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Integrated micro-and miniscale electromechanicalsystems with permanent-magnet servo-motors andVLSI drivers–controllersSergey Lyshevski

Alexander Nazarov

John Boggs

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Recommended CitationMechatronics, Vol. 12, No. 6, pp. 1115-1131

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Integrated micro- and miniscaleelectromechanical systems with

permanent-magnet servo-motors andVLSI drivers–controllers

Sergey Edward Lyshevski *, Alexander Nazarov, John Boggs

Department of Electrical and Computer Engineering, Purdue University at Indianapolis,

723 West Michigan Street, Room SL160, Indianapolis, IN 46202-5132, USA

Abstract

The current trends in development and deployment of advanced micro- and miniscale

electromechanical systems (MEMS) have facilitated the unified fundamental, applied, and

experimental research activities in the analysis and design of state-of-the-art motion devices

(rotational and translational electromechanical motion devices), integrated circuits (ICs), and

controllers. The objectives of this paper are to design, develop, and compare different control

algorithms for high-performance MEMS with permanent-magnet rotational servo-motors

controlled by ICs (VLSI driver–controller is fabricated using CMOS technology). The prob-

lems to be solved are very challenging because a number of long-standing issues in design,

hardware integration, control, nonlinear analysis, and robustness have to be solved. The major

emphases of this paper are the analysis and design of robust servo-systems, as well as the

comparison of the dynamic performance of closed-loop MEMS with different control algo-

rithms. We synthesize, verify, and test proportional–integral, integral with state feedback

extension, relay, and sliding mode controllers. It is illustrated that the sliding mode control

laws drive the states and tracking error to the switching surface and maintain (keep) the states

and tracking error within this nonlinear switching surface in spite of different references,

disturbances, parameter variations, and uncertainties. That is, robust tracking, desired accu-

racy, and disturbance attenuation are achieved. We report the experimental setup which was

built to perform the advanced studies of high-performance MEMS. The testbed was built to

integrate permanent-magnet microscale servo-motor and ICs (driver–controller).

� 2002 Published by Elsevier Science Ltd.

Mechatronics 12 (2002) 1115–1131

*Corresponding author. Tel.: +1-317-278-1960; fax: +1-317-274-4493.

E-mail address: [email protected] (S.E. Lyshevski).

0957-4158/02/$ - see front matter � 2002 Published by Elsevier Science Ltd.

PII: S0957-4158 (02 )00017-X

mail to: [email protected]

1. Introduction

In many applications, e.g., avionics, medicine, robotics and telecommunication,microscale drives and servos are required and will be widely used. It was reported in[5,9] that superior high torque density high-speed microtransducers can be devisedand fabricated using the surface micromachining technology. Microtransducers(microscale motion devices which can be used as actuators and sensors) with di-ameter 1–2 mm were designed and fabricated. The angular velocity is up to 100 000rad/s and the electromagnetic torque is in the lN-m range. These microtransducersmust be integrated with microelectronics and sensors in order to regulate motiondevices. In fact, micro- and miniscale permanent-magnet servo-motors with VLSIdrivers–controllers are widely used in high-performance mechatronic and electro-mechanical systems because these motors and drivers are simple, efficient, affordable,and reliable. Excellent dynamic characteristics, high accuracy precision and ex-panded operating envelopes can be achieved by using robust controllers augmentedwith pulse-width-modulated amplifiers––MOSFETs four quadrant power stage tocontrol the average applied voltage supplied to the motor windings. High-perfor-mance VLSI drivers with embedded controllers (capable to implement advancedcontrol algorithms) are the current trends in design of high-performance MEMS[2,5].

Many difficulties and unsolved problems in design and development of MEMShave prompted research to improve closed-loop system performance, hardwareflexibility and usability. New trends in motion control of MEMS have fosteredsynthesis and deployment of sophisticated algorithms. Innovative inroads in analysisand design of high-performance MEMS are taking place. However, an unifiedanalysis and design theory has not been developed yet, and this paper reports in-novative concepts. Micro- and miniscale electromechanical motion devices can beregulated using VLSI drivers–controllers fabricated using CMOS technology [5]. Theaverage voltage, applied to the armature winding, is regulated by changing the dutyratio which varies between þ1 and �1. That is, the control signal is bounded. Inaddition, the motor parameters are varying. For example, the armature resistanceand inductance, the back emf (torque ) constant, and the moment of inertia vary dueto the temperature and load changes.

To approach and solve the motion control problem, this paper uses a completemodel of MEMS integrating lumped-parameters mathematical models of micro- andminiscale permanent-magnet servo-motors and ICs. While this research has beenpursued extensively from modeling perspectives, there exist challenging unsolvedproblems in analysis and design. In particular, different constrained control algo-rithms must be designed, analyzed, verified, and tested. These advanced controllersare needed to guarantee stability, precise tracking, accuracy, disturbance attenua-tion, specified steady-state and dynamic behavior, etc. We design and examine dif-ferent control laws. It is illustrated that nonlinear controllers must be synthesizedand deployed in high-performance MEMS. This paper highlights a specific appli-cation of the nonlinear analysis and control theory, and the bounded controllers aresynthesized. The capabilities of the designed MEMS are thoroughly studied and

1116 S.E. Lyshevski et al. / Mechatronics 12 (2002) 1115–1131

illustrated. Our goal is to integrate the current leading-edge engineering and tech-nology developments and apply most promising fundamental research for high-performance micro- and miniscale rotational electromechanical motion devices, ICs,and sensors with ultimate objective to design superior MEMS. From theoreticalstandpoints, this paper solves modeling, identification, and motion control problemsfor integrated MEMS which include actuators, sensors, and ICs with controller.By using an explicit representation of nonlinear dynamics, fundamental problemsin analysis and control are approached and solved to ensure a spectrum of perfor-mance objectives imposed on MEMS. The results reported are the attractive mean toenhance the hardware capability and flexibility, integrate advanced analysis andcontrol, reduce system sensitivity to parameter variations, design robust controlalgorithms which guarantee stability, reduce system complexity, etc. By using thereported innovative inroads in nonlinear analysis and control, MEMS servos anddrives are designed.

2. Modeling of MEMS

The problems of modeling and control of MEMS are very important in manyapplications. A mathematical model is a mathematical description (in the form offunctions or equations) of electromechanical systems which integrate electrome-chanical motion devices (actuators and sensors), ICs and other components. Thepurpose of the model development is to understand, comprehend and utilize differentphenomena and effects. The analysis of the end-to-end behavior and efficiency,modeling, optimization, simulation and other important design steps are performed.The starting point is the mathematical model development. The process of mathe-matical modeling and model development is given below.

The first step is to formulate the modeling problem:

• examine and analyze the integrated MEMS using a multi-level and systematic-level hierarchy concept. That is, develop multi-level input–output subsystem(components) pairs, e.g., actuator––ICs (power stage)––controller, sensor––ICs(input/output microelectronics)––controller, etc.;

• comprehend the structure, device, and system configurations;• gather the data and information;• develop input–output variable pairs, identify the independent and dependent con-

trol, disturbance, output, reference (command), state and performance variables,as well as events;

• making assumptions simplify the problem to make the studied system mathemat-ically tractable (mathematical models, which are the idealization of physical phe-nomena, are never absolutely accurate, and even high-fidelity mathematicalmodels simplify the reality to allow the designer to perform the thorough analysisand accurate predictions of the system performance).

The second step is to derive equations that relate the variables and events:

S.E. Lyshevski et al. / Mechatronics 12 (2002) 1115–1131 1117

• define and specify the basic laws (Ampere, Kirchhoff, Lagrange, Maxwell, andNewton) to be used to obtain the equations of motion: models of electrical, elec-tronic, and mechanical subsystems and devices can be found and augmented toderive a mathematical model of the MEMS using defined variables and events;

• derive mathematical models in the form of differential and difference equations.

The third step is the simulation, analysis, and validation:

• analytically and/or numerically solve differential, difference and hybrid equations;• using information variables (which can be directly measured or observed), synthe-

size the fitting (regret/mismatch) functional;• verify the results through the heterogeneous data-intensive comparison using

model and experimental input-state-output mapping sets, calculate the fittingfunctional and minimize this functional refining mathematical models (revisingdifferential and difference equations as well as adjusting their coefficient basedupon the evidence data);

• examine the analytical and numerical data against new experimental data and ev-idence.

If the matching with the desired accuracy is not guaranteed, the mathematicalmodel must be refined, and the designer must start the cycle again.

Electromagnetic theory and classical mechanics form the basis for the develop-ment of mathematical models. In particular, MEMS can be modeled using Max-well’s equations and torsional–mechanical equations of motion [5,9]. However, fromcontrol perspectives the mathematical models as given by ordinary differentialequations can be used.

Control of the motor angular velocity xr is achieved by changing the armaturevoltage ua using pulse-width-modulation switching. Fig. 1 shows the micro- orminiscale permanent-magnet motor with a high-frequency switching four-quadrantIC controller–driver (e.g., the monolithic 30 V/1A MC33030 ICs controller–driver isfabricated in the plastic package, 648 case).

The applied voltage to the armature winding ua is controlled by the IC driver, andthe output voltage ua is regulated changing the duty ratio dD by IC controller. Ingeneral, the duty ratio is a function of the switching frequency, turn on and turn offtime [2]. For four-quadrant IC power stage, dD 2 ½�1 1�. The settling time of theVLSI drivers–controllers is nanoseconds, while the transient behavior of micro- andminiscale servo-motors in the microseconds range. Thus, the ICs mathematicalmodel to describe transient dynamics can be simplified. Applying the Lagrangeequations of motion, the following mathematical model is developed to modelMEMS with permanent-magnet micromotors and VLSI drivers–controllers [1,2].

duadt

¼ � 1

TIC

ua þkICTIC

dD;

diadt

¼ 1

La

ua �raLa

ia �kaLa

xr;


dxr

dt¼ kaJia �

BmJ

xr �1

JTL;

dhr

dt¼ xr: ð1Þ

Here, ua and ia are the armature voltage and current; xr and hr are the rotor angularvelocity and displacement; dD is the duty ratio (control variable); TL is the loadtorque; kIC and TIC are the coefficient and time constant of the ICs; ra and La are thearmature resistance and inductance; ka is the back emf (torque) constant; Bm is theviscous friction coefficient; J is the moment of inertia.

From (1), in the state-space form we have

_xxðtÞ ¼ Axþ Bu; ð2Þduadtdiadtdxr

dtdhr

dt

266666666664

377777777775¼

� 1

TIC

0 0 0

1

La

� raLa

� kaLa

0

0kaJ

�BmJ

0

0 0 1 0

2666666664

3777777775

uaiaxr

hr

2664

3775þ

kICTIC

0

0

0

2666664

3777775dD �

0

01

J0

2666664

3777775TL:

In servo-systems, the angular or liner displacements are the outputs. Hence, theoutput equation is

yðtÞ ¼ kgearhrðtÞ; ð3Þ

where kgear is the kinematics gear coefficient.

Fig. 1. MEMS: permanent-magnet motor and IC controller–driver.


Using differential and output Eqs. (2) and (3), one obtains the block diagram ofthe open-loop MEMS as documented in Fig. 2.

In MEMS drives, the output is the angular velocity. Thus, one has the followingoutput equation

yðtÞ ¼ kgearxrðtÞ:

3. Identification of MEMS

Consider the identification problem for a linear single-input/single-output MEMSas described by the following difference equation in state-space form

xðiÞ ¼ Fmxði� 1Þ þ Gmuði� 1Þ:

This equation is found by discretizing differential Eq. (2) using procedure docu-mented in [10]. Our goal is to identify the unknown matrices Fm 2 Rkk and Gm 2Rk1 of the difference equation found. The least-squares estimation is used to obtainthe vector of estimated parameters p in Fm and Gm [10]. One identifies the unknownparameters

pn ¼ ðUTmnUmnÞ�1UT

mnxmðiÞ¼^

WnxmðiÞusing the measured data

xmðiÞ ¼ Up; xm 2 Rnk1:

Here, U is the regression matrix; xmðiÞ is the vector of measured states.Taking note of (k þ 1) measurements, the measurement vector is described as

xmði; kÞ ¼ Uxfm þ Uugm;

where

xmði; kÞ ¼x1ði; kÞ

..

.

xnði; kÞ

264

375; x1ði; kÞ ¼

x1ðiþ 1Þ...

x1ðiþ kÞ

264

375; xnði; kÞ ¼

xnðiþ 1Þ...

xnðiþ kÞ

264

375

Fig. 2. Block diagram of MEMS.


Ux ¼Ux1 � � � 0

..

. ... ..

.

0 � � � Uxn

264

375 2 Rnknn; Uu ¼

Uu1 � � � 0

..

. ... ..

.

0 � � � Uun

264

375 2 Rnknl

Ux1 ¼ Uxn ¼ ½x1ði; k � 1Þ � � � xnði; k � 1Þ� 2 Rkn;

Uu1 ¼ Uun ¼ ½u1ði; k � 1Þ � � � ulði; k � 1Þ� 2 Rkl;

fm ¼ ½f1 � � � fn�T 2 Rnn1; f1 ¼ ½F11 � � � F1n�T; fn ¼ ½Fn1 � � � Fnn�T;gm ¼ ½g1 � � � gn�T 2 Rnl1; g1 ¼ ½G11 � � �G1l�T; gn ¼ ½Gn1 � � �Gnl�T:

Thus, the unknown parameters are found as

p1 ¼ W1f1g1

� �2 RðnþlÞ1; � � � ; pn ¼ Wn

fngn

� �2 RðnþlÞ1; W1 ¼ Wn:

4. Control of MEMS

4.1. Proportional–integral control

In [2,3,10], the bounded control laws are synthesized in the nonlinear propor-tional–integral form. In particular,

uðtÞ ¼ satþ1�1 e;

Zedt

�

¼ satþ1�1

X1

j¼0

kpje2jþ12bþ1

proportional

0BB@ þ

Xr

j¼0

kij1

se

2jþ12lþ1

integral

1CCA; �16 u6 þ 1; ð4Þ

where kpj and kij are the proportional and integral feedback gains; 1, b, r and l arethe nonnegative integers assigned by the designer to attain the specified stabilitymargins, tracking, accuracy, and disturbance attenuation.

Letting 1 ¼ b ¼ r ¼ l ¼ 0, the liner controller is

uðtÞ ¼ satþ1�1 kp0eðtÞ

þ ki0

ZeðtÞdt

�; �16 u6 þ 1: ð5Þ

The tracking error, used in (4), is expressed as eðtÞ ¼ rðtÞ � yðtÞ ¼ hreferenceðtÞ�kgearhrðtÞ.

For MEMS drives we have eðtÞ ¼ rðtÞ � yðtÞ ¼ xreferenceðtÞ � kgearxrðtÞ.

4.2. Tracking integral control

Tracking integral control algorithms can be designed.Augmenting the MEMS dynamics (2) _xxðtÞ ¼ Axþ Bu with the exogeneous sys-

tem _xxrefðtÞ ¼ rðtÞ � yðtÞ ¼ hreferenceðtÞ � kgearhrðtÞ or _xxrefðtÞ ¼ rðtÞ � yðtÞ ¼ xreferenceðtÞ�kgearxrðtÞ, one has the following state-space differential equation


_xxRðtÞ ¼ ARxR þ BRuþ NRr; y ¼ hx;

where

xR ¼ xxref

� �2 R5

is the augmented state vector;

AR ¼ A 0�h 0

� �2 R55;

BR ¼ B0

� �2 R51

and

NR ¼ 01

� �2 R51

are the matrices of coefficients.The quadratic performance functional is

J ¼ 1

2

Z tf

t0

xTRQxR

�þ uTGu

�dt;

where Q 2 R55 is the positive semi-definite constant-coefficient matrix; G 2 R1 is thepositive weighting coefficient.

Making use of the quadratic performance functional, one finds the control lawusing the first-order necessary condition for optimality. We have

u ¼ �G�1BTR

oVoxR

¼ �G�1 B0

� �ToVoxR

:

The solution of the Hamilton–Jacobi–Bellman equation

� oVot

¼ 1

2xTRQxR þ oV

oxR

�T

AxR � 1

2

oVoxR

�T

BRG�1BTR

oVoxR

is satisfied by the quadratic return function V ¼ 12xTRKxR. Here, K 2 R55 is the

symmetric matrix which must be found by solving the nonlinear differential equation

� _KK ¼ Qþ ATRK þ KTAR � KTBRG�1BT

RK; Kðtf Þ ¼ Kf :

The controller is given as

u ¼ �G�1BTRKxR ¼ �G�1 B

0

� �TKxR:

From _xxrefðtÞ ¼ eðtÞ, one has xrefðtÞ ¼ReðtÞdt.

Therefore, we obtain the integral control law

uðtÞ ¼ �G�1 B0

� �TK

xðtÞReðtÞdt

� �:


In this control algorithm, the error vector is used in addition to the state feedback. Itwas illustrated that the duty ratio is bounded, and �16 u6 1.

Let us approximate the saturation characteristic by the hyperbolic tangent. Then,applying the procedure given in [4,10], to analytically design a constrained con-troller, one minimizes the nonquadratic functional

J ¼Z tf

t0

xTRQxR

þ G

Ztan�1 udu

�dt;

and the constrained controller is found as

uðtÞ ¼ � tanh G�1 B0

� �TK

xðtÞReðtÞdt

� � !

� �satþ1�1 G�1 B

0

� �TK

xðtÞReðtÞdt

� � !; �16 u6 1:

4.3. Relay (time-optimal) control

Using the method reported in [10], we minimize the following performancefunctional

J ¼ 1

2

Z tf

t0

xTRQxR dt:

The Hamilton–Jacobi equation is

� oVot

¼ min�16 u6 1

1

2xTRQxR

�þ oVoxR

T

ARxRð þ BRuÞ�:

Hence, one finds the control law as

u ¼ �sgn BTR

oVoxR

�; �16 u6 1:

This relay-type control, which theoretically guarantee minimum-time dynamics,cannot be implemented in practice due to the chattering phenomenon. Therefore,relay-type control laws with dead zone are commonly used. The dead zone is definedusing the circuitry topology and armature inductance.

4.4. Sliding mode control

Hard- and soft-switching sliding mode control algorithms are synthesized in[6,10], and it is shown that the variable structure theory can be straightforwardlyapplied to design high-performance MEMS. The smooth sliding manifold is


M ¼ ðt; x; eÞ 2 RP 0f X E tðt; x; eÞj ¼ 0g

¼\mj¼1

ðt; x; eÞ 2 RP 0

� X E tjðt; x; eÞ

�� ¼ 0�:

The time-varying linear and nonlinear switching surfaces are

tðt; x; eÞ ¼ KtxðtÞ KteðtÞ½ � xðtÞeðtÞ

� �¼ KtxðtÞxðtÞ þ KteðtÞeðtÞ ¼ 0;

and tðt; x; eÞ ¼ Ktxeðt; x; eÞ ¼ 0:The soft-switching control law is found as

uðt; x; eÞ ¼ �G/ðtÞ; G > 0;

where /ð�Þ is the continuous real-analytic differentiable function, e.g., tanh anderf.

5. Control of a servo-MEMS

We study the mini-servo system with the following parameters [8]:kIC ¼ 30, TIC ¼ 0:0001 s, rað�Þ 2 ½2:7T¼20 �C 3:7T¼140 �C� X, La ¼ 0:004 H,kað�Þ 2 ½0:11T¼20 �C 0:094T¼140 �C� V s/rad (Nm/A); J ¼ 0:0001 kgm2,Bm ¼ 0:00008 Nm s/rad and kgear ¼ 0:1.The duty ratio is bounded as �1; i.e., �16 dD 6 þ 1.Our goal is to design and verify different control algorithms, and four control laws

are synthesized.

5.1. Proportional–integral controller

Using the procedure reported in section 4.1, the following bounded proportional–integral controller is designed

u ¼ satþ1�1 0:6e

þ 0:03

Zedt�:

Employing the conventional notations, one has rðtÞ ¼ hreferenceðtÞ and yðtÞ ¼ kgearhrðtÞ.It must be emphasized that the proportional–integral controller synthesized is

bounded. The analysis of the transient behavior must be performed. Fig. 3 depictsthe evolution of the state variables and the MEMS output yðtÞ. The reference inputwas assigned to be rðtÞ ¼ 2. The settling time is 0.3 s, and for the worst-case per-formance (if the temperature is 140 �C), the overshoot for yðtÞ is 15%.

5.2. Tracking integral controller

To design a tracking integral control law, the procedure reported in section 4.2 isapplied.

Assigning q11 ¼ 0:0001, q22 ¼ 0:007, q33 ¼ 0:00001, q44 ¼ 0:01, q55 ¼ 4 108 andG ¼ 0:0001, the following controller is found


u ¼ satþ1�1

� 3:1ua � 19:9ia � 1:3xr � 31:6hr þ 2818:8

Zedt�:

Fig. 4 illustrates the transient dynamics of the closed-loop MEMS.

Fig. 3. System dynamics with proportional–integral control law.


5.3. Relay controller

We synthesize the relay controller with dead zone. Using the method documentedin section 4.3, one obtains

u ¼ sgnð�0:001ua � 0:0001ia � 0:00085xr � 0:0002hr þ 1:5eÞjDead zone� 0:035:

The MEMS transients are documented in Fig. 5. For rðtÞ ¼ 2, the settling time is0.12 s and the overshoot for yðtÞ is 6% for the rated MEMS parameters (the tem-perature is 20 �C). Using the MEMS parameters which correspond to the worst-case

Fig. 4. System dynamics with tracking integral control law.


performance (the temperature is 140 �C), the overshoot for yðtÞ is 13%, and thesettling time is 0.15 s.

5.4. Sliding mode controller with soft switching

Using the variable structure design concept, the synthesis of a sliding modecontroller is performed. The nonlinear switching surface is designed as

k1ua þ k2ia þ k3xr þ k4hr þ k5eþ k6e13 ¼ 0:

Fig. 5. System dynamics with relay-type control law.


Using the Lyapunov stability theory, the feedback gains are found [6,9,10], and acontrol law with soft switching is

u ¼ tanh13ð�0:001ua � 0:01ia � 0:17xr � 0:0002hr þ 23eþ 600e

13Þ:

Fig. 6 illustrates the dynamics of the closed-loop system with the sliding controller.The settling time is 0.1 s with no overshoot. For the worst-case performance (the

Fig. 6. Dynamics with sliding mode control law.


temperature is 140 �C), the settling time and overshoot for yðtÞ are 0.14 s and 11%.As a final analysis, the disturbance attenuation capabilities are studied. Let the initialdisplacement is 1 m, and

TL ¼0 Nm; 8t 2 ½0 0:08Þ s0:75 Nm; 8t 2 ½0:08 0:12Þ s�0:75 Nm; 8t 2 ½0:12 0:16� s

8<:

Fig. 7. Dynamics with sliding mode control law: analysis of disturbance attenuation.


Fig. 7 depicts the MEMS responses, and the disturbance attenuation features areevident analyzing the output dynamics for yðtÞ.

6. Analysis, identification, and design of a MEMS drive

We consider the MEMS drive actuated by a Hitachi minimotor 004A191E (24 V,0.5 A, 1000 rad/s) with ICs controller–driver MC33030 [7]. Experimental results wereperformed. Using the identification algorithm reported in section 3, the parameterswere identified using the MATLAB files given in [10]. The validity of the identifi-cation results was verified measuring the available parameters (e.g., armature re-sistance, inductance, viscous friction and moment of inertia). We have the followingparameters ra ¼ 33 X, La ¼ 0:0013 H, ka ¼ 0:0176 V s/rad (Nm/A), J ¼ 9 10�7

kgm2 and Bm ¼ 3:7 10�7 Nm s/rad.Using the tracking angular velocity error eðtÞ ¼ xreferenceðtÞ � xrðtÞ, the nonlinear

proportional–integral control law was synthesized. We have

u ¼ satþ1�1 12eþ 4:8e3 þ 27

Zedt þ 0:9

Ze3 dt

�:

Experimental validation for different operating conditions and scenarios werestudied to analyze the dynamic performance of the closed-loop MEMS. The ex-perimental results are documented in Fig. 8, and the scale for the angular velocity is100 rad/s per division. The reference angular velocity was assigned to be 615 rad/sand 125 rad/s. For the step speed command, the settling time is 0.055 s. The MEMSdynamics was studied for the sinusoidal command, and the experimental results forthe xrefðtÞ ¼ 125þ 110 sin t are documented in Fig. 8. The analysis of the experi-mental results indicates that the tracking error converges to zero. From the exper-imental data it follows that the desired performance has been achieved, and theangular velocity precisely follows the reference speed assigned.

Fig. 8. Transient dynamics of the MEMS drive for the step and sinusoidal reference speed.


7. Conclusions

In this paper, we addressed and solved the problems of nonlinear analysis anddesign of high-performance MEMS. The mathematical model was found, and theunknown parameters of differential and difference equations were identified applyingthe reported identification procedure. Different nonlinear control algorithms weredesigned minimizing quadratic and nonquadratic performance functionals as well asusing PID design method. To design sliding mode (variable structure) controllers, wesynthesized the switching surface to guarantee the desired evolution of states andtracking error. The results illustrate that in order to guarantee good performance,stability, robustness, zero steady-state tracking error, and disturbance attenuation,advanced control algorithms should be used. In particular, it was illustrated thatsliding mode soft switching algorithms provide superior performance and thechattering effect is eliminated. Furthermore, superior robustness and expandedstability margins result. The transient dynamics and three-dimensional state evolu-tions were documented for different control laws. The results were compared anddiscussed for MEMS in servo and drive applications. It was illustrated that con-tinuous and discontinuous control algorithms designed guarantee robustness toparameter variations and stability in the full operating envelopes. Experimental re-sults were reported to support the methods documented, software developed, andhardware built.

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