Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3276-3281 3276 www.etasr.com Kebbab et al.: Frequency Speed Control of Rotary Travelling Wave Ultrasonic Motor using … Frequency Speed Control of Rotary Travelling Wave Ultrasonic Motor Using Fuzzy Controller Fatima Zohra Kebbab Department of Electrical Engineering Laboratory DAC HR Ferhat Abbas University Setif I, Algeria fatimazohra.kebbab@univ-setif.dz Dalel Jabri Department of Electrical Engineering Laboratory DAC HR Ferhat Abbas University Setif I, Algeria dalel.jabri@yahoo.fr Djamel Eddine Chouaib Belkhiat Department of Physics Laboratory DAC HR Ferhat Abbas University Setif I, Algeria djamel.belkhiat@univ-setif.dz Saâd Belkhiat Department of Electrical Engineering Laboratory DAC HR Ferhat Abbas University Setif I, Algeria belsa_set@yahoo.fr Abstract—This paper proposes frequency speed control of rotary travelling wave ultrasonic motor (TWUSM), type Daimler Benz AWM90-X motor. The control characteristics of TWUSM are complicated, highly nonlinear and varying in time. This can lead to deterioration of the performance of conventional controller such as proportional integral (PI). In order to achieve high control performance of the TWUSM, fuzzy logic controller (FLC) has been designed and compared to the conventional PI controller. To validate the performance of the proposed FLC, simulation of the speed response has been performed and analyzed for a varying load. The simulation results show that the FLC has smaller settling time, smaller rising time and minimum error in steady state. Furthermore, the fuzzy controller provides good results for large load variations. The frequency output of the controller has been validated with experimental measurements of AWM90-X. Keywords-nonlinear control; fuzzy logic controller; travelling wave ultrasonic motor type Daimler–Benz; AWM90-X I. INTRODUCTION TWUSMs have structural and operational advantages compared to conventional electromagnetic motors, such as compact size, lighter weight, very low speed operation, high torque, nonmagnetic operation, freedom of constructional design, very low inertia, high speed response, possibility of electromagnetic noise reduction and miniaturization [1]. Moreover, the settling time in ultrasonic motors is very short, fast response is one of the most important TWUSM advantages, which makes it suitable for applications with fast response demands such as robot actuators and auto-focus cameras. Several types of ultrasonic motors have been suggested and designed in the last 25 years [2]. Their operating principle is based on piezoelectric vibrations that convert electric energy to mechanical energy in the form of elastic vibrations [3]. It consists of two basic parts: the stator with piezoelectric ceramics, and the driven part (rotor). Apart from the advantages of TWUSM, deriving mathematical model for TWUSMs is a difficult task due to their complicated and highly nonlinear characteristics. In addition, the dynamic speed characteristics of TWUSM are time-varying due to the increase in temperature and depend on operating conditions such as driving frequency, source voltage and load torque [4, 5]. The speed control of TWUSMs is one of the important issues under consideration [5-7]. Three kinds of speed control strategies exist in the literature. The TWUSM speed can be controlled by the driving frequency, the phase difference or the voltage amplitude of the two excitation sinusoidal voltage of TWUSM. However, aimed at these problems, several researchers have opted for the driving frequency of the sinusoidal voltage as control variable [6–8]. There is no perfect control scheme for TWUSMs. The ultrasonic motor speed controllers belong to several conventional and numeric controller types. A speed tracking control system using both neuro-fuzzy control and direct pulse width modulation for TWUSM has been developed in [8]. In the same way, authors in [9] used also a fuzzy neural network controller. Authors in [4, 10, 11] studied a servo speed control system for traveling- wave ultrasonic motor [4] and a servo position control for TWUSM [10] where fuzzy neural network was the control tool [11]. Authors in [12] proposed a position control scheme for TWUSMs. Authors in [13] used H∞ strategy to control rotary travelling wave ultrasonic motor TWUSM while authors in [14] proposed an intelligent PID speed controller of TWUSM. In a nutshell, most of developed works for ultrasonic motors control focused on a motor of USR60 type. However, the speed control for Daimler–Benz AWM90-X motor has rarely been explored so far, which motivated us to make this study as a continuation of our previous works [15-17]. The main contribution of this work consists to the design of a fuzzy logic controller to drive the speed of the Daimler–Benz AWM90-X motor. The robustness of the proposed controller against load var com FL per has AW A. spe and ord ass      B. 1. ma cer C. ult sta sup sta not pre illu exc Engineerin www.etasr riation is ve mparative stu LC and those rformed in thi s been valid WM90-X. Basic Assump The structur ecial. They in d the whole der to simpl sumptions mus The rotor is a The friction neglecting th The surface neglecting th Coulomb fri between stato The friction system indep Model Struct The model o The model o ain modules: ramic, stator-r Fig. 1. Func Model of the Stator is the trasonic motor ator generates perposition of ator ensures a te that the sta esented as a ustrated in F citation system Fig. 2. Equations (1 ng, Technology r.com erified in th udy, between obtained by is paper. Fina dated with II. 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Equ d tangential sp  onance frequen ween the stator ator ( x) is not a new coordin moving accord eed and directi express (6) an chanism betwe ve can be seen act zone length e the same tan k kx x  ), causes the c 3277 sonic Motor usi 1SF (1) 2SF (2) igidity of the s zoelectric cera two modes, odal forces. waves creates  (3)  is the wave le he stator surfa x   (4) (5) complex part o uations (6) an peed. (6) (7) ncy. The mod r and the rotor t effective. It ate system mo ding to the in on of the trave nd (7) as: (8) (9) een stator and n in [16]. In su h, xl and xr ar ngential speed (10) interpenetratin creation of no ing … stator, amics, UP1, s the ength ace is of the nd (7) deling r with turns oving nertial elling rotor uch a re the with ) ng of ormal con sta exp wh fric for wh of wh E. hav Eq mo vel equ cro for F. TW inc fre in com err con Engineerin www.etasr ntact pressure ator and rotor i ˆ cosw w  Line force d pressed by (12   Nf x C w here NC is the ctional force c rce is describe s k k x x F n    k k x norm x F n    here μ is the d wave crests. T mT R F   here mR is the Modeling of Rotor of tra ve two degre quations (16) otion of the rot rotorJ T   rotor R rom w d where J is t locity of the uivalent mass tor is the equiv rce. 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The 9) con are Fig. log the [19 univ and in F cho and repr The adju outp the defu the The Z, neg and spe Vol. 8, No. 4, 20 ed Control of R KP and KT a ntroller and TS given in the T 3. Speed–fre Fig. 4. Gain V IV. SPEED Fuzzy logic ic enables the system in a 9]. The design verse of disco d rules. A fuzz Figure 5. To oose different d trapezoidal s resent designe e performanc usting membe put is convert process ca fuzzification m centroid meth e linguistic va PM, PB}, w gative medium d PB means p eed is presented Fig. 5. 4.65 0 5 10 15 20 25 30 35 40 45 R o to r sp ee d [ tr /m in ]] 018, 3276-3281 Rotary Travellin are proportion S denotes the Table I. equency character Speed control TABLE I. coefficient Values CONTROL USIN controller is e designer to d linguistic man n steps are: ourse, 2) defin zy logic contro define fuzzy shapes based shapes are ver er’s ideas and ce of the co ership function ted into real v alled defuzzi methods are av hod that requ ariables in this where NB me m, Z means ze ositive big. T d in Figure 7. . Structure of 4.7 4.75 4. Fre 1 ng Wave Ultras nal and integr sampling peri ristics of USM for l system using PI PI CONTROLLER V KP 0.02 NG FUZZY LOG a rule-based describe the g nner by formi 1) defining i ning fuzzy mem ol block diagra y membership d on experien ry used becaus d require less ontroller can n and rules. Ot value output i ification. Eve vailable, the mo uires less comp s study are def eans negative ero, PM mean he control str f fuzzy logic con 8 4.85 4.9 equency [HZ] 3278 sonic Motor usi ral gains in th iod. PI gain v r different load to controller. VALUES. KT 100 GIC CONTROLLE controller. F general behavi ing IF-THEN inputs, output mbership func am [21] can be p function, we nce. The trian se they are ea computation be improved therwise, the f i.e. crisp outpu en though m ost preferred o putation time fined as {NB, e big, NM m ns positive me ategy of the m ntroller. 4.95 5 x 10 4 T= 0Nm T= 2Nm T=1.5Nm ing … he PI values orques. ER Fuzzy ior of rules t and ctions e seen e can ngular asy to time. d by fuzzy ut by many one is [22]. NM, means edium motor con set and res eff mo are shi mo Re equ A. are con res Fro and TW tha val tes Engineerin www.etasr Fig. 6. Fig. 7. Sp V. S Speed respo nsidered TWU ttling time, ste d compared t sults of speed fectiveness of otor condition e: 570V is exc ift between th otor [17] used esults have be ual to 45.5rpm No Loaded M The speed re e presented in ntrollers). Fro sponse of both om Table III, d settling time WUSM withou at it has been r lidate the rob sted for differe F 0 0 5 10 15 20 25 30 35 40 45 50 R o to r sp ee d [ rp m ] ng, Technology r.com Membership fun eed Control of TW SIMULATION R onse for load USM. The p eady state error to those obtain response are p f the proposed ns. The param citation voltag he two excitati d for the simu een obtained m. Motor Conditio esponse chara Figure 8 for t om the simulat h PI and FLC we can see t e than the PI c ut controllers reduced for the bustness of the ent loads at t  Fig. 8. Rotor 0.5 1 1.5 y & Applied Sci K nctions obtaine WUSM using log RESULTS AND D ded motor is performance p r, overshoot ar ned by PI con presented in o d FLC for n meters of the p ge’s amplitude ions. The para ulation are pre by keeping t ons acteristics of m the two contro tion results, an controllers is that the FLC h controller. The is equal to 3 e case of the c e proposed FL 2.5ms . speed without l 2 2.5 3 3.5 Time [s] Fuz Re PI ience Research Kebbab et al.: F d from fuzzy gic fuzzy controlle DISCUSSION s analyzed fo parameters su re obtained fo ntroller. Simu order to valida no load and l piezoelectric e and π/2 rad ameter values esented in Tab the reference motor without ollers (Fuzzy a nalysis of the s given in Tab has better rise e settling time .5ms [23], we controlled mot LC, the moto load 5 4 4.5 x 10 -3 zzy ference speed h V Frequency Spee er or the uch as r FLC ulation ate the loaded motor is the of the ble II. speed t load and PI speed ble III. e time of the e note or. To or was D C B. part trac resu Co C. pro sim that abil var Vol. 8, No. 4, 20 ed Control of R TA Resistances o Ceramics ca Capacity of Rotor Ine Radiu Effective Mass of r Rotor rig Rotor atten Friction coe Distance between points of s Number of wa Frequency of r Wavelen Wave num Contact zone Antiresonance Modal mass o Transfer Stator rig Disturbance Damping r TABLE III. ontroller Ris PI Fuzzy The First Loa From the resp t 3.3 3.8ms m ck the referen umed in the Ta TABLE IV. ontroller Rise PI Fuzzy The Second L At this stage oposed FLC ag mulation result t the PI contro lity and only iation. 018, 3276-3281 Rotary Travellin ABLE II. SIM of entries apacity f stator ertia us mass rotor gidity nuation efficient n the surface stator ave crests resonance ngth mbers e rigidity frequency of stator ratio A A gidity e factor ratios COMPARISON P e time (ms) P 1.000 0.73 ad, 1.5Nm. ponse plots sh ms , the propo nce speed. Th able IV. COMPARISON PARAMET e time (ms) Pe 1.000 0.73 Load,1.6Nm. e of study, w gainst a load ts are illustrat oller lose its p the FLC H∞ 1 ng Wave Ultras MULATION PARAM Rp1=R Cp1= Cp2=7 Cps1=0 Cps2=0 JR=3.3436 Rw=4 Meff=113 mR=(meff+22 CR=30 dR=50 μ= α=4 n= 1 2 2res res   2   k= CN=850 1 2 2 ant ant    0m    21 1 1antA mCp    22 2 2antA mCp  1S resC   2S resC   ε1=ε2 ds1=ds2= OF CONTROL SYS PARAMETERS Peak time (ms) 4.5 0.893 hown in Figur osed FLC driv he controller’s N OF CONTROL SYS TERS (LOADED MO eak Time (ms) 4.5 0.893 we check the condition equ ed in Figure performance in can be resisti 3279 sonic Motor usi METERS [17] Rp2=5Ω =7.8e-9F 7.87e-9F 0.42e-9F 0.428.e-9F 67e-0.004kgm2 0.5e-3m 3.93·10-3Kg 2.8+3)·1e-3Kg 00e3N/m 0e3Ns/m =0.21 .5e-3m =11 32 43.365 e Hz  w R m n  =2π/λ 00e6N/m2 3 2 43.425 e Hz  .082Kg     1/22 2 1res KgFs       1/22 2 2res KgFs   21s m N m 22es m N m 2=0.02 =10Ns/m STEMS PERFORMA Settling time ( 2.500 1.200 re 9(a), in zoo ve the TWUS s performance STEMS PERFORMA OTOR) Settling time ( 2.700 1.100 robustness o ual to 1.6Nm. 9(b). We can n terms of trac ing this param ing … 1/2 1/2 ANCE (ms) omed M to es are ANCE (ms) of the . The n note cking metric Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3276-3281 3280 www.etasr.com Kebbab et al.: Frequency Speed Control of Rotary Travelling Wave Ultrasonic Motor using … D. The Third Load 3.3Nm The motor has been loaded with a big load larger than the torque that can be supported by the PI controller. From the results given in the Figure 9(c), we note that the FLC can drive, similar to the previous cases, the TWUSM to track the reference speed. In the range 2.5 3t ms ms  , the motor speed decreases under the load effect and then it increases to reach the reference speed. Noting that for a large load, greater than 3.3Nm, the TWUSM under FLC diverges. This phenomenon, called pull out phenomenon, has been signaled in the literature [24]. It is due especially to the variation of the resonance frequency. Finally, FLC is more robust than the PI controller and it presents low error. Therefore, it is well suited to this actuator type which can be employed for varying loads. Fig. 9. Rotor speed, loaded motor a) 1.5Nm, b) 1.6Nm, c) 3.3Nm VI. SIMULATION RESULTS AND EXPERIMENTAL DATA VALIDATION To ensure the good operation of the TWUSM, the motor should be driven with the antiresonance frequency to reach the maximum of its efficiency [25]. To determine the antiresonance frequency of the TWUSM AWM90-X, the stator parameters were calculated with finite elemet method (FEM), obtained from the recorded admittance curve of the stator. The admittance curve of the free-vibrating stator was recorded with the impedance analyzer with a step size of 10Hz. Figure 10 shows the resulting measured curve. From Figure 10, the antiresonance frequency is equal to 43.425kHz [25]. Fig. 10. Recorded admittance curve of AWM90-X stator Regarding the proposed TWUSM model, we can note that it was validated in our previous work [17] without control speed. In fact, the simulation frequency of the proposed model was equal to 43.425kHz which is the same with the one obtained in experimental validation [25]. Moreover, to validate the proposed controller, the frequency output of the FLC is illustrated in Figure 11. Hence, the simulation frequency has been found equal to 44.6kHz, which is closer to the experimental antiresonance frequency (43.425kHz). This result validates the efficiency of the FLC. Fig. 11. Frequency output of the FLC VII. CONCLUSION In this paper, the frequency speed control of the TWUSM, type Daimler Benz AWM90-X, has been studied. The design of FLC and PI controllers has been presented and discussed. To illustrate the efficiency of the proposed controllers to drive the TWUSM to track perfectly the reference speed, thorough simulations were performed. The obtained results have revealed that the FLC controller performs better than the PI controller with very good tracking performance, namely low rise time, low settling time and high steady state accuracy. Likewise, the FLC controller seems more robust that the PI controller against load variations. Finally, the frequency output of the FLC has been validated with experimental measurements of the TWUSM AWM90-X. REFERENCES [1] D. Zhang, S. Wang, J. Xiu, “Piezoelectric parametric effects on wave vibration and contact mechanics of traveling wave ultrasonic motor”, Ultrasonics, Vol. 81, pp. 11-126 ,2017 [2] Y. Wang, W. Huang, “A piezoelectric motor with two projections using two orthogonal flexural vibration modes”, Sensors and Actuators A: Physical, Vol. 250, pp. 170-176, 2016 [3] F. R. M. Romlay, W. A. W. Yusoff, K. A. M. Piah, “Increasing the efficiency of traveling wave ultrasonic motor by modifying the stator geometry”, Ultrasonics, Vol. 64, pp. 177-185, 2016 [4] G. Bal, E. 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She is an assistant professor in the Electrical Engineering Department, Ferhat Abbas University, Setif 1, Algeria. She works on the traveling wave motor. Djamel Eddine Chouaib Belkhiat was born in Algeria. He is an associate professor in the Department of Physics at the Ferhat Abbas University, Setif 1, Algeria, where he is also a member of DAC HR Laboratory. He earned his Bachelor of Engineering degree in Electrical Engineering at Ferhat Abbas University, Setif 1, Algeria, Master's degree in Automatic Control from the University of Poitiers, France, and PhD degree in Automatic Control from the University of Reims Champagne Ardenne, France, in 2007, 2008, and 2011, respectively. His research interests lie in the area of monitoring and diagnosis of dynamic systems. He has published several research papers in scientific journals, international conferences, and book chapters. Dalel Jabri was born in Tunisia. She is an associate professor in the Electrical Engineering Department at the Ferhat Abbas University, Setif 1, Algeria, where she is also a member of DAC HR Laboratory. She earned her Bachelor of Engineering degree in Electrical Engineering in 2006, her Master's degree in Automatic Control in 2007 at National Engineering School of Gabes, Tunisia, and her PhD degree in Automatic Control at the University of Reims Champagne Ardenne, France and the University of Gabes at 2011. Her research interests lie in the area of robust control of nonlinear systems. She has published several research papers in scientific journals, international conferences, and book chapters. Saad Belkhiat was born in Algeria. He received an Electronic Engineering degree from Polytechnic School of Algiers, Algeria, in 1979. He has worked as an engineer in the control and automatic departments in the production industry and as an engineering professor in the Department of Electronics, Setif, Algeria. He received an MPh degree from the Electronics Department, and PhD degree in Physics, from University of Setif in 2001. He is full- professor in the Electrical Engineering Department at the Ferhat Abbas University, Setif 1, Algeria. His research interests include electrical engineering materials and their applications such as piezoelectric materials, dielectric and surface science.