID controller are described as follow:
21
Discrete type plant model:
)1(*)1(*)( nxnyny (3.1)
PID controller:
)(*)( neknupp
(3.2)
)1(*)1()( neknunuii
(3.3)
))1()((*)( neneknudd
(3.4)
))1()((*)1(*)(*)1()()()()( neneknekneknununununudipdip
(3.5)
Figure 3.4: Closed-loop control system
Implementation can be divided into two methods:
(1) Full hardware implementation: the plant and the PID controller are implemented
by hardware.
(2) Hardware and software implementation: The plant is implemented by hardware,
but the PID controller is implemented by software.
Method 1: All hardware realization
In this method, the closed-loop control system is implemented by hardware. In Figure
3.5 shows block diagram of PID controller, plant and the overall integrated program,
respectively. Firstly, implement coding of the PID controller and the implement coding
of the plant. Secondly, connect the PID controller block with the plant block.
22
Figure 3.5: Circuit and the separate block diagram of overall control system
(a) Overall control system (b) PID controller (c) Plant
Figure 3.6: VHDL code of overall closed-loop control system
23
Hardware design has two kinds of implementation: The parallel processing and
sequential processing using Finite state machine(FSM). But in this case does not
require fast operation. So we can use Finite state machine (FSM) to simplify and
consume at least chip resources.
Figure 3.7 show the circuit design of plant using FSM method and seven-step machine
to carry out the overall computation of plant which mathematical model are shown in
(3.1).
Figure 3.7: The circuit design of plant using Finite State Machine (FSM)
In Figure 3.8 shows the VHDL code of plant follow the circuit design in Figure 3.7.
From the code’s lines 1 to 27 declare all of input, output of plant, the signals, one
multiplier and one adder are used to compute for plant execution. The code’s line 28
and 29 initial the parameters of plant Teta ( ) and phi ( ). And from the code’s lines
30 to 56 execute the process to implement seven steps from S0 to S6.
24
Figure 3.8: VHDL code of Plant
25
Figure 3.9 show the circuit design of PID controller using FSM method in 12 steps to
execute the PID controller which mathematical model are shown in (3.2), (3.3), (3.4),
(3.5).
e1mulr(30..15)
Ki
-e1
Ui
e1<=en
mulr(30..15)
mulr(30..15)en
-Yn
Xn en
de
Yn
Kp
S1S0 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12
Kd
Ui
Figure 3.9: The circuit design of PID controller using Finite State Machine (FSM)
In Figure 3.10 shows the VHDL code of PID controller follow the circuit design in
Figure 3.9. We execute steps S0 ~ S12 from the code’s lines 40 to 72.
26
Figure 3.10: VHDL code of PID controller
27
Simulation in QUARTUS II and MATLAB
To investigate the correctness of the proposed closed loop control algorithm, three
simulation cases with different conditions are carried out.
- Case 1: The parameters of PID as Kp=0.15, Ki=0.1, Kd=0.01 and the parameters of
plant is as 8.0 , 5.0 . And the input of closed loop control is Xn=0.5
- Case 2: The parameters of PID as Kp=0.22, Ki=0.1, Kd=0.01 and the parameters of
plant is as 8.0 , 5.0 . And Xn=0.5
We simulate the closed loop control in QUARTUS II and the values are transferred to
Q15 format values and the simulation results are shown in Figure 3.11(case 1) and
Figure 3.13(case 2).
(Case 1) PID values: Kp = 0.15, Ki = 0.05, Kd = 0.01 (4915, 1638 and 328 for Q15)
Figure 3.11: Simulation results in QUARTUS II (case 1)
End value of output Yn: 16376 for Q15 after 170 ns, maximum value = 20430 (0.4997
and 0.6234 for real value).
And at the same time, we use the simulation result in MATLAB to compare with the
result in QUARTUS II. The MATLAB’s simulation results are shown in Figure 3.12 for
case 1 and Figure 3.14 for case 2.
28
Figure 3.12: Simulation results in MATLAB (case 1)
(Case 2) PID values: Kp = 0.15, Ki = 0.22, Kd = 0.01 (4915, 7209 and 328 for Q15)
Figure 3.13: Simulation result in Quartus II (case 2)
End value of output Yn: 16384 for Q15 after 560 ns, maximum value = 28777,
minimum value = 6975(0.5, 0.878 and 0.212 for real value)
29
Figure 3.14: Simulation result in MATLAB (case 2)
We can summarize the results of our simulation as follows:
Table 3.2: The simulation results using method 1
Case
2
QUARTUS II MATLAB
1
End valueMax value End valueMax value
Software
0.623 0.499 0.587 0.5
0.878 0.5 0.718 0.5
The overshoot in case of the QUARTUS II simulation is greater than the one in the
MATLAB simulation case. And we can observe that when Ki increases, the final value
of the output will be closer to that of the input. We can also see that during the first
steps, the initial error is greater.
30
Method 2: Hardware and software co-design
In this section, hardware and software co-design method is presented. The plant is
implemented by hardware in FPGA, while the PID controller is implemented by
software using Nios II processor. The closed loop control is implemented with interrupt
time 1 kHz. And overall structure is shown in Figure 3.15. It can be divided into two
parts: Nios system and plant. In Nios system, the controller operation can be done and
control signal is transferred to the plant through FPGA Avalon Bus’s I/O. After the
feedback signal and the response results are buffered to the memory, wait until the
interrupt active.Then they can be printed on the screen of the PC and can be collected.
Then, the response results are plotted by using the MATLAB software. Therefore, under
the procedure, the response result is shown in Figure 3.17.
Figure 3.15: Hardware and software co-design of closed-loop servo control system
31
PID controller software is written by C language in Nios II software in Figure 3.16.
Figure 3.16: The C languages for PID controller
32
Figure 3.17: Simulation results when using hardware and software co-design
Summarize all of simulation results as follow:
Table 3.3: The simulation results using method 1 and 2
Case
2
All hardware
realizationMATLAB
1
End valueMax value
Method
0.623 0.499 0.587 0.5
0.878 0.5 0.718 0.5
Min valueEnd valueMax value Min valueEnd valueMax value Min value
Hardware and software
co-design
0.618 0.5
0.727 0.5
0.471
0.397 0.418
0.489
0.212
0.324
Conclusions: Compared with all hardware realization method, the hardware and
software co-design implementation in the closed loop control system has the following
benefits.
1) The speed processing is faster than the one done by hardware realization.
2) The overshoot is smaller than the one in the hardware realization case.
3) We can observe that the values of the hardware and software co-design method
are very similar with the values in MATLAB simulation.
However, when we implement hardware/software co-design method (8% LEs resource)
the Chip resource is occupied more than using all hardware realization (1% LEs
resource). Because the Nios II processor occupy with 3,652/40,877 LEs chip resource.
33
Chapter 4
Hardware realization of the neural fuzzy
controller for linear X-Y table
In this chapter, the FPGA-realization of neural fuzzy controller for the X-Y table
is introduced. However, only the single-axis table is considered, and the hardware
architecture is shown in Figure 4.1. In this figure, it includes three IPs which one is
position controller IP, another is speed controller IP and the other is plant IP. Detailed
circuit design of these three IPs will be presented at the following sections.
Figure 4.1: FPGA-realization of single axis position controller
based on neural fuzzy controller
4.1 Plant IP
The Plant is modelled by mathematical model of PMLSM has been described in
(2.6). Taking Laplace transformation of (2.4) and (2.6) and applying the bilinear
transformation, the digital transfer function of the drive system of single axis can be
obtained as
34
)1)(*1(
*
)(
)(
11
1
*
zz
z
ki
kx
q
p (4.1)
with Φ = exp(−BmT / Jm) , Ψ = Kt (1−Φ)/Bm . The z−1
is a back-shift operator and T is the
sampling period. In Figure 4.2, ke is represent an encoder factor, which transforms the
displacement of the table to the pulse number, and xe is represent the pulse number
generated from the linear encoder. Therefore,
epekxx * (4.2)
In hardware realization, (4.1) needs to be transformed to the difference equation form as
follows:
)1()1(*)2(*)1(*)(*
kxkxkxkikxpppqp
(4.3)
and its digital circuit design using the FSM method is shown in Figure 4.2, which uses
only one 12-b multiplier, one 12-b adder, and seven-step machine to carry out the
overall computation of PMLSM. Inputs and outputs of the block diagram of plant are
defined as follows:
Clk : clock signal with frequency 50MHz
Clk_200n : clock signal with frequency 5MHz
Uk_in ( )1(*
kiq
) : values of input
fi (Ф) : The parameter of plant
kr (Ψ) : The parameter of plant
rate (ke) : The parameter of plant
xp_out (xp) : Output of plant
xe : Output of plant (Transform from xp)
16 bits
(Q0)
I*q(k-1)
Xp (k-2)
Ф
-
Ф
Xp (k-1)
mulr(22..11)
mulr(22..11)
Xp (k-1)
S0 S1 S2 S3 S4 S5 S6
Ke gain and
Q format Transform
Xp(k) Xe(k)
Xp (k-1)=>Xp(k-2)
Xp (k)=>Xp(k-1)
I*q (k)=>I*q(k-1)
12 bits
(Q11)
12 bits
(Q11)
*
* Note that: Xe(15..0) = Xp(11)&Xp(11)&Xp(11)&leftshift((11..0)*0.9,1)&’0'
Ψ
Figure 4.2: State diagram of FSM for describing the Plant
35
Figure 4.3: The block of Plant
4.2 Speed controller IP
The inputs of speed loop are the speed command (cmd_speed) and the feedback
signal. And the feedback speed signal (info_speed) is calculated as follow
)1()(_. kxkxspeedfoinpp
(4.4)
The digital P controller in the speed controller is formulated as follows.
ekkispeedpq
*)(_
(4.5)
where the kp_speed is the P controller gain and the e is the error between command speed
and feedback speed value (e = cmd_speed*speed_gain- info_speed), the iq is the P
controller output.
Figure 4.4 is state diagram of FSM to describe how to calculate the feedback
speed signal from encoder (info_speed) in steps S0~S1 and execute the speed P
controller in steps S2~S5.
Speed_gain
Iq
Cmd_speed
Info_speed_out
S1S0 S2 S3 S4 S5
Kp_speed
_
xp(k)
xp(k-1)
xp(k)=>xp(k-1)
info_speed
e
_
Figure 4.4: State diagram of FSM for describing the Speed P controller
36
Figure 4.5: The block of Speed controller
4.3 Position controller IP
Inference
Mechanism DFIFI
Reference
model
1-Z-1
1-Z-1
Z-1
neural fuzzy controller based on RBF identification
Radial Basis Function
Neural Networks
PI
cmd_speed
u
xe
xe
xm
+-
e
de
uf
yrbf
+-
Jacobian
transformationcmd_speed
info_position
Adjusting
Mechanism
Figure 4.6: The block diagram of neural fuzzy controller
Position controller is shown in Figure 4.6 which includes a fuzzy controller, a
reference model, a RBF neural network and an adjusting mechanism. The sampling
frequency of position loop is designed with 2 kHz. To implement the overall control
system, FSM technology is used and shown in Figure 4.7. Here, overall 112 steps are
needed to complete the computation of neural fuzzy controller. Steps s0~s6 execute the
computation of reference model output; steps s6~s9 are for the computation of mover
velocity, position error and error change; steps s9~s12 execute the function of the
37
fuzzification; s13~s22 describe the look-up table and defuzzification; steps s23~s25 execute
the PI controller in position loop; steps s27~s104 execute the computation of RBF neural
network; and s105~s111 execute the tuning of fuzzy rule parameters. The operation of
each step in FPGA can be completed within 80ns (12.5 MHz clock); therefore total 112
steps need 8.96 s operation times.
kxm
*
a0
1*
kxm
a1
2*
kxm
a2
1kxm
b1
2kxm
b2
S1 S 2 S 3
kx p
-
kxm
- ke
1ke
kde
SD -e i 1
SD -de j 1
ke
kde
RS,
1
eA
1
RS,
1
deBj
&i
j
j&i
-
1
eA
1
eA
1
1
d ji ,
-
1
deB j
deBj
deBj
d ji ,1
deBj
1
eA
1
d ji 1,
d ji 1,1
d ji ,
c ij ,
d ji 1,
c ij ,1
d ji ,1
c ij 1,
c ij 1,1
d ji 1,1
u f
k p
ku
S 7 S 8 S9 S 10 S11S 12
S 13 S 15 S 16 S 17 S 18 S19 S 20 S 21 S 22 S 23 S 24 S 25
-
-
k i
1kui
Look-up
Fuzzy rule
table
c ij ,
c ij 1,
c ij ,1
c ij 1,1
S 14
j&i
S 101 S 102 S 103
α
e(k)
jacobian
k p
d ij , c ji,
c ji,
d ij ,1
c ji 1,
d ij 1,
c ji 1,
c ji ,1
c ji ,1
d ij 1,1 c ji 1,1
c ji 1,1
Neuro-1
computation
Neuro-2
computation
Neuro-3
computation
kx p
1kxp
1out
2out
3out
1J
2J
3J
xrbf
S 0 S 4 S 5 S 6
S 26
SS 10027~ S 104 S105 S 106 S 107
Computation of reference model output Computation of position error
and error changeFuzzification
Look-up fuzzy table Defuzzification PI controller
Computation of RBF neural network
k i
Adjustment of fuzzy rule parameters
S 108 S 109 S 110 S 111
ku
1ku
∆u(k)
∆u(k)
Figure 4.7: State diagram of FSM for describing the overall position controller IP
38
The inputs and outputs of the function block of NFC shown in Figure 4.8 as follow:
clk : clock signal with frequency 50MHz
clk_80n : clock signal with frequency 12.5 MHz
model : select Reference Model or not
ruleout_enable : read the current value of rule
cmd_position : position command
kp_position : kp in position control loop
ki_position : ki in position control loop
learning_rate : learning_rate of fuzzy parameters
Max,Max_M,Max_S : Maximum value of fuzzy parameters
rule_PS,rule_PM,rule_PL : values transferred to fuzzy rule table
em_PS,em_PM,em_PB,em_range : tops of membership functions and range
dem_PS,dem_PM,dem_PB,dem_range : tops of membership functions and range
A0_in,A1_in,A2_in,B1_in,B2_in : parameters of reference model
en : enable neural network
ne_core_in : the number of nodes in hidden layer
order_in : the order of estimation of exponential
c_data_1, c_data_2, c_data_3 : initial centers of neurons
b_data : initial width of neurons
w_data : initial weight of neurons
fuzzy_out : output of fuzzy-neural controller
position_out : position of linear motor
ruleout : fuzzy rule table
refcmd_output : output of reference model
39
Figure 4.8: The function block of neural fuzzy Controller
4.3.1 Reference Model
Second order system with natural frequency, n and damping ratio, is usually
as the RM in the fuzzy-neural control system. Applying the bilinear transformation, the
second order system can be transformed to a discrete model:
2
2
1
1
2
2
1
10
1*
1
1)(
)(
zbzb
zazaa
zx
zx
m
m (4.6)
Furthermore, the difference equation is written as:
)2()1()()2()1()(*
2
*
1
*
021 kxakxakxakxbkxbkx
mmmmmm (4.7)
where the z1 is back shift operator and bbaaa and
21210,,,, are the parameters of
the discrete model.
40
To present float number computation, we use Q31-format representation.
If 40 n , 1 , and sampling frequency is 2kHz, the parameters of RM in the
difference equation will be:
1
0
1
5
2
4
1
5
0
10*3726078815802.9
03969603960396.1
10*698029604940.9
10*1389605920988.1
10*698029604940.9
a
b
a
a
a
(4.8)
The difference equation is
)2(*10*698029604940.9
)1(*10*1389605920988.1
)(*10*698029604940.9
)2(*10*3726078815802.9
)1(*03969603960396.1)(
*5
*4
*5
1
kx
kx
kx
kx
kxkx
m
m
m
m
mm
(4.9)
To avoid overflow occurred, reformulated it as
)2(*10*03454901480247.0
)1(*10*0699802960494.0
)(*10*03454901480247.0
)2(*10*11864803940790.0
)1(*01989801980198.02/)(
*5
*4
*5
1
kx
kx
kx
kx
kxkx
m
m
m
m
mm
(4.10)
Finally, changing float numbers to 32 bit binary (Q31-format)
)2(*105528
)1(*210516
)(*105258
)2(*1031638429
)1(*2104959219)(
*
*
*
kx
kx
kx
kx
kxkx
m
m
m
m
mm
(4.11)
Reference model is implemented by 6 steps computation using FSM description and
shown in Figure 4.8.
41
kxm
*
a0
1*
kxm
a1
2*
kxm
a2
1kxm
b1
2kxm
b2
S1 S 2 S 3
-
-
S 0 S 4 S 5
kxm
Figure 4.9: State diagram of FSM for describing the reference model
4.3.2 PI type Fuzzy Controller
From the design method is presented in chapter 2 and two equation (2.11) and
(2.12) use to calculate the output of FC we can show the method of hardware design for
PI type fuzzy controller in position loop in Figure 4.10.
The overall computation needs 21 steps from S6 to S26. From steps SS 86~ are
for the computation of table position, position error and error change; steps SS 129~
describe the fuzzification; steps SS 2213~ are for the look-up table and defuzzification;
and steps SS 2623~ execute the PI controller and computation of position command
output.
42
kxp
-
kxm- ke
1ke
kde
SD-
ei 1
SD-
de j 1
ke
kde
RS,1
eA
1
RS,1
deBj
&i
j
j &i
-
1
eA
1
eA
11
d ji,
-
1
deBj
deBj
deBj
d ji ,1
deBj
1
eA
1
d ji 1,
d ji 1,1
d ji,
c ij,
d ji 1,
c ij ,1
d ji ,1
c ij 1,
c ij 1,1
d ji 1,1
u f
kp
ku
S 7S
8 S9 S 10 S11S 12
S 15 S16S 17 S 18 S19 S 20 S 21
S 22 S 23 S 24 S 25
ki
1kui
S 14
1ku
ku
S6
S 26
S 13
Look - up
Fuzzy rule
table
c ij ,c
ij 1,
cij ,1
c ij 1,1
Figure 4.10: State diagram of FSM for describing the Fuzzy + PI controller
4.3.3 Radial Basis Function Neural Network (RBFNN)
Figure 4.11 describes RBF neural network. It has three inputs in input layer,
three RBFs in hidden layer, and one output in output layer. Corresponding to the RBF
NN structure shown in Figure 4.11, Figure 4.12 describes the computing sequence of
RBF network implemented in FPGA. Steps SS 10027~ are the computation of neural
cores.
x1
exp
x3
x2
exp
exp kxe
kyrbf
ke
w
w
w
Output
layerHidden
layer
Input
layer
3 3 1
Figure 4.11: Structure of the proposed RBF NN
43
Neural core
Neural core
Neural core
Σ
resulttotal
ett
ratelearning
w
b
c
c
c
x
x
x
_
arg
_
3
2
1
3
2
1
total_ result
Jacobian
rbf_out
rbf_out
rbf_out
j
j
j
S27 SS 10027~ S101 S104
~
Figure 4.12: State diagram of FSM for describing the RBF NN
4.3.3.1 Radial basic function
The radial-basic function is calculated by:
mjb
cxy
j
rbf
j
....,4,3,2,1,2
exp2
2
(4.12)
Figure 4.13 are state diagram of FSM to compute one radial basic function.
Steps SS 137~ are computation of norm and steps SS 4614
~ are computation of
exponential function.
norm
x1
c1(k-1)
x2
c2(k-1)
x3c3(k-1)
b(k-1)
b(k-1)<<1
÷
2b_p2(k-1)
norm_outexp
-exp_in h
w(k-1)
one_rbf_out
S 7 S 12 S 13 S 14 SS 4614~ S 47 S 48
Figure 4.13: State diagram of FSM for describing the radial-basic function
44
1. Norm function
Norm of cx j is defined as follow
cxcxcxcxnorm j 332211
222
(4.13)
And square of norm is defined as
cxcxcxcxnorm j 332211
2222
2
(4.14)
The computation of square of norm needs 4 steps using FSM description shown in
Figure 4.14.
x_data_1
x_data_2
x_data_3
-c_data_1
-c_data_2
-c_data_3
S 0 S 1 S 2 S 3
norm_out
Figure 4.14: State diagram of FSM for describing the norm
2. Exponential function
Using Maclaurin series solution to estimate exponential function as follow
!!3!211
!
32
0
)(
n
xxxx
n
xe
n
n
n
x
(4.15)
Hardware design algorithm to compute this formula is illustrated by FSM in Figure 4.15.
Inputs and outputs of the block of exponential function:
Clk : clock signal with frequency 50MHz
en : enable signal
data_in : the input of data
order_in : the input of order
exp : the result of exponential function
45
1/m
M=1,2,3...n
If m=order
TIME+TIME+1Section=1
(to S1)
1xd 1xeout
xd xeout xeout
then
else
order
e in
80001
80001
x
xd
e out
m
S 0 S 1
1 xx ee outout
S 2
1 xdxd
S 3 S 4
Figure 4.15: State diagram of FSM for describing the exponential function
clk
en
data_in[19..0]
order_in[5..0]
exp[19..0]
exponential
inst2
Figure 4.16: The block of exponential function
4.3.3.2 Training of Radial Basic Function
Iterative algorithm for training RBF NN is as follow:
khkekwkw jjj 1 (4.16)
kb
kckxkhkwkekckc
j
jii
jjjiji2
1
(4.17)
kb
kckxkhkwkekbkb
j
jjjj
jii
3
2
1
(4.18)
All steps to compute the training RBF are shown in Figure 4.17, in which Steps
SS 5451~ describe update RBF w; steps SS 5655
~ describe update RBF b; steps
SS 6957~ describe update RBF c1, c2, and c3.
46
÷
÷
÷
÷
h
lr
target
-total_result
Ihe
w(k-1)
w(k)
2b_p2(k-1)>>1
b(k-1)exp_in
w(k-1)
Ihew
b(k-1)
b(k)
S 51 S 52 S 53 S 54 S 55 S 56 S 57
update RBF w update RBF b
x1
-c1(k-1)
2b_p2(k-1)>>1 Ihew c1(k-1)
c1(k)
x2
-c2(k-1)
2b_p2(k-1)>>1 Ihew c2(k-1)
c2(k)
S 57 S 58 S 59 S 60 S 61 S 62 S 63 S 64 S 65
update RBF c1 update RBF c2
x3
-c3(k-1) 2b_p2(k-1)>>1 Ihew c3(k-1)
c3(k)
S 65 S 66 S 67 S 68
133
122
111
1
1
kckc
kckc
kckc
kbkb
kwkw
S 69
update RBF c3
Figure 4.17: State diagram of FSM for describing the training RBF NN
4.3.3.3 Jacobian
Jacobian is defined as follow:
b
chw
j
j
j
jj
kuJacobian
2
13
1
(4.19)
Figure 4.18 uses 5 steps to describe the computation of Jacobian transformation.
47
÷
b(k-1)
b(k-1)
c1(k-1)
-x1
h w(k-1)
jacob
S 69 S 70 S 71 S 72 S 73
Figure 4.18: State diagram of FSM for describing jacobian
4.3.4 Adjusting Mechanism
The formula to adjust fuzzy parameters is computed as follow:
))(
(**)(*)(*)(2
1
1
,,
j
j
j
l
j
jmnipnmb
kuchwdkkkekc
(4.20)
The computation of this formula includes 8 steps using FSM description and shown
in Figure 4.19.
S104 S105 S106 S107 S108 S109 S110 S111
α
e(k) jacobian
d ij, cji,
c ji,
d ij ,1
cji 1,
d ij 1,
c ji 1,
c ji ,1
c ji ,1
d ij 1,1 c ji 1,1
c ji 1,1
kp
ki
Figure 4.19: State diagram of FSM for describing jacobian
48
Chapter 5
Software realization of the motion trajectory for
linear X-Y table
Figure 5.1 illustrates the internal architecture of the proposed FPGA
implementation of the position neural fuzzy controller IP, the speed controller and plant
IP for linear X-Y table. The FPGA chip adopted herein is Altera Stratix II
EP2S60F672C5 with 48,352 ALUTs, maximum 492 user I/O pins, 36 DSP blocks,
2,544,192 bits of RAM. The Nios II embedded processor has a 32-bit configurable CPU
core. The internal circuit in Figure 5.1 comprises a Nios II embedded processor IP
(Intelligent Properties) and an application IP. The application IP (hardware) includes the
circuits of X axis and Y axis. Each one axis includes the position controller (NFC),
speed P controller and PMLSM plant IP. And the Nios II processor performs the
function of generating the motion trajectory, collecting the response data and the
communication with external device by software. The operating clock rate of the
designed FPGA controller is 50 MHz, and the frequency divider generates 50MHz (Clk),
12.5MHz (Clk-step), and 5MHz (Clk-plant).
Figure 5.1: The architecture of a motion controller for X-Y table
49
The FPGA utility of overall motion control IC for X-Y table in Figure 5.1 is
evaluated. The results are listed in Table 3.1, which presents that the overall circuits of
the proposed motion control IC including a Nios II embedded processor IP (40,877 LEs
and 571,136 RAM bits), use 85% LEs resource and 37% RAM resource of a Stratix II
EP2S60.
Table 5.1 Utility evaluation of motion control IC for Linear X-Y table in FPGA
5.1 The Nios II software
The Nios II software development environment in Figure 5.2 is called Nios II
Integrated Development Environment (IDE). The Nios II IDE is based on the GNU
C/C++ compiler and the Eclipse IDE, and it provides an established environment for
software development.
50
Figure 5.2: Nios II IDE development system diagram
Many embedded systems require Interrupt Service Routines (ISRs) to process
external hardware interrupts in a timely manner. The CPU runs the ISR after it is
interrupted. The Nios development kits include software subroutines that make it easy
to implement ISRs in your Nios system. These routines allow you to spend your time
writing the ISR instead of working on the overhead necessary to set up the ISR. For
example, one line of C code installs the ISR and saves and restores the context when the
interrupt occurs.
Exceptions interrupt the processor: they stop the current operation to take care of
something more important. Different sources can cause exceptions, including external
hardware, direct software interrupts, and internal exceptions during normal execution of
code. Figure 5.3 illustrates a simple case of what happens in most embedded systems
when an exception occurs
1. Save the current state (context)
2. Retrieve the ISR address from vector table based on the interrupt number
3. Jump to the ISR routine and run to completion
4. Restore saved context.
5. Resume program
51
Figure 5.3: Exception handling process
Figure 5.4: Typical initialization settings 2 kHz interrupts
The Nios II processor IP used in our proposed system performs the function of
motion trajectory in software. The clock frequency of the Nios II processor is 50MHz.
Figure 5.5 illustrates the flow charts of the main program and the interrupt service
routine (ISR), where the interrupt interval is designed with 0.5ms. All programs are
coded in the C programming language.
52
Figure 5.5: Flow chart of main and ISR program
5.2 Motion trajectory[36]
The motion trajectory is very important to control the X–Y table. In practical
applications, the motion commands of X-axis and Y-axis are designed individually
through motion trajectory to achieve two dimensions motion control. This section will
present the motion trajectory planning for X-Y table, including one axis control point-
to-point motion trajectory and two axis of the motion trajectory planning which the
circle, flexuous, star and window motion trajectory are used to evaluate the motion
control performance of the proposed NFC control system in X-Y table.
5.2.1 Point to Point motion trajectory
The motion trajectory of a linear motor is based on the point-to-point motion
control scheme with a trapezoidal constant acceleration/deceleration velocity profile
shown in Figure 5.6. In this scheme, the designed parameters are the overall
displacement x p (millimeters), the maximum velocity W (millimeters per second), the
acceleration and deceleration periodT acc, and the sampling interval td. Therefore, based
53
on the velocity profile in Figure 5.6, the command of instantaneous position, x pat each
sampling interval can be determined by the following procedure.
Step 1: Computation of the overall running time. First, compute the running
time without considering acceleration/deceleration:
WxT p/
1 (5.1)
This T 1must exceed acceleration timeT acc
. Next, the acceleration/deceleration
design is considered, and the overall running time is
TTTT accaccMAX ,
10 (5.2)
Step 2: Adjustment of the overall running time to meet the condition of multiple
of the sampling interval.
tTtT ddaccNandN //
0 (5.3)
Where N is the interpolation number and [ ] refers to the Gauss function with
integer output. Therefore,
tTtT ddaccNandN *'* '' 0
(5.4)
Step 3: Modification of the maximum velocity
TTx accpW
0/ (5.5)
Step 4: Calculation of the acceleration/deceleration
T accWA / (5.6)
Step 5: Calculation of the position command at the mid-position
a) Acceleration region:
txx Arop
2*
**2
1 (5.7)
Where t dnt * , 0 < n ≤ N’, and x ro
is the initial position.
b) Constant speed region:
tWxx rp'*
1
*
(5.8)
Where t dnt * , Nn
10 , and x r 1
is the final position in the
acceleration region and '*21
NNN .
c) Deceleration region:
txx AtW
rp
2
2
*
**2
1'* (5.9)
where t dnt * , 0 < n ≤ N and x r 2
is the final position in the constant speed region.
54
Figure 5.6: Point-to-point trapezoidal velocity profile
5.2.2 Circular motion trajectory
A circular trajectory is shown in Figure 5.7 and its equation is described as
follows:
)cos(
)sin(
1
ii
ii
ii
ry
rx
(5.10)
Where is the variation value of the angle; r is the radius of the circle;i
x is the
motion command of the X-axis; i
y is the motion command of the Y-axis.
Figure 5.7: Circular motion trajectory
55
5.2.3 Star motion trajectory
The star trajectory is shown in Figure 5.8 and can be divided into six parts from
a to f. The star trajectory can be described as follows:
a trajectory:
1
1
ii
ii
yy
xSx (5.11)
b trajectory:
1
0
1
0
36sin
54sin
ii
ii
ySy
xSx (5.12)
c trajectory:
1
0
1
0
72sin
18sin
ii
ii
ySy
xSx (5.13)
d trajectory:
1
0
1
0
72sin
18sin
ii
ii
ySy
xSx (5.14)
e trajectory:
1
0
1
0
36sin
54sin
ii
ii
ySy
xSx (5.15)
Where S is a constant and the size of the trajectory can be changed with different value
of S; xi is the motion command of the X-axis; yi is the motion command of the Y-axis.
Figure 5.8: Star motion trajectory
56
5.2.4 Window motion trajectory
The window trajectory is shown in Figure 5.9 and can be divided into 9 parts
from a to i. The window trajectory can be described as follows:
1ii
(5.16)
a trajectory:
1
1
ii
ii
ySy
xx (5.17)
b trajectory: )24
6:(
i
)sin(
)cos(
1
1
iyi
ixi
rOy
rOx
(5.18)
c trajectory:
1
1
ii
ii
yy
xSx (5.19)
d trajectory: )4
6:(
i
)sin(
)cos(
2
2
iyi
ixi
rOy
rOx
(5.20)
e trajectory:
1
1
ii
ii
ySy
xx (5.21)
f trajectory: )2
1:(
i
)sin(
)cos(
3
3
iyi
ixi
rOy
rOx
(5.22)
g trajectory:
1
1
ii
ii
yy
xSx (5.23)
h trajectory: )2
10:(
i
)sin(
)cos(
4
4
iyi
ixi
rOy
rOx
(5.24)
57
i trajectory:
1
1
ii
ii
ySy
xx (5.25)
Where S is also a constant and the size of the trajectory can be changed with different
value of S, and the tracking speed of the trajectory can be changed with the value of .
According to trajectory function, the window trajectory can be generated by the
accumulation of the angle with the changing of time.
Figure 5.9: Window motion trajectory
5.2.5 Flexuous motion trajectory
The flexuous trajectory is shown in Figure 5.10 and can be divided into 7 parts
from a to g. The flexuous trajectory can be described as follows:
1ii
(5.26)
a trajectory:
1
1
ii
ii
yy
xSx (5.27)
b trajectory: )2
3
2
1:(
i
)sin(
)cos(
1
1
iyi
ixi
rOy
rOx
(5.28)
c trajectory: )2
1
2
1:(
i
58
)sin(
)cos(
2
2
iyi
ixi
rOy
rOx
(5.29)
d trajectory:
1
1
ii
ii
yy
xSx (5.30)
e trajectory: )2
1
2
3:(
i
)sin(
)cos(
3
3
iyi
ixi
rOy
rOx
(5.31)
f trajectory: )2
3
2
1:(
i
)sin(
)cos(
4
4
iyi
ixi
rOy
rOx
(5.32)
g trajectory:
1
1
ii
ii
yy
xSx (5.33)
Where S is also a constant and the size of the trajectory can be changed with different
value of S, and the tracking speed of the trajectory can be changed with the value of .
According to trajectory function, the window trajectory can be generated by the
accumulation of the angle with the changing of time.
Figure 5.10 Flexuous motion trajectory
59
5.3 Perfomance measures[19]
To measure the performance of various controllers, the average tracking error m
and the standard deviation of the tracking error Ts for the motion tracking are defined as
follows:
n
k n
kTm
1
)(
(5.34)
Where )()()(22
kTkTkTyx
And )()()( kdkdkTimii
yxi ,
n
k
sn
mkTT
1
2))((
(5.35)
Where dmi is the command for each axis, di is the feedback for each axis; Ti is the error
between the values of command and feedback for each axis. The comparison of the
control performance can be easily shown using the average tracking error. Moreover,
the oscillation of the motion tracking can be evaluated by the standard deviation of the
tracking error.
60
Chapter 6
Simulation results of the motion controller
To prove the effectiveness and correctness of our proposed controller and
motion control IC used in X-Y table; some simulations results by step response and by
the two dimensional motion includes circular, star, window and flexuous motion
trajectory demonstrated in MATLAB and in FPGA are evaluated.
6.1 Simulation in MATLAB
Prior to simulate in FPGA, the simulation in MATLAB is first used to evaluate
the correctness of the proposed controller and motion control IC of the X-Y table. For
this evaluation, the comparison of two controllers includes fuzzy controller and neural
fuzzy controller are carried out.
6.1.1 One dimensional motion trajectory
The architecture of fuzzy controller and neural fuzzy controller for single axis
are respectively shown in Figure 6.1 and 6.2. And the controller parameters are
designed as following figure.
Figure 6.1: Diagram of fuzzy control for PMLSM drive
61
Figure 6.2: Diagram of Neural fuzzy control for PMLSM drive
Firstly, the reference model (RM) is carried out to help the system easy to track the
following command. Second order system is used:
22
2
*2)(
)(
nn
n
p
m
sssx
sx
(6.1)
with selection by 1,/20 sradn
. The discrete model of RM is obtained as follow
by using bilinear transformation at the sampling frequency be 2 kHz.
2
2
1
1
2
2
1
10
1*
1
1)(
)(
zbzb
zazaa
zx
zx
p
m
(6.2)
with a0=0.000098; a1=0.000196; a2=0.000098; b1=-1.960396; b2=0.960788
Secondly, according to our experience, the initial fuzzy rule table is chosen in Figure
6.3.
Figure 6.3: Membership functions, fuzzy rule table and control effort surface
62
and Ke, Kde, Ku in Fig 6.1 and Fig 6.2 are chosen as 2, 500, and 1, respectively.
In Figure 6.3, the output of FC is calculated by
mn
i
in
j
jm
nmi
in
j
jm
BA
i
in
j
jm
BAnm
fdc
dee
deec
deeu
mn
mn
,
1 1
,1 1
1 1
,
*
)(*)(
)(*)(
),(
(6.3)
The output of PI type fuzzy controller is:
)(*)()1()( kukkkukufipi
(6.4)
Thirdly, RBF network is designed with 3-3-1 structure In Figure 6.4. This structure has
three inputs in an input layer, chose three neurons in hidden layer and one output in an
output layer. The initial parameters in wj, bj, cj are selected as follow
The weight from the hidden layer neuron to the output layer neuron
5.05.05.0
jw
(6.5)
The width of 3 neurons:
5.05.040
jb
(6.6)
The center of 3 RBF unit:
5.05.040
5.05.040
5.05.040
jc
(6.7)
and the learning rate of neural network is chosen 5.0
The RBF neural network will supply Jacobian information to adjust fuzzy parameters.
Further, the formulation of output of RBF neural network and Jacobian are:
b
cxwhwy
jj
j
j
jjrbf
j
2
2
3
1
3
1 2exp (6.8)
3
1
2
1
1)(
j j
j
jjb
kuchwJacobian (6.9)
63
x1
exp
x3
x2
exp
exp kxe
kyrbf
ke
w1
w2
w3
Output
layerHidden
layer
Input
layer
3 3 1
)(ku
)( kx
)1( kx
Figure 6.4: Radial basis function neural network
Two tested cases with different PMLSM parameters in (6.10) are considered to evaluate
the controller performance, in which we have the following cases.
Case 1: Light-load condition
Kt = 64, Mm = 1, Bm = 0.1
Case 2: Heavy-load condition (6.10)
Kt = 64, Mm = 7, Bm = 0.7
The PI gains are chosen by Kp = 5 and Ki = 0.09 and the learning rate α is set as 0.07.
Square-wave step response is used as a tested input command. Compare the tracking
performance of the aforementioned two controllers at various system conditions. The
system parameters are initially designed at the light-load condition in case 1 then
changed to the heavy-load condition in case 2 after 2s. Therefore, under the
aforementioned designed condition, the simulation results are shown in Figure 6.5 and
Figure 6.6. In Figure 6.5, the mover position has a good following response at the light-
load condition by using the Fuzzy controller. However, after 2 s, when the system
parameters change to the heavy-load condition, about 8.7% overshoot by using the
fuzzy controller, as shown in Fig. have occurred. It reveals that FC is affected by the
various loads. To cope with this problem, an NFC is adopted, and its simulation result is
shown in Figure 6.6. In the case 2 condition, initially, the mover of PMLSM track the
output of the RM with oscillation and only 0.9% overshoot, while the parameters of ci,j
in Figure 6.7 are continuously tuned to reduce the error between the output of the RM
and the position of the mover at each control sampling interval. After one square-wave
position commands have been tracked, the ci,j parameters shown in Table 6.1 are tuned
to adequate values, and the position of the mover can accurately track the output of the
RM.
64
Figure 6.5: Position response and control effort when using FC
(simulation in MATLAB)
Figure 6.6: Position response and control effort when using NFC
(simulation in MATLAB)
65
Figure 6.7: Rule table after adjusted and the control effort surface for
Step response with neuron fuzzy controller (simulation in MATLAB)
6.1.2 Two dimensional motion trajectory
6.1.2.1 FC using in position loop (simulation in MATLAB)
This section shows the simulation results of the motion controller for the X-Y
table by using Fuzzy controller in position loop. The architecture of FC is shown in
Figure 6.8. The parameters of FC are used the same parameters using in section 6.1.1.
Initial controller parameters in X axis and Y axis are selected the same and the
parameters of plant are initialled as follow
X axis: Kt = 64, Mm =7, Bm = 0.7
Y axis: Kt = 64, Mm = 5, Bm = 0.5
The simulation results shown in Figure 6.9 ~Figure 6.12. In the circular trajectory result,
we can find in some locations of the position response not follow to the command
position; in the window trajectory, the position response doesn’t track to the command
position in the bend and the straight line; in the corner of star trajectory, the tracking is
better than in the band of the window trajectory and in the band of the flexuous
trajectory has poor tracking. Finally, the tracking errors of the trajectory motion
response include the average tracking error and the standard deviation errors are shown
in table 6.1.
66
Figure 6.8: Diagram of fuzzy control for linear X-Y table
-6 -4 -2 0 2 4 6-6
-4
-2
0
2
4
6
X-axis Position
Y-a
xis
Positio
n
0 0.5 1 1.5 2 2.5 3-10
0
10
X-a
xis
Positio
n
0 0.5 1 1.5 2 2.5 3-10
0
10
Time
Y-a
xis
Positio
n
0 1 2 3-50
0
50
X-a
xis
Iq
0 1 2 3-50
0
50
Time
Y-a
xis
Iq
0 1 2 3-0.5
0
0.5
X-a
xis
positio
n e
rror
0 1 2 3-0.5
0
0.5
Time
Y-a
xis
positio
n e
rror
(b)
(d)
(a)
(c)
Figure 6.9: FC using circular trajectory tracking response (Simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
67
-0.5 0 0.5 1 1.5 2 2.5 3-2
-1.5
-1
-0.5
0
0.5
1
1.5
X-axis Position
Y-a
xis
Pos
ition
0 1 2 3 4 5-4
-2
0
2
4
X-a
xis
Pos
ition
0 1 2 3 4 5-4
-2
0
2
4
Time
Y-a
xis
Pos
ition
0 1 2 3 4 5-40
-20
0
20
40
X-a
xis
Iq
0 1 2 3 4 5-40
-20
0
20
40
Time
Y-a
xis
Iq
0 1 2 3 4 5-0.1
0
0.1
X-a
xis
posi
tion
erro
r
0 1 2 3 4 5-0.1
0
0.1
Time
Y-a
xis
posi
tion
erro
r
(a) (b)
(d)(c)
Figure 6.10: FC using star trajectory tracking response (Simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
-1 0 1 2 3 4 5-3
-2
-1
0
1
2
3
X-axis Position
Y-a
xis
Pos
ition
0 1 2 3 4 5 6-5
0
5
X-a
xis
Pos
ition
0 1 2 3 4 5 6-5
0
5
Time
Y-a
xis
Pos
ition
0 1 2 3 4 5 6-50
0
50
X-a
xis
Iq
0 1 2 3 4 5 6-50
0
50
Time
Y-a
xis
Iq
0 1 2 3 4 5 6-0.1
0
0.1
X-a
xis
posi
tion
erro
r
0 1 2 3 4 5 6-0.1
0
0.1
Time
Y-a
xis
posi
tion
erro
r
(a) (b)
(d)(c)
Figure 6.11: FC using window trajectory tracking response (Simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
68
1 2 3 4 50.5
1
1.5
2
2.5
3
3.5
X-axis Position
Y-a
xis
Positio
n
0 1 2 3 40
2
4
6
X-a
xis
Positio
n
0 1 2 3 40
2
4
6
Time
Y-a
xis
Positio
n
0 1 2 3 4-50
0
50
X-a
xis
Iq
0 1 2 3 4-20
0
20
Time
Y-a
xis
Iq
0 1 2 3 4-0.1
0
0.1
X-a
xis
positio
n e
rror
0 1 2 3 4-0.1
0
0.1
Time
Y-a
xis
positio
n e
rror
(a)
(c) (d)
(b)
Figure 6.12: FC using flexuous trajectory tracking response (Simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Table 6.1: The tracking error of trajectory response in case using FC
(Simulation in MATLAB)
6.110.00420.0108
6.100.00050.0062
6.90.00120.0135
Figure
Circular
Standard
deviation
The error values of the response trajectory and the command
trajectory when using Fuzzy controller
Average errrorTrajectory
planing
Star
Window
Flexuous 6.120.00070.0053
69
6.1.2.2 Neural fuzzy controller using in position loop
The architecture of NFC is shown in Figure 6.13. The parameters of NFC are
used the same parameters using in section 6.1.1. Initial controller parameters in X axis
and Y axis are selected the same and the parameters of plant are initialled in FC. The
simulation results shown in Figure 6.14 ~Figure 6.17. In the simulation result, we can
see the position response close to the command position; and in the bend and the
straight line; in the corner of the trajectories, the tracking is better than using FC. The
tables 6.2~6.5 show the ci,j parameters are tuned to adequate values, and the position of
the mover can accurately track the command position. Finally, the tracking errors of the
trajectory motion response include the average tracking error and the standard deviation
errors are shown in table 6.6.
Figure 6.13: Diagram of neural fuzzy control for linear X-Y table
70
-6 -4 -2 0 2 4 6-6
-4
-2
0
2
4
6
X-axis Position
Y-a
xis
Pos
ition
0 0.5 1 1.5 2 2.5 3-10
0
10
X-a
xis
Pos
ition
0 0.5 1 1.5 2 2.5 3-10
0
10
Time
Y-a
xis
Pos
ition
0 0.5 1 1.5 2 2.5 3-50
0
50
X-a
xis
Iq
0 0.5 1 1.5 2 2.5 3-50
0
50
Time
Y-a
xis
Iq
0 0.5 1 1.5 2 2.5 3-0.5
0
0.5
X-a
xis
posi
tion
erro
r
0 0.5 1 1.5 2 2.5 3-0.5
0
0.5
Time
Y-a
xis
posi
tion
erro
r
(c)
(a) (b)
(d)
Figure 6.14: NFC using circular trajectory tracking response (simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Table 6.2: The rule table after adjusted in the circular simulation case
(Simulation in MATLAB)
71
-0.5 0 0.5 1 1.5 2 2.5 3-2
-1.5
-1
-0.5
0
0.5
1
1.5
X-axis Position
Y-a
xis
Positio
n
0 1 2 3 4 5-4
-2
0
2
4
X-a
xis
Positio
n
0 1 2 3 4 5-4
-2
0
2
4
Time
Y-a
xis
Positio
n
0 1 2 3 4 5-50
0
50
X-a
xis
Iq
0 1 2 3 4 5-50
0
50
Time
Y-a
xis
Iq
0 1 2 3 4 5-0.1
0
0.1
X-a
xis
positio
n e
rror
0 1 2 3 4 5-0.1
0
0.1
Time
Y-a
xis
positio
n e
rror
(a)
(c)
(b)
(d)
Figure 6.15: NFC using star trajectory tracking response (simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Table 6.3: The rule table after adjusted in the star simulation case
(Simulation in MATLAB)
72
-1 0 1 2 3 4 5-3
-2
-1
0
1
2
3
X-axis Position
Y-a
xis
Pos
ition
0 1 2 3 4 5 6-5
0
5
X-a
xis
Pos
ition
0 1 2 3 4 5 6-5
0
5
Time
Y-a
xis
Pos
ition
0 1 2 3 4 5 6
-50
0
50
X-a
xis
Iq
0 1 2 3 4 5 6-50
0
50
Time
Y-a
xis
Iq0 1 2 3 4 5 6
-0.1
0
0.1
X-a
xis
posi
tion
erro
r
0 1 2 3 4 5 6-0.1
0
0.1
Time
Y-a
xis
posi
tion
erro
r
(a) (b)
(c) (d)
Figure 6.16: NFC using window trajectory tracking response (simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Table 6.4: The rule table after adjusted in the window simulation case
(Simulation in MATLAB)
73
1 2 3 4 50.5
1
1.5
2
2.5
3
3.5
X-axis Position
Y-a
xis
Positio
n
0 1 2 3 40
2
4
6
X-a
xis
Positio
n
0 1 2 3 40
2
4
6
Time
Y-a
xis
Positio
n
0 1 2 3 4-50
0
50
X-a
xis
Iq
0 1 2 3 4-20
0
20
Time
Y-a
xis
Iq
0 1 2 3 4-0.1
0
0.1
X-a
xis
positio
n e
rror
0 1 2 3 4-0.1
0
0.1
Time
Y-a
xis
positio
n e
rror
(a) (b)
(c) (d)
Figure 6.17: NFC using flexuous trajectory tracking response (simulation in MATLAB)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Table 6.5: The rule table after adjusted in the flexuous simulation case
(Simulation in MATLAB)
74
Table 6.6: The tracking error of trajectory response in case using NFC
(Simulation in MATLAB)
6.160.00540.0125
6.150.00070.0078
6.140.00170.0182
Figure
Circular
Standard
deviation
The error values of the response trajectory and the command
trajectory when using Neural Fuzzy controller
Average errrorTrajectory
planing
Star
Window
Flexuous 6.170.00350.0098
6.1.2.3 Tracking performance analysis when simulation in MATLAB
The index values in (5.34) and (5.35) are used, to evaluate the trajectory tracking
performance of FC and NFC. Figure 6.18 and Figure 6.19 show the average tracking
error and tracking error of the standard deviation while controllers using FC and NFC in
X-Y table, respectively. From the performance analysis of the average error in tracking,
the circular trajectory of the neural fuzzy controller is better than fuzzy controller with
decrease about 36%; the window trajectory of the neural fuzzy controller is lower than
fuzzy controller about 14%, the star trajectory of neural fuzzy controller is better than
fuzzy controller by reduction about 21% and the flexuous trajectory about 46%. In the
standard deviation tracking error, the circular trajectory of neural fuzzy controller is
lower than fuzzy about 30%, the window trajectory of the neural fuzzy controller is
lower than about 22%; star tracking of the neural fuzzy controller than is reduced by
about 29% with star tracking of the fuzzy controller and about 46% with flexuous
tracking.
75
Figure 6.18: Average of the tracking error (simulation in MATLAB)
Figure 6.19: Standard deviation of the tracking error (simulation in MATLAB)
76
6.2 Simulation in FPGA
After verifying the effectiveness of our proposed control algorithm for X-Y table
in MATLAB, the simulation in FPGA is further evaluated. However, the control system
architectures in Figure 6.1, Figure 6.2 and Figure 6.8 are used to evaluate the
performance of FC and NFC. The motion trajectory command is implemented by
software using Nios II and the other parts including the neural fuzzy controller for
position loop, speed loop and plant model are implemented by hardware in FPGA. In
simulation, the sampling frequency is chosen to 2 kHz by hardware in FPGA and the
clock frequency of Nios II processor is 50MHz.
6.2.1 One dimensional motion trajectory
In this section, present simulation in FPGA for single axis with two architectures
includes FC and NFC. The parameters are chosen as follow
- According to our experience, the membership functions of two inputs and initial rule
table of FC are shown in Figure 6.20.
Figure 6.20: Rule table and the control effort surface (Simulation in FPGA)
µ(e)
A0 A1 A2 A3 A4 A5 A6
-600 -400 -200 0 200 400 600
e
µ(d
e)
1B
0B
1B
2B
3B
4B
5B
6
-30
--2
0-
10
01
02
03
0
de
- 900 - 900 - 900 - 900 - 600 - 300 0
- 900 - 900 - 900 - 600 - 300 0 300
- 900 - 900 - 600 - 300 0 300 600
- 900 - 600 - 300 0 300 600 900
- 600 - 300 0 300 600 900 900
- 300 0 300 600 900 900 900
0 300 600 900 900 900 900
77
- The initial parameters of RBF neural network structure are selected as follow
The weight from the hidden layer neuron to the output layer neuron
0028.00028.00028.0j
w (6.11)
The width of 3 neurons:
0038.00038.00038.0j
b (6.12)
The center of 3 RBF units:
0028.00028.000019.0
0028.00028.000019.0
0028.00028.000019.0
jc
(6.13)
- The specific values of parameters in control loops are as follow
Position loop: Kp=0.91 and Ki=0.004; Learning rate of fuzzy: 0.001; Learning rate of
neural: 0.0095; Speed loop : Kp=0.91
As the same with the simulation in MATLAB, two tested cases with different PMLSM
parameters are considered to evaluate the controller performance. The cases as follow
Case 1: Ψ =0.018; Ф=0.8; rate=0.8
Case 2: Ψ =0.018; Ф=0.5; rate=0.8
The simulation results are shown in Figure 6.21 and Figure 6.22. In Figure 6.21, the
mover position has a good following response at the case 1 condition by using the FC.
When the system parameters change to the case 2 condition, about 9% overshoot as
shown in Figure 6.21 have occurred. It reveals that FC is affected by the various plant
parameters. However, when NFC is used in the case 2 condition, the mover of PMLSM
track the output of the RM well with little oscillation and only 0.6% overshoot, which is
shown in Figure 6.22. Further, the parameters of ci,j can be continuously tuned to reduce
the error between the output of the RM and the position of the mover at each control
sampling interval. After one square-wave position commands have been tracked, the ci,j
parameters shown in Figure 6.23 are tuned to adequate values, and the position of the
mover can accurately track the output of the RM.
78
Figure 6.21: Step response and control effort when using FC (simulation in FPGA)
Figure 6.22: Step response and control effort when using NFC (simulation in FPGA)
79
Figure 6.23: Rule table after adjusted and the control effort surface for
Step response (simulation in FPGA)
6.2.2 Two dimensional motion trajectory
6.2.2.1 FC using in position loop (simulation in FPGA)
This section shows the FPGA simulation results of the motion controller for the
X-Y table by using Fuzzy controller in position loop. The parameters of FC are used the
same parameters using in section 6.2.1. Initial controller parameters in X axis and Y
axis are selected as follow
- Position loop: Kp=0.91 and Ki=0.0006; Learning rate of fuzzy: 0.001; Learning rate of
neural: 0.0095; Speed loop : Kp=0.91
- The parameters of plant are initialed as follow
X axis: Ψ =0.02; Ф=0.5; rate=0.8
Y axis: Ψ =0.02; Ф=0.75; rate=0.9
The simulation results shown in Figure 6.24 ~Figure 6.27. We also can find in some
locations of the position response in the results not follow to the command position such
as in the bend and the straight line of window trajectory response; in the corner of star
trajectory and in the band of the flexuous trajectory has poor tracking. The Table 6.1
shows the tracking errors of the trajectory motion response include the average tracking
error and the standard deviation errors.
80
Figure 6.24: FC using circular trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Figure 6.25: FC using star trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
81
Figure 6.26: FC using window trajectory tracking response (simulation in FPGA)
Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Figure 6.27: FC using flexuous trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
82
Table 6.7: The tracking error of trajectory response in the case using FC
(Simulation in FPGA)
6.260.004222.4074
6.250.000523.5104
6.240.001240.8001
Figure
Circular
Standard
deviation
The error values of the response trajectory and the command
trajectory when using Fuzzy controller
Average errrorTrajectory
planing
Star
Window
Flexuous 6.270.000714.7543
6.2.2.2 NFC using in position loop (simulation in FPGA)
Using NFC in position loop is present in this section and the parameters of NFC
are used the same parameters using in section 6.1.1. The initial controller parameters in
X axis and Y axis are selected the same and the parameters of plant are initialed in FC.
Figure 6.28 ~Figure 6.34 show the simulation results, rule table after adjusted and the
control effort surface for motion trajectories, respectively. We also can see the position
response close to the command position; and in the bend and the straight line; in the
corner of the trajectories, the tracking is better than using FC as the same with the
simulation in MATLAB.
83
Figure 6.28: NFC using circular trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Figure 6.29: Rule table after adjusted and the control effort surface for
Circular motion trajectory
84
Figure 6.30: NFC using star trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Figure 6.31: Rule table after adjusted and the control effort surface for
star motion trajectory
85
Figure 6.32: NFC using circular trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Figure 6.33: Rule table after adjusted and the control effort surface for
Window motion trajectory
86
Figure 6.34: NFC using flexuous trajectory tracking response (simulation in FPGA)
(a) Trajectory response (b) Axis response (c) Axis control effort (d) Tracking error
Figure 6.35: Rule table after adjusted and the control effort surface for
Flexuous motion trajectory
87
Table 6.8: The tracking error of trajectory response in the case using NFC
(Simulation in FPGA)
6.3216.674515.3015
6.3016.672613.9198
6.2828.692726.8106
Figure
Circular
Standard
deviation
The error values of the response trajectory and the command
trajectory when using Neural Fuzzy controller
Average errrorTrajectory
planing
Star
Window
Flexuous 6.3413.5910.3505
6.2.2.3 The X-Y table motion trajectory tracking performance analysis
For the detail comparison of the control performance of various controllers, the
performance measures of the Fuzzy controller and neural fuzzy controller are depicted
in Figure 6.36 and Figure 6.37. Figure 6.36 demonstrates the average tracking errors of
two controllers, and Figure 6.37 demonstrates the standard deviation of tracking errors
of two controllers with simulation results in FPGA. From the performance analysis of
the average error in tracking, the circular trajectory of the neural fuzzy controller is
better than fuzzy controller with decrease about 5%; the window trajectory of the neural
fuzzy controller is lower than fuzzy controller about 22%, the star trajectory of neural
fuzzy controller is better than fuzzy controller by reduction about 20% and the flexuous
trajectory about 32%. In the standard deviation tracking error, the circular trajectory of
neural fuzzy controller is lower than fuzzy about 7%, the window trajectory of the
neural fuzzy controller is lower than about 10%; star tracking of the neural fuzzy
controller than is reduced by about 18% with star tracking of the fuzzy controller and
about 29% with flexuous tracking.
88
Therefore, we can easily find that the proposed neural fuzzy controller has the least
average and standard deviation of tracking error and is more suitable to control the X-Y
table under the occurrence of uncertainties at various reference trajectories.
Figure 6.36: The average tracking error (simulation in FPGA)
Figure 6.37: Standard deviation of the tracking error (simulation in FPGA)
89
Chapter 7
Conclusion and future works
7.1 Overview
A motion control IC using a neural fuzzy controller for X-Y table based on
FPGA technology is successfully demonstrated in this thesis. The work herein is
summarized as follows.
1. The functionalities required to build a digital motion controller of X-Y table, such as
two RBF Neural-fuzzy controllers and one motion trajectory planning, have been
integrated in one FPGA chip.
2. The behavior of a Neural-fuzzy controller has been successfully described by VHDL,
and proven with a well motion trajectory performance in X-Y table.
However, the simulation results by step response, point to point motion control
tracking, circular, window, star and flexuous motion trajectory tracking in MATLAB
and in QUARTUS II software environment have been revealed that the software and
hardware co-design technology with the parallel processing well in the motion control
system of X-Y table.
7.2 Future works
The following research work can be studied in the future:
1. Fuzzy membership function can be tuned based on RBF NN identification, or fuzzy
membership function can adopt Gauss function.
2. Implement high sampling rate in the position loop to increase controller performance
is possible in the further study.
3. Apply this proposed control algorithm for X-Y table experimental system or XYZ
table.
90
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95
BIOGRAPHY
Name ： Nguyen Khanh Quang
Place of Birth ： Hue, Vietnam
Date of Birth ：May 07th
, 1983
Education and Certificates ：Southern Taiwan University
[2008-2010] Master Program in Electrical
Engineering
Da nang University of Technology
[2001-2006] Undergraduate Program in
Electrical Engineering
[Publication]
1. Ying-Shieh Kung, Nguyen Khanh Quang and Le Thi Van Anh, “FPGA-
based Neural Fuzzy Controller Design for PMLSM Drive,” Accepted to
the 8th International Conference on Power Electronics and Drive Systems
(PEDS'09), Nov. 10, 2009, Taipei, Taiwan.
