Fuzzy logic based DSP controlled servo position control for ultrasonic motor

Energy Conversion and Management 45 (2004) 3139–3153www.elsevier.com/locate/enconman

Fuzzy logic based DSP controlled servo positioncontrol for ultrasonic motor

G€ung€or Bal a,*, Erdal Bekiro�glu b, S�evki Demirbas� a, _Ilhami C�olak a

a Faculty of Technical Education, Electrical Department, Gazi University, 06500 Besevler, Ankara, Turkeyb Faculty of Engineering and Architecture, Department of Electrical and Electronics Engineering,

Abant _Izzet Baysal University, Bolu, Turkey

Received 2 December 2003; received in revised form 2 December 2003; accepted 3 February 2004

Available online 11 March 2004

Abstract

In this paper, position control of an ultrasonic motor was implemented on the basis of fuzzy reasoning.A digitally controllable two phase serial resonant inverter was developed to drive the ultrasonic motor by

using a TMS320F243 digital signal processor. The driving frequency was used as a control input in the

position control loop. The position characteristics obtained from the proposed drive and control system

were demonstrated and evaluated by experiments. The experimental results verify that the developed

position control scheme is highly effective, reliable and applicable for the ultrasonic motor.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Ultrasonic motor; Position control; Fuzzy logic; Digital signal processor

1. Introduction

The ultrasonic motor (USM) is a new type of motor that has different construction, charac-teristics and operating principles than the commonly used conventional electromagnetic motors.In recent years, a variety of novel types of USMs featuring high holding torque, high torque atlow speed, no electromagnetic noise, silent operation, compactness and flexible design possibilitiesin their configuration have attracted special interest as servo actuators in direct drive motioncontrol applications [1,2]. The USM is particularly superior in high holding torque and highresponse characteristics. As a result, it was expected to be used as a precise and accurate posi-tioning actuator [3].

* Corresponding author. Tel.: +90-312-212-3962; fax: +90-312-212-7575.

E-mail address: [email protected] (G. Bal).

0196-8904/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2004.02.001

mail to: [email protected]

3140 G. Bal et al. / Energy Conversion and Management 45 (2004) 3139–3153

The driving principle of the USM is based on high frequency mechanical vibrations and fric-tional forces. Owing to this drive mechanism, it is difficult to derive a mathematical model of anUSM. Moreover, the control characteristics of USMs are complicated and highly nonlinear. Theexact values of the motor parameters cannot be obtained easily, and the motor parameters aretime-varying due to increases in temperature and changes in motor drive operating conditions,such as driving frequency, source voltage and load torque [4,5].

Fuzzy logic control is especially preferred when the mathematical model of a control plant isdifficult to obtain. The fuzzy logic controller (FLC) is designed for control purposes on the operatingexperience of the plant without using a mathematical model [6–8]. The fuzzy logic control techniquehas been applied successfully to control ultrasonic motor drives in recent years [3,9,10]. However, theposition tracking characteristics under various load conditions have not yet been examined suffi-ciently from a practical point of view, especially for small and rapid position references.

The purpose of this study is to achieve highly effective position control for a Shinsei�s travelingwave type USR60 USM. A drive system based on the high frequency two phase serial resonantinverter was developed. Because of the complexity of the mathematical model and control of theUSM, a fuzzy logic approach was used in this study. A FLC was designed and integrated into theposition control loop. This drive system was controlled digitally by 16 bit fixed pointTMS320F243 digital signal processor (DSP).

The speed, ramp and periodical step position response characteristics of the traveling waveultrasonic motor (TWUSM) were obtained for different references and loads. The proposed fuzzylogic based DSP controlled position control technique was tested and verified by experiments. Theexperimental results show that the developed drive and control system is a very suitable methodfor position control of the TWUSM.

2. USM and energy conversion

An ultrasonic motor is a special type of motor that is driven by the mechanical vibration forceof a piezoelectric ceramic in the stator. Although several USM types have been designed, therotary TWUSM is a commonly used USM type. The operating principle and theoretical back-ground of a TWUSM are given in this section.

The energy conversion of a piezoelectric system is based on the piezoelectric element and amechanical vibration system. When the piezoelectric elements are excited by an electrical supplywith ultrasonic frequency, an ultrasonic vibration is produced in the mechanical vibration system,composed of the rotor and stator. The stator amplifies the mechanical vibrations and transmitsthem as a driving force to the rotor [11].

The speed of the USM is controlled by the,

• frequency of the two phase voltages,• amplitude of the two phase voltages and• phase angle between the two phase voltages.

An elliptic motion of points on the surface of the stator is generated by the traveling wave in thestator. The vibrations are excited by a piezoelectric ceramic layer bonded to the lower surface of

G. Bal et al. / Energy Conversion and Management 45 (2004) 3139–3153 3141

the stator. The rotor is pressed against the stator by means of a disc spring and is driven by thefrictional forces in the contact layer. The rotation direction of the rotor is opposite to the directionof the traveling wave [12].

To generate a traveling wave within the stator, it is necessary to have control of two mechanicalorthogonal modes. Electrode pattern A provides the cos kh and the pattern B provides the sin khBy driving these two modes at 90� out of phase, a traveling wave is produced. Each patternprovides a standing wave individually. The superposition of these standing waves produce thetraveling wave used in TWUSMs [13]:

- ¼ cosxt cos khþ sinxt sin kh; ð1Þ

- ¼ cosðxt � khÞ; ð2Þ

k ¼ 2pk; ð3Þ

where k is the wavenumber of the piezoelectric ceramic. k is the wavelength of the (+) and ())polarized one section. By changing the sign of one of the drive signals, the direction of thetraveling wave and, thus, the direction of the rotor reverses.

The speed of the USM can be controlled by the amplitude, frequency and phase difference ofthe two phase voltages. Since changing the driving frequency method gives a more flexible controlrange than the other methods [14], in the present study, the speed of the USM is controlled by thedriving frequency. Fig. 1 shows the speed–frequency characteristic of the USM, which has anonlinear behavior. In this study, the motor speed is controlled within the 41.3–43.3 kHz fre-quency range, which can be accepted as a linear frequency range. The speed–torque relation isalso an important characteristic. In Fig. 2, the speed–frequency characteristics of the USM are

40.5 41 41.5 42 42.5 43 43.50

20

40

60

80

100

120

140

Frequency( kHz)

Spee

d(r

pm)

41.3

Fig. 1. Speed–frequency characteristic of USM.

41 41.5 42 42.5 43 43.50

20

40

60

80

100

120

140

frequency(kHz)

spee

d(rp

m)

T=0.0NmT=0.1NmT=0.2NmT=0.3Nm

Fig. 2. Speed–frequency characteristics of USM under the different load torques.


given under different load torques. When the load torque increases, the speed of the motor de-creases.

3. DSP controlled USM drive system

To drive the USM, high quality semiconductor devices that can follow the optimum operatingpoint of the motor are required. It is difficult to drive the piezoelectric ceramic owing to its highdamping capacitance. For easy drive of the piezoelectric ceramic of the USM, a resonant fre-quency approach is used. Fig. 3 shows a newly developed drive system of a two phase, highfrequency, voltage fed, serial resonant inverter for the USM. This inverter has features of bothpulse width modulation (PWM) and pulse frequency modulation (PFM) control techniques. TheLA and LB inductances have been connected in series with each phase to obtain resonance with thedamping capacitance (Cd) of the USM. The inverter outputs are two phase high frequency ACvoltages with 90� phase difference. The rotating direction has been controlled by letting VA or VBlead. The CW and CCW inputs provide direction control signals [15]. In practice, the drivingfrequency is set higher than the resonant frequency of the mechanical vibration system because ofthe basic operating characteristics of the USM [16,17].

Speed control of the USM was achieved by a variable driving frequency. The value of thedriving frequency was determined by comparing the AC voltage (Vs) of the feedback electrode ofthe USM and a reference DC voltage (Vdc). The frequency signal was then applied to the opto-isolator, split phase and voltage control oscillator (VCO) circuits.

The control input of the drive system was the switching frequency, fs. This input was obtainedfrom a comparison of the feedback electrode voltage (Vs) and the reference DC voltage.According to the demanded speed, the value of switching frequency was adjusted. This was

C1

C2

LA

AC

phase-Ainverter

phase-Binverter

S1

S3

S2

S4

LB

USM

phase split,VCO,opto-coupler circuit

comparatorfilter

Vs

VdcfsCW CCW

GND

FLC

encoder

referenceposition

rotorposition

control signal

Fig. 3. Drive system of USM.


achieved by changing the level of the reference DC voltage. To change the level of the DC voltage,the duty cycle of the PWM signal was changed. So, according to the duty ratio of the PWMsignal, the DC output of the low pass (LP) filter was controlled. Detailed explanations about thedesign of the low pass filter and the produced PWM signals were given in Ref. [18]. The duty cycleof the PWM was controlled with respect to the output of the FLC.

The USM drive system was controlled by the 16 bit fixed point TMS320F243 EVM digitalsignal processor (DSP). The block diagram of the TMS320F243 controlled USM drive system isgiven in Fig. 4. The event manager and general purpose input/output (GPIO) units of the DSPwere used for control of the USM. The PWM signal was generated by the general purpose timer-1(GPT1). The GPT1 was set in the continuous up count mode to provide an asymmetric PWMsignal. Two pins of the GPIO were set as digital output to provide the CW and CCW directionsignals. The quadrature encoder pulse (QEP) circuit of the event manager was used for encodersignals. The encoder is 500-ppr and has two quadrature encoder signals and one index signal.These encoder signals were encoded digitally by the QEP circuit and converted to the speed andposition information for control purposes.

4. Fuzzy logic controller (FLC)

Basically, the FLC is based on the error signal of the control plant and change in this error. Theaim of this controller is to obtain robust control characteristics in tracking the reference commandunder the parameter variations and variable operating conditions.

The block diagram of the constructed FLC is given in Fig. 5. The inputs of the FLC are po-sition error (Dh) and speed (x), and the output is the manipulated value of the driving frequency

two-phase half-bridgeserial-resonant inverter

FlashEEPROM

Datamemory

Programmemory

Eventmanager

GPIO

QEPcircuit

TMS320F243 EVM

USM drive system

encoder

CW

CCW

VA

VB

GNDVd

+

-

LPfilter

comparator Vs

VCO, phase split,opto-coupler circuit

S1 S2 S4S3

fsPWM Vdc

USM

QEP-AQEP-BIndex

Fig. 4. TMS320F243 controlled USM drive system.

USM

∆θ

∆ fθ

d/dt ωf(t-1)

f

θ ref

FLC

Fig. 5. The block diagram of FLC.


(Df ). The manipulated value of the driving frequency (Df ) is added to the previous driving fre-quency (f ðt � 1Þ) to obtain the new control input (current driving frequency (f )) and applied tothe USM. Where href is the reference position; h is the actual position; Dh is the position error; x isthe speed; f ðt � 1Þ is the driving frequency; f is the current driving frequency; Df is themanipulated value of the driving frequency.

The relation between the driving frequency and rotary speed (x) of the USM cannot be ex-pressed as a simple equation. The speed decreases as the frequency increases in a stable frequencyrange [10]. Also the f –x characteristics depend on the load variations (Fig. 2). The manipulatedvalue of the driving frequency (Df ) is obtained using the FLC based on the position error (Dh)and the speed (x). The position error and speed of the motor are determined as follows:

Dh ¼ href � h; ð4Þ

x ¼ dhdt

: ð5Þ


In position control of the USM, to allow design flexibility and tuning of the controller, theinput and output variables are represented in terms of per unit (pu) values. KDh, Kx and KDf arerelated gain factors of the fuzzy logic controller. In this study, the values of these gain factors wereset to 0.5, 5 and 1000, respectively, and defined as follows:

Fig. 6

freque

DhðpuÞ ¼ Dh=KDh; ð6Þ

xðpuÞ ¼ x=Kx; ð7Þ

Df ðpuÞ ¼ Df =KDf : ð8Þ

Fig. 6 shows the membership functions of the FLC. Fig. 6(a) shows the membership functionsof position error; Fig. 6(b) shows the membership functions of speed; and Fig. 6(c) shows themembership functions of the manipulated value of driving frequency. While the inputs of the FLC

1-1 0.6-0.6 0.2-0.2 0

PBPS PMZNSNMNB

∆θ (rad)

(a)

1-1 0.6-0.6 0.2-0.2 0

PBPS PMZNSNMNB

ω(rad/s)

(b)

0.50

PBPMZNMNB

1-0.1-0.5 0.1-1

NS PS

∆f(Hz)

(c)

. Membership functions of FLC: (a) position error (Dh), (b) speed (x) and (c) manipulated value of driving

ncy (Df ).

Table 1

Control rules of FLC

x Dh

NB NM NS Z PS PM PB

NB Z PS PM PB PM PS Z

NM NS Z PS PM PS Z NS

NS NM NS Z PS Z NS NM

Z NB NM NS PB NS NM NB

PS NM NS Z PS Z NS NM

PM NS Z PS PM PS Z NS

PB Z PS PM PB PM PS Z

PB is positive big, PM is positive medium, PS is positive small, Z is zero, NB is negative big, NM is negative medium

and NS is negative small.


are determined as triangular membership functions, for easy and rapid calculation, the output isselected as singleton membership functions.

The control rules of the FLC are obtained according to the expert experience and controlengineering as follows. If the position error is very big and the rotary speed is very slow, the USMhas to be accelerated. To accelerate the USM, the driving frequency should be decreased as shownin Fig. 1. In this case, the manipulated value of the driving frequency should be a negative value todecrease the driving frequency. Conversely, if the position error is very small and the speed is veryfast, the speed of the USM should be reduced. To reduce the speed, the driving frequency must beincreased. So, the manipulated value of the driving frequency should be a positive value to in-crease the driving frequency. In this approach, the fuzzy control rules of all cases are given inTable 1.

The implementation of the FLC for position control of the USM is summarized as follows:

1. The position of the USM is sampled.2. The position error and the speed are calculated.3. Fuzzy sets and membership functions of the position error and the speed are determined.4. Change of control action (Df ) is determined with respect to the individual fuzzy rules.5. The value of Df is calculated by using the center of gravity (COG) defuzzification method.6. The new control signal is calculated as f ðtÞ ¼ f ðt � 1Þ þ KDf � Df ðpuÞ and applied to the con-

trol plant.

5. Experimental results

In this section, the experimental results obtained from the fuzzy logic controlled positioncontrol of the USM are presented. The technical specifications of the driver and the USM aregiven in Appendix A.

Firstly, to see how the two phase outputs of the inverter are obtained, an example is given.While the motor speed is 95 rpm, the measured AC voltage of the feedback electrode is shown in

Fig. 7. Voltage of feedback electrode.


Fig. 7. The value of this voltage is 34.6 V (rms) with 42.05 kHz frequency. To obtain the de-manded speed, this voltage was compared with the fixed 2 V DC voltage. By comparing thesevoltages, a switching signal with t ¼ 2:394� 10�5 s (fs ¼ 41:74 kHz) was produced. This switchingsignal was applied to four switches via the voltage control oscillator and phase split circuits toprovide the two phase AC voltages. Fig. 8 shows the waveforms of these output voltages with thefrequency of 41.74 kHz, which is equal to the switching signal frequency. The output voltages areequal and 120 V (rms).

By changing the level of the DC voltage, the switching frequency (fs) is changed, so the speed ofthe motor is controlled. The required DC voltage for the comparing process is produced by thelow pass filter circuit. This circuit converts the PWM signal to the reference DC voltage accordingto the duty cycle of the PWM. When the duty cycle is changed, the value of the produced DCvoltage also changes, so the switching frequency is changed. As a result, the speed of the motor isvaried to the demanded value.

Fig. 8. Output voltages of inverter.

0 100 200

time (ms)

spee

d (r

pm)

300 400 5000

25

50

75

100

125

Fig. 9. Speed responses of USM at 75, 100 and 130 rpm.


Fig. 9 shows the speed responses of the USM at three different reference speeds, which are 75,100 and 130 rpm. As is clearly seen from the figure, the USM tracks the reference speeds smoothlywithout any overshoot or undershoot.

In order to examine the behavior of the motor, an experiment was performed for three differentramp position commands, and the results, as illustrated in Fig. 10, show that the USM tracks thecommand positions for all of the ramp responses robustly.

The developed FLC position control for the USM is highly load adaptive as illustrated in Fig.11. Fig. 11(a) shows the reference position command applied as a periodical function with pradians; Fig. 11(b) shows the actual position without load; and Fig. 11(c) shows actual positionwith 0.2 Nm external load. As seen from Fig. 11, good tracking control performance of the USM

0 1 2 3 4 5 0

time (s)

posi

tion

(rad

)

reference position

2

4

6

8

10

12

14

16

actual position

Fig. 10. 1, 2 and 3 rad/s ramp responses of USM.

Fig. 11. Periodical p radian step response of USM: (a) reference position, (b) actual position without load and

(c) actual position with 0.2 Nm load.


drive and control system was obtained for the periodical step position command when the motorwas unloaded and loaded.

Fig. 12. Periodical p/2 radian periodical step response of USM.


In this study, the position responses of the USM are also obtained for faster position com-mands. While Fig. 12 shows the periodical p/2 step response of the USM, Fig. 13 shows the p/4periodical step response of the USM. It is clearly seen from these figures that the USM tracks thedemanded position in a short time accurately, although the position command is very fast forrotary motors. From Figs. 12 and 13, it can be said that the USM can operate like a steppingmotor having 45� or 90� step angle.

A 2p radian single step position response of the USM without load is given in Fig. 14(a) andwith 0.2 Nm external load torque in Fig. 14(b). These figures demonstrate that the developed FLCposition control system gives precise and robust position response for a single step positioncommand.

Fig. 13. Periodical p/4 radian step response of USM.

Fig. 14. 2p radian single step position response of USM: (a) without load and (b) with 0.2 Nm load.


6. Conclusions

In this paper, a highly effective position controller for a TWUSM was implemented. A fuzzylogic controller was designed to provide effective position tracking performance of the USM. Thiscontrol was achieved and optimized by a TMS320F243 DSP.

A high frequency, voltage fed, serial resonant inverter was designed to drive the USM. Thespeed and position of the USM were controlled by the driving frequency with detecting theresonant state by the generated voltage of the feedback electrode mounted on the USM. Thiscontrol system compensates the speed and position characteristics variations of the motor. Firstly,a digitally controllable drive system was designed, and then, it was integrated successfully with aDSP.

The positioning servo system incorporating the USM was realized by controlling the drivefrequency on the basis of the designed FLC. The performance of the proposed driving and controlsystem was examined for step speed and ramp responses and periodical step position responses.The control technique is simple and effective since only the driving frequency of the two phasevoltages is controlled. The robustness of the proposed drive and control system was demonstrated


and evaluated by experimental investigations. The experimental results verify that the developeddrive and control system give superior speed and position characteristics for the USM.

Acknowledgements

This work was supported by The Scientific and Technical Research Council of TurkeyTUBITAK, through grant number 100E-012.

Appendix A

Technical specifications of driver and ultrasonic motor:

DriverPower source voltage 12 V DCDrive frequency 40–44 kHzDrive voltage 100–130 VrmsInverter power 12 VA

USM

Rated torque 0.4 NmRated power 4 WRated speed 10 rad/sTorque per volume 10,000 Nm/m3

Power per volume 66,700 W/m3

Torque density 3.5 Nm/kgPower density 23 W/kg

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Fuzzy logic based DSP controlled servo position control for ultrasonic motor

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