Journal of ELECTRICAL ENGINEERING, VOL. 63, NO. 4, 2012, 224–232

ACTIVE FAULT TOLERANT CONTROL FORULTRASONIC PIEZOELECTRIC MOTOR

Moussa Boukhnifer∗

Ultrasonic piezoelectric motor technology is an important system component in integrated mechatronics devices workingon extreme operating conditions. Due to these constraints, robustness and performance of the control interfaces should betaken into account in the motor design. In this paper, we apply a new architecture for a fault tolerant control using Youla

parameterization for an ultrasonic piezoelectric motor. The distinguished feature of proposed controller architecture is that itshows structurally how the controller design for performance and robustness may be done separately which has the potentialto overcome the conflict between performance and robustness in the traditional feedback framework. A fault tolerant controlarchitecture includes two parts: one part for performance and the other part for robustness. The controller design works

in such a way that the feedback control system will be solely controlled by the proportional plus double-integral PI2performance controller for a nominal model without disturbances and H∞ robustification controller will only be activatedin the presence of the uncertainties or an external disturbances. The simulation results demonstrate the effectiveness of theproposed fault tolerant control architecture.

K e y w o r d s: fault tolerant control, robust control, ultrasonic motor

Nomenclature

Symbol DescriptionSi,j , Dn,Σ Strain, Electrical displacement, Entropy

Ti,j , En, θ Stress, Electrical field, Temperature

sθ,Ei,j,k,l Elastic compliance

ϵT,θn,m, dθn,i,j Electrical permittivity and piezoelectric

constantpTm, αE

i,j Pyroelectric and thermal expansionconstant

ρCT,E

θ Thermal constant

(α, β), (d, q) Stator’s and rotor’s reference frames

v, w,Ψ(v, w) Voltage phasor, Rotating traveling wave,Phase

θc, k, R(kθc) Angular position, Contact points, Rota-tional matrix

VNid, VTid Ideal normal and transversal velocity

Vd, Vq Voltage in the (d,q) rotor’s reference frame

FN , FT Normal and tangential force

N,T, f0 Real rotor speed, Torque, Friction coefficient

frα, frβ Feedback forces in the (α, β)’s referenceframe

A,m, Force factor, Modal mass

ds, c Stator’s damping term and stiffness

1 INTRODUCTION

Nowadays, the market for mechatronics systems insuch high tech sectors as aeronautics, aerospace, automo-tive or defense is booming. In these expanding industrialsectors, mechatronics systems are put to test in extreme

operating conditions such as thermal cycling or large ther-mal variations, radiations, corrosion [2], demanding vibra-tory environments, intense pressures or ultra high vacuumconditions [3], sharp accelerations and severe shocks. As aresult the robustness of these embedded mechatronic sys-tems prove to be of paramount importance with respectto their harsh operating environment.

In this context, the ultrasonic motor technology suitsmechatronics perfectly due to its powerful performanceto compare with its electrical servomotor counterparts.Indeed, its main characteristics are compactness, hightorque at low speed without gears, high holding torquewithout power, low power consumption and fast response.Thus, the ultrasonic motor (USM) has found its place inthe industrial sectors. In particular, the traveling waveultrasonic servomotor (TWUM) has been tested recentlyby the NASA to operate in cryogenic temperature [4]as well as in ultra high vacuum conditions [3]. Moreoverfor aeronautics, in the current “fly-by-wire” technology,ultrasonic motor control strategies have been developedto implement active control sticks that allow pilots to feelthe force feedback from the rudders [5, 6].

Numerous TWUM control strategies have alreadybeen implemented in the literature. The speed controlstrategy [7] with one of the TWUM natural variables (fre-quency, voltage or phase difference) is the most classicalone. However, it is very sensitive to the temperature vari-ations and performances of the motor are not optimized.Another strategy consists in controlling the wave am-plitude using the integrated piezoelectric sensor. Thoughthis control is more thermally stable, it is still sensitive totorque variations. Finally, a TWUM model leading to thestationary waves control has also been developed [6, 8, 9].

∗ Laboratoire Commande et Systemes, ESTACA, 34 rue Victor Hugo, F-92300 Levallois-Perret, France, moussa.boukhnifer@estaca.fr

DOI: 10.2478/v10187-012-0032-8, ISSN 1335-3632 c⃝ 2012 FEI STU

Journal of ELECTRICAL ENGINEERING 63, NO. 4, 2012 225

With STATCOM (VAR control mode)

(a)

Va Vd

W

Vq

V

Vb

b

w

d

q

a

Y

VNid

Va

Vb

Wb

FT

Electromechanical

conversion b)

VTid

fra

a,b

d,q

N

T

a,b

d,q

W,Qc

G(T,E,Q)

FNfrb

Stator/rotor contact

transmission

TIFt

PiezoceramicWa

Fig. 1. Causal TWUM model in the stator (α, β) reference frame

In [10], the authors have used the model of [5] and usedH∞ robust control for the wave and torque loop. In theliterature cited thus far, fault tolerance was not consid-ered. However, the faults Sensors affect the systems per-formance in the closed-loop system when the data sensoris used to define the input. However, even if there is ascheme to detect the fault, due to the nature and con-fined space of mechatronics, it might not be feasible tointervene and rectify the problem safely in a timely way.Face to the external mechanical disturbances occurringduring mechatronics operations a high degree of robust-ness with good performances with a good fault tolerantcontrol (FTC) is required [1]. It should be mentioned asfar as we know, several works have been reported for faulttolerant control of mechatronic systems, ie induction mo-tors [11], hydraulic [12], vehicle [13] driving systems butfew works report fault tolerant control of ultrasonic mo-tor. This paper proposes to combine both fault tolerantcontrol and robust control areas to control a piezoelectricultrasonic motor.

This paper presents a general architecture for fault tol-erant control using Youla parametrization for a piezoelec-tric ultrasonic motor (USM). The distinguished feature ofthe proposed controller architecture is that it shows struc-turally how the controller design for performance and ro-bustness may be done separately which has the potentialto overcome the conflict between performance and robust-ness in the traditional feedback framework. When a sen-

sor fails or degrades, the controller switches and uses theobserver’s output instead of the original system’s output.The controller architecture includes two parts: the firstone for performance and the second one for robustness.The controller architecture works in such a way that thefeedback control system will be solely controlled by theproportional plus double-integral PI2 performance con-troller for a nominal model and the H∞ robust controllerwill only be activated in the presence of the uncertaintiesor external disturbances.

This paper can be summarized as follows. An ultra-sonic motor model is presented briefly in Section 2. InSection 3, we recall the standard Youla parametrizationbefore introducing the proposed FTC control architec-ture in Section 4. Then, Section 5 presents the simula-tion results without and with the proposed robust FTCcontroller when subjected to external perturbations andfaulty sensor operation.

2 ULTRASONIC MOTOR MODELING

2.1 General Layout

With the objective to implement a robust fault tol-erant control strategy for the travelling wave ultrasonicmotor, the motor model considered must be neither toosimplistic so as to take an accurate account of its nonlin-ear characteristics, nor overly realistic and consequentlyhard to implement on a Digital Signal Processor [14] or ona Field Programmable Gate Array [15]. Usually, the ul-trasonic motor speed control is implemented and achievedusing the equivalent electromechanical model. However,the usual equivalent electrical model though generallysufficient to model the steady-state operation does notaccurately model the transient operation. Furthermore,that speed control strategy is very sensitive to thermaland torque variations. Hence, an original causal TWUMmodel which meets this study objectives was developedrecently [5]. Indeed, this original model enables to set uptorque control law with a relatively low complexity [5].The causal TWUM model is described next.

2.2 Causal TWUM model in the stator’s refer-ence frame

The operation principle of a travelling wave ultrasonicmotor is quite similar to that of an induction motor. In-deed, its principle is perfectly similar to the inductionmotor where the fluctuating magnetic field produced inthe air-gap by the two-phase stator supply spawns rotortorque through induction. Consequently, the same math-ematical formalism was applied to express the TWUMmodel through space vectors [10], firstly in the stator’s(α, β) reference frame, then in the rotating (d ,q ) frame(as shown in Fig. 1(b)). In a first stage, the two-phaseelectrical supply, providing respectively the sinusoidalvoltages vα and vβ , feeds the two alternate piezoelectricsectors. It results into two purely sinusoidal stationary

226 M. Boukhnifer: ACTIVE FAULT TOLERANT CONTROL FOR ULTRASONIC PIEZOELECTRIC MOTOR

waves, respectively wα and wβ , expressed within the sta-tor’s (α, β) reference frame. The combination of those vi-brating stationary waves propagates consequently alongthe stator, a rotating travelling wave w forming in the(α, β) frame an angle Ψ from the voltages phasor v (Cf.Figure 1(a)). It is interesting to point out that the TWUMstructure provides k permanent contact points with therotor, corresponding to the kth excited mode.

Finally, the angular position θc and the wave crest ware deduced in the (α, β) frame as follows

tan(kθc) =wβ

wα, (1)

w =√

w2α + w2

β . (2)

In a second stage, The propagation of the acoustictraveling wave in the stator body makes the individualparticles of the stator move in an elliptical fashion. Con-sequently, the rotor placed on the top of the vibratingstator would be rotated in a direction retrograde to thedirection of the traveling wave. That’s to say, that the kcontacts are considered punctuals with no slidings and noenergy storing. This assumption at this point enhances,by means of the rotational matrix R(kθc) in order to ex-press within the (d, q) rotating frame the ideal transver-sal velocity VTid along the quadratic axis q and the idealnormal velocity VNid along the direct axis d . Unfortu-nately, due to the elastic layer required to improve thecontact transmission, the k contacts are not ideal. Ac-tually, the area at the stator/rotor is distributed and asliding effect occurs, which is essential to provide torquesimilar to that in induction motor. Numerous previousworks have explored modeling of this highly nonlinearcontact transmission, resulting in sophisticated modelswith excellent accuracy. However, in order to implementa straightforward model, despite the fact that the frictioncoefficient f0 varies due to the nonlinear contact trans-mission, the relation between the real rotor speed N andthe torque T is approximated and considered in the over-all model as linear

T = f0(1

bVTid

−N) |T | < Tmax . (3)

In addition to the friction phenomenon, the TWUM re-quires to produce the torque T and consequently to drivethe load, a normal force FN to maintain contact conditionat the rotor/stator interface as well as a tangential forceFT . The application of those mechanical stresses resultsin some feedback forces on the stator. Those feedbackforces, respectively frα and frβ , are then rotated fromthe rotating (d ,q ) frame to the stator’s (α ,β ) frame us-ing the previously used rotational matrix R(kθc). At thispoint, it is important to notice that those feedback forceshave a direct influence on the TWUM. Indeed, those ex-ternal mechanical stresses provoke on the stator side, thepiezoelectric ceramic energy to evolve and as a result theresonance pulsation ωr to drift; which is expressed in thecausal TWUM model by kθc variations.

2.3 Model equations in the rotating (d, q) refer-ence frame

The causal TWUM model expressed in the stator(α ,β ) reference frame enable to implement a straightfor-ward control by means of simplistic mechanical contacts.Nevertheless, it appears that the variable from the nor-mal α axis and the tangential β axis are coupled, whichis shown through the rotational matrix R(kθc). Thus, soas to remedy to this coupling, the control is then givenin the rotating reference frame. The feeding voltages vαand vβ are then deduced from Vd and Vq by means ofthe rotational matrix R(kθc) and the ultrasonic motorequations are deduced for small pulsation variations [5]

mVNid+dsVNid+(c−(kθc)2)

∫VNiddt = NVd−FN , (4)

2mVTid + dsVTid = NVq − FT (5)

In view of those equations it is interesting to notice that,due to reference frame change, the variables are not cou-pled. Finally, those model’s equations allow to determinethe TWUM behaviour in the steady-state and in thetransient-state. This straightforward model will be usedin the next section in order to implement the FTC robustcontrol.

Figure 2 shows the simulation results of the TWUMbehavior with a load torque TL = 0.5 Nm at 50 msec.

3 FTC CONTROLLER ARCHITECTURE

In this section, Youla parametrization is used in adifferent way and the use the FTC architecture in orderto ensure both performance and robustness outcomes isexplained.

Firstly, we consider the feedback diagram presentedin Fig. 3, in which the reference signal r enters intothe system from a different location. Nevertheless, theinternal stability of the system is not changed since thetransfer function from y to u is not changed. Thus, thiscontroller implementation also stabilizes internally thefeedback system with plant P0 for any Q ∈ H∞ such

that det(V (∞)−Q(∞)N(∞)) = 0.

Due to the similarity with the well-known IMC (In-ternal Model Control), we shall call proposed controllerframework as generalized internal model control (GIMC)[16].

The distinguished feature of this controller implemen-tation is that the inner loop feedback signal f is alwayszero, ie f = 0, if the plant model is perfect, ie if G = G0 .The inner loop is only active when there is a model un-certainty or other sources of uncertainties such as distur-bances and sensor noises [17]. Thus, Q can be designedto robustify the feedback system. It follows that the newcontroller design architecture has a clear separation be-tween performance and robustness [18].

Journal of ELECTRICAL ENGINEERING 63, NO. 4, 2012 227

W (m) ´10-6

0

1.0

0.5

T (Nm)

-1

1

0

Speed (turn/min)

0

100

50

Time (s)0.002 0.004 0.008 0.0100.006

Fig. 2. Simulation results of the causal TWUM modelI0(A)

rV -1~

G

Q G0

U~

e

q

u

fsignalynominal

-

-

yreal

Fig. 3. GIMC structureI0(A)

W

K)

G(s)

Y

U

Z

Fig. 4. H∞ robust control

4 CONTROLLER DESIGN

A high performance robust system can be designed intwo steps:

1) Design K0 = V −1U to satisfy the system performancespecifications with a nominal plant model P0

2) Design Q to satisfy the system robustness require-ments. Note that the controller Q will not affect thenominal performance of the system.

It should be emphasized that K0 is not just any stabi-lizing controller as in most of controller parameterizationsused in the literature, it is designed to satisfy certain per-formance specifications. For example, K0 may be a sim-ple proportional plus double-integral PI2 controller

K0 =Kp(s+ a)

s2

that satisfies our design specifications, in which case we

can take U = 1 and V = K0 =Kp(s+a)

s2 . The output error

f defined in Fig. 3 is the residual signal. In the fault diag-nosis literature, f is used to detect the possible faults inactuator and/or sensors. f = 0 signifies nominal systemwithout any failure. If f = 1 a robust controller is imple-mented using the standard feedback structure shown inFig. 4. The fault-tolerant controllers can be designed suchthat they provide adequate performance when there areno faults in the systems and as much tolerance as possibleusing a robust controller in the presence of the faults.

Such controllers can be designed in two steps:

1) Design K0 = V −1U to satisfy the performance for anominal system.

2) Design Q to tolerate possible actuators and/or sen-sors failures (and model uncertainties). This Q can befound using standard robust control technique, fuzzycontrol, sliding mode control, etc. In our case, we usethe robust H∞ technique.

5 ROBUSTIFICATION

In this section, the design of controller K for a highdegree of system robustness is considered.

Consider the system described by the block diagramof the Fig.figure6, where G is the generalized plant andK is the controller. Only finite-dimensional linear timeinvariant (LTI) systems and controllers will be consid-ered in this paper. The generalized plant G containswhat is usually called the plant in a control problem in-cluding all the weighting functions. The signal w con-tains all external inputs, including disturbances, sensornoise, and commands; the output z is an error signal;y is the measured variables; u is the control input.The diagram is also referred to as a linear fractionaltransformation (LFT) on K , and P is called the co-efficient matrix for the LFT. The resulting closed-looptransfer function from w to z is denoted by Tzw . Theproblem of H∞ control is to synthesize a controller Kwhich stabilises the system G and minimize the normH∞ of Tzw [19].

G =

A B1 B2

C1 0 D12

C2 D21 0

(6)

The following assumptions are made:

1) (A,B1) is stabilizable and (C1, A) is detectable.

2) (A,B2) is stabilizable and (C2, A) is detectable.

3) D′12[C1 D12] = [0 I] .

4) [B1 D21]TD′

21 = [0 I]T .

The problem of H∞ control is to synthesize a controllerK which stabilises the system G and minimizes the H∞norm of ∥Tzw∥∞ .

Recall that the H∞ controller is

K∞ =

[A∞ | −Z∞L∞F∞ 0

], (7)

228 M. Boukhnifer: ACTIVE FAULT TOLERANT CONTROL FOR ULTRASONIC PIEZOELECTRIC MOTOR

I0(A)

FTC

controller

Fit

Tref PI

controller

Stator

transfert

function

Stator/rotor

transfert

function

Wref

Wave amplitude control

W T

Disturbances

+

- +-

gQQ

Disturbances

Torque control

Fig. 5. Cascaded controllers with inner-loop control (PI controller of the wave amplitude control of the stator) and FTC controller forthe torque control loop

I0(A)

C(s)

Vqreg

Wref^

Y

Vsin N+

- +

-

Kb

b2

1

2m.s + ds

Controllere

W^

TI

Fig. 6. Block diagram Hw(s) of the wave amplitude control of thestator

I0(A)

CT(s)

Wref

^

TrefF0

+

- +

-W^

TL

HW(s) khw/b2

1/Js

W id

W

T

-

+

Fig. 7. Outer torque control loop

A = A+ γ−2B1B′1X∞ +B2F∞C2 ,

F∞ = −B′2X∞, L = −Y∞C2, Z∞ = (I−γ−2Y∞X∞)−1 .

where X∞ = Ric(H∞) and Y∞ = Ric(J∞). The nec-essary and sufficient conditions for the existence of anadmissible controller such that of ∥Tzw∥∞ < γ are asfollows [20]:

1) H∞ ∈ dom(Ric) and X∞ = Ric(H∞) ≥ 0.

2) J∞ ∈ dom(Ric) and X∞ = Ric(H∞) ≥ 0.

3) ρ(X∞Y∞) < γ2 .

where Ric stands for the standard solution of Ricattiequation.

The Hamiltonian matrices are defined as

H∞ =

[A γ−2B1B

⊤1 −B2B

⊤2

−C⊤1 C1 −A⊤

]J∞ =

[A⊤ γ−2C1C

⊤1 − C⊤

2 C2

−B1BT1 −A

]

6 WAVE AMPLITUDE ANDTORQUE CONTROLLER

In this section, we present two cascaded controller ar-chitectures composed of both inner-loop and outer-loopcontrollers (Fig. 5). The inner loop controller regulates

in Hw(s) the vibrational travelling wave amplitude Wprovided by the stator with a simple PI controller. Theouter-loop controller consists of the torque feedback con-trol of the motor shaft when subjected to variational loadswith a simple FTC controller. In this study the distur-bance of the outer loop is taken into account and the dis-turbance of the inner loop is neglected. Particularly, onlyan FTC controller for the torque control loop is proposed.

6.1 Wave Amplitude Control

The first block of the control scheme of the Fig. 6regulates the wave amplitude. The transfer functions inthe open-loop of the wave amplitude is given by [5]

W =1

w.

NVq − k hb2Ti

(2m+ (k hb2 )

2J).s+ ds. (8)

For the synthesis of the wave amplitude controllerC(s), PI controller for C(s) is chosen. Therefore, welet

C(s) = Kw1 + τws

τws. (9)

In order to limit the effect of the resonance, the timeconstant of the PI controller is adjusted on its crest, soτw = 1/(2π ∗ F0) with F0 is the crest frequency. Thepass-band of the open loop transfer function, which istuned by Kw , is then adjusted so as to have a phasemargin ∆Φ = 45 . For a pass-band of 3000 Hz, we selectKw = 8× 10−3 .

6.2 Torque Control

Piezoelectric actuators are often used to achieve posi-tion or active vibration control; in addition, they are welladapted for these applications. As for torque, or more

Journal of ELECTRICAL ENGINEERING 63, NO. 4, 2012 229I0(A)

z1

P

D

Q

d1

d2z2

y r

f q

Fig. 8. The standard setup for design of Q for systems with

additive faults

generally force control, it is an important goal for hapticapplications. For the actuators, this implies that controlschemes are able to reproduce the force or the torque re-sponses of virtual objects. Piezoactuators are also wellsuited to these tasks, given their generally low speed andcapacity for producing significant force.

The block of the control scheme of the Fig. 7 regu-lates the torque. One of the drawbacks of this control isthe acquisition of the actuator torque. Generally, for thetorque sensor we use the strain gauge force. The transferfunctions in the open loop of the torque is given by [5]

T = Hw(s)kh

b2wf0

J.sf0

1 + J.sf0

Wref . (10)

The synthesis of the FTC torque controller TL(s) isobtained according to the implementation in Fig. 3, we

use the proportional plus double-integral PI2 controller

for the ideal model and the H∞ controller in the presence

of the fault. For the ideal model, the loop controller is

chosen so as to minimize static error. Thus, a corrector

with a double integration is chosen, Tc(p) = Kc((1 +

τcp)/τcp2), Kc, τc are computed in order to ensure a good

margin of stability. The H∞ controller Q can be designed

using the standard robust techniques as shown in Fig. 8,

where ∆ includes the additive fault.

The fault tolerant control problem depends strongly

on the type of faults that can appear in the system. In

this paper, the faults are described as additive faults. In

connection with FTC, this might not be very useful. The

reason is that the additive faults can be considered as

external input signals to the system. which will not cause

any changes in the system dynamics. Specifically, they are

not able to change the stability of the closed-loop system

but the performance of the system will be affected.

The synthesis of the H∞ torque controller Q(s) is

obtained according to the implementation in Fig. 8 and

by using the command hinfsyn of MATLAB µ-Analysis

and Synthesis Toolbox, the H∞ design of controller Q(s)

and weights may be carried out with reference to equation

z =

[W1(r − y)

W2u

], w =

rd1d2

y =

[r +W3d1y +W4d2

], u = us

(11)

I0(A)

Time(s)

W (mm)

0.10

0.00

0.20

1086420

0

-0.4

0.4

0.8T (Nm)

TrefT

Fig. 9. Response of the USM motor without a fault sensor withPI2 controller

I0(A)

Time(s)

W (mm)

0.10

0.00

0.20

1086420

0

-0.4

0.4

0.8T (Nm)

Tref T

Fig. 10. Response of the USM motor without a fault sensor withH∞ controller

230 M. Boukhnifer: ACTIVE FAULT TOLERANT CONTROL FOR ULTRASONIC PIEZOELECTRIC MOTOR

I0(A)

No of points

T (Nm)1000-100

0

6´104

4´104

2´104

Fig. 11. Faulty sensor with histogram

7 SIMULATION RESULTS

In this part, an architecture for fault tolerant con-troller has been proposed, based on the GIMC structureshown in the block diagram in Fig. 3. There is a num-ber of reasons for using the architecture from the Youlaparametrization in connection with FTC. In this architec-ture, the Q parameter represents the FTC characteristicof the controller. This means that the FTC part of thefeedback controller is a modification of the existing con-troller. Thus, a controller change when a fault appearsin the system is not a complete shift to another con-troller, but only a modification of the existing controller

by adding a correction signal in the nominal controller,the r signal in Fig. 3.

In short, for the torque control loop, we use the pro-portional plus double-integral PI2 controller for the idealmodel and the H∞ controller in the presence of the fault.The simulation results given in Fig. 9 show the idealtorque and wave responses with a good performances ofthe proposed system using PI2 controller.

For the H∞ controller design, the specifications aretaken to ensure the torque should track the referencetorque. The control U should not exceed a pre-specifiedsaturation limit and rejects the fault. It ensures∥f(G,Q)∥∞ < γ for all ∥∆∥∞ < 1. The controller syn-thesis is based on the equation (11) where the weightingmatrices are chosen as follows [21]:

w1 = α110s+10000s2+10s+0.1 , w2 = α2

ss+1000 , w3 = α3

s0.1s+1 ,

w4 = α4 .

The weighting matrices for the design are used to scalethese closed loop transfer functions to specify the fre-quency information on the tracking performances and ondisturbance rejection. The weighting function W1 of theerror is chosen in such a way to make the norm from r toW1(r − y) small leading to the choice of a transfer func-tion of the form W1 . The choice of weighting functionW2 is based on limiting the saturation with the controlU . Finally the choices of weighting functions W3 and W4

are made in order to have a loop gain large at low fre-quencies to achieve good performance and small at highfrequencies to guard against unmodeled actuator dynam-ics saturation and noise.

I0(A)

Tref

T (Nm)

-1.0

1.0

0.0

Time (s)1086420

T

W (mm)

Time (s)1086420

-0.8

0.4

0.0

-0.4

Fig. 12. Response of the USM motor with a fault sensor

0.0

-0.4

0.4

0.8

-0.8

T (Nm)

T

TrefPI controller

H infinity controller

0.10

0.00

0.20

Time(s)

W (mm)

1086420

Fig. 13. Response of the USM motor using FTC controller at 5 Sec

Journal of ELECTRICAL ENGINEERING 63, NO. 4, 2012 231

Time(s)

W (mm)

0.10

0

0.20

1086420

0.0

-0.4

0.4

0.8

-0.8

T (Nm)

TTref

PI controller H infinity controller

Fig. 14. Response of the USM motor using FTC controller

at 5.1 Sec

As an illustration of the controller, the Fig. 10 showsthe response of our system using H∞ controller with anacceptable performance.

7.1 Simulation Results

For FTC architecture, the system has been simulatedwith a sinusoidal reference and a sensor fault appearsat t = 5 sec , the noisy sensing signals provided by thestrain gauge force sensors is given as a normally Gaus-sian distributed random signal with 0.2 mean value anda variance at 250 as shown in Fig. 11. The results ofthe simulations are shown in Fig. 12, the proportionalplus double-integral PI2 can not ensure good responsein presence of the fault sensor.

A sinusoidal response of the system with fault inducedby a noisy sensing torque signal applied on a USM motor(random disturbance) is shown in Fig. 12. It can be seendirectly from this figure that the faulty closed-loop sys-tem is unstable. For stabilizing the faulty servo system aQ controller needs to be included. As calculated above,the robust controller Q can be applied for stabilizing thefaulty closed-loop system. In this example, the Q con-troller is implemented with a switching system which isactivated by the residues signal f . If the system modelwith its parameters are not well identified, which is cor-rect in real case, so the inner feedback f will be alreadydifferent to zero, In order to resolve this identificationproblem, we can impose the following condition to f .

f = 1 if T (P )− T (P0) > Tn/10 , (12)

f = 0 if T (P )− T (P0 < Tn/10 . (13)

T (P ), T (P0) are respectively the torque of the real andnominal system. Tn is the nominal torque given by themanufacturer.

Based on the design of Q (see Fig. 8), the sinusoidalresponse of the USM motor is shown in Figs. 13 and14 where it should be noticed that the standard robustcontroller is independent of the nominal PI2 controller.In the worst case, our controller implementation will beequivalent to the existing robust control design. Similarresults of robustness and fault-tolerance will be obtainedin the presence of the faults produced by temperature,mechanical stress and noisy sensing signals during mecha-tronics tasks (see Fig. 5).

Of course, if there is no uncertainty, proposed con-troller will perform as well as a nominal controller does.In fact, our framework provides a great flexibility in con-troller design, for example, one could still use all the ro-bust and H∞ design techniques here. All one has to dois to start with a good performance controller and thenfollow the standard robust control design procedure tofind the robust controller Q . The only difference is thatone may not be interested in using Q into the controllerparametrization to find the total controller, rather onemay implement the performance controller and the ro-bust controller Q separately.

8 CONCLUSION

In this paper, an architecture for fault tolerant controlhas been used for driving in closed-loop a piezoelectrictravelling-wave ultrasonic motor. By applying the GIMCstructure, an additional controller parameter has been in-troduced as the main tool to achieve fault tolerance. Afeature of the GIMC structure is that it automaticallyincludes a diagnostic signal. The presented simulation re-sults show that the GIMC provides adequate performancewhen there are no faults in the system and provides tol-erance by using a H∞ robust controller. In the future,the authors shall introduce this architecture fault tol-erant control with the speed control and shall integratethe controller architecture into the ultrasonic motor for afault-tolerant on-board mechatronics system.

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Received 29 September 2011

Moussa Boukhnifer is an associate professor at Labora-

toire Commande et Systemes, ESTACA of Paris (France). He

received the MSc degree in electrical engineering from INSA of

Lyon, France, in 2002. In December 2005, he received the doc-

torate degree in Control and Engineering from the University

of Orleans, France. In 2007, he was a Researcher at INRETS

of Paris. His main research interests are focused on the de-

sign, modeling and fault tolerant control with its applications

to power electronics and electrical drives.