Intrinsic properties of ultrasonic motor (high torque for low speed, high static torque, compact in size, etc.) offer great advantages for industrial applications. However, when load torque is applied, dead-zone occurs in control input. Therefore, sliding mode controller, which is a nonlinear controller, is adopted for ultrasonic motor. The state quantities, such as acceleration, speed, and position are needed to apply the sliding mode controller for position control. However, rotary encoder causes quantization errors in the speed information. This paper presents a robust position control method for ultrasonic motor by using Variable Structure System(VSS) observer. The state variables for sliding mode controller are estimated by the VSS observer. Besides, a small, low cost, and good response sliding mode controller is designed in this paper by using a micro computer that is essential in embedded system for the developments of industrial equipments. The effectiveness of the proposed method is verified by experimental results

Darba, Araz

Odomari, Shogo

Senjyu, Tomonobu

Uchida, Kosuke

Yona, Atsushi

English

Ghent University Academic Bibliography

Robust Position Control of UltrasonicMotor using VSS ObserverShogo Odomari1, Araz Darba1, Kosuke Uchida1, Tomonobu Senjyu1, Atsushi Yona11Department of Electrical and Electronics Engineering, University of the Ryukyus, JapanE-mail: b985542@tec.u-ryukyu.ac.jpAbstract—Intrinsic properties of ultrasonic motor(high torque for low speed, high static torque, compactin size, etc.) offer great advantages for industrial ap-plications. However, when load torque is applied, dead-zone occurs in control input. Therefore, sliding modecontroller, which is a nonlinear controller, is adoptedfor ultrasonic motor. The state quantities, such as ac-celeration, speed, and position are needed to apply thesliding mode controller for position control. However,rotary encoder causes quantization errors in the speed in-formation. This paper presents a robust position controlmethod for ultrasonic motor by using Variable StructureSystem(VSS) observer. The state variables for slidingmode controller are estimated by the VSS observer.Besides, a small, low cost, and good response slidingmode controller is designed in this paper by using a microcomputer that is essential in embedded system for thedevelopments of industrial equipments. The effectivenessof the proposed method is verified by experimentalresults.I. INTRODUCTIONIn recent years, ultrasonic motor(USM) is gainingattention as it has good characteristics and is small insize. The drive source of ultrasonic motor is ultrasonicvibration of piezoelectric element. USM is expected tobe applied to robot actuator, high precision positioningand medical equipments[1]. The operating principle ofan USM has complicated speeds characteristics com-pared to conventional electromagnetic motor whichmakes it a special kind of motor.However, an USM has dead-zone in its controlinput with applied load torque[3]. Since H∞ controlleris a linear controller[2], it cannot control the USMwith unknown dead-zone. Therefore, sliding modecontroller[4]-[6], which is a nonlinear controller, isused for robust position control of USM with unknowndead-zone. To apply sliding mode controller for posi-tion control of USM, state variables such as accel-eration, speed and position of the USM are needed.Speed information detected by a rotary encoder havequantization errors, especially in low speed region.Therefore, to estimate actual rotor speed accuratelyby a using VSS observer[7] is proposed with thepossibility of decreasing quantization error.Essential industrial equipments are developed insmall size, lightweight and power-saving technology,by using embedded system. Use of micro computer inembedded system, has advantages(such as it can dis-cretize all processing, can design stable and small sizeUSMD1D2L1S1S2L2S3S4D4C2C1 3DERELoadMOS   FETdriver− Microfφ computerVVabPersonalcomputerryyeyeFig. 1 Drive system of USM.-100-50 0 50 100 150Control input V AV B,[V]Time [msec] 0  5  10  15 20Va VbFig. 2 Output voltages of two-phase inverter.circuit in comparison to analog circuit, can constructcontrol system at low cost, can upgrade response, andcan make the system easily design easy and change).This paper presents a digital implementation[8]-[9]of a sliding mode controller and a VSS observer byusing a micro computer for efficient position control ofthe USM with unknown dead-zone. The state variablesare estimated by the VSS observer and are used insliding mode controller. The proposed sliding modecontroller is found satisfactory.II. SYSTEM CONFIGURATIONA. Driving system of USMAll configuration of the USM control system usedin this study is shown in Fig. 1. The USM used inthe experiment is a traveling wave USM(SHINSEICORPORATION : USR-60). Output voltages of thetwo-phase inverter are shown in Fig. 2. A travelingwave is formed on the stator surface when impressTable 1. Design specifications of USM.Drive frequency 40 kHzDrive voltage 100 VrmsRated current 53 mA/phaseRated torque 0.314 NmRated output power 3 WRated speed 9.0 rad/sMass 0.240 kg-1 0 1 2 3 4 5 6PWM Voltage[V]Time [μsec] 0  5  10  15 20S1 S2Fig. 3 PWM signal.Fig. 4 Equivalent circuit of USM.this voltage to stator, a rotor moves, and USM turnsto the opposite direction of the traveling wave.Specification of the USM is shown in Table 1. Elec-tromagnetic brake of the load and the rotary encoderare connected by a coupling. Electromagnetic brake isused to apply the load torque when applied voltage.The rotary encoder is used for detecting the producedpulse in proportion to angle of the rotation of themotor shaft. Micro controller detects the rotor positionfor pulse number by rotary encoder(10,000 pulse/rev.).Reference position r and measured position ye of theUSM are recorded. There are two control methodsof USM[10]: driving frequency control and appliedvoltage phase difference control. In position controlof the USM, applied voltage phase difference controlhas higher efficiency than driving frequency control.In this study, we use applied voltage phase differencecontrol, and the driving frequency f is constant at 41kHz.B. Driving circuit configurationPower MOS-FET are used an switching device. TheUSM is a large capacitive load by looked from theinverter side. For improved efficiency to decrease ca-pacitive load, intercalate inductances are set in series.In PWM signal to generate micro computer inputto inverter circuit, short to switch on both arm of topsand bottoms, brake switching devices by over current,we should input PWM signal with off time of botharm(dead time). Generated PWM signals with deadtime are shown in Fig. 3. In Fig. 3, to generate deadtime in input signal to switching device S1 and S2can check. The inverter produces rectangular wave+-z u USMSMCrxVSS Observerr y Rotary Encoder yey.Fig. 5 System configuration.forms with these PWM signals. However, we canget sinusoidal voltage by making resonance with theequivalent circuit of the USM of Fig. 2 as shown inFig. 4.III. CONTROL ALGORITHMSystem configuration in this study is shown in Fig.5. This section is designed sliding mode controller andVSS observer.A. Sliding mode controller designIn this paper, we assume that the USM is a linearsystem. USM state equation of second order is givenas follows.x˙(t) = Ax(t) + Bu(t), (1)where,A =⎡⎣ 0 1 00 0 10 − ω2n − 2ζωn⎤⎦ , B =⎡⎣ 00Kfω2n⎤⎦.(2)Kf is the variable in changeable by the drive fre-quency.Sliding mode controller applied to the servo system,is shown in Eq. (3). To configure, servo system stateequation is shown in Eq. (4).z(t) =∫ t0(r(t) − y(t))dt, (3)⎡⎢⎢⎣z˙x˙1x˙2x˙3⎤⎥⎥⎦ =⎡⎢⎢⎣0 − 1 0 00 0 1 00 0 0 10 0 − ω2n − 2ζωn⎤⎥⎥⎦⎡⎢⎢⎣zx1x2x3⎤⎥⎥⎦+⎡⎢⎢⎣000ω2n⎤⎥⎥⎦u +⎡⎢⎢⎣1000⎤⎥⎥⎦ r (4)where r is the reference position, y is the rotorposition. This equation is rewritten asx˙z = Azxz + Bzu + Ezr. (5)where, switching function is defined asσ = Sxz. (6)where, S is a constant of switching hyperplane vari-able. Switching function on sliding mode isσ = 0. (7)By σ˙ = Sx˙z , σ˙ is 0 when sliding mode is0 = SAzxz + SBzueq + SEzr. (8)and it obtains the following equivalent input.ueq = −(SBz)−1(SAzxz + SEzr). (9)Control input u is configured as linear control termul and nonlinear control term unl, if ul = ueq• •unl = −k sgn(σ), control input u is presented bythe following equation.u = ul + unl= −(SBz)−1(SAzxz + SEzr)− k sgn(σ). (10)where, k is a constant.Next, Lyapunov function is selected as followingequation.Vc = σT (SBz)−1σ2. (11)Differentiating the equation, we haveV˙c = σT (SBz)−1σ˙= σT (SBz)−1[SAzxz + SBzu + SEzr]= σT {(SBz)−1[SAzxz + SEzr] + u}, (12)andV˙c = −σTk sgn(σ) = −k σ2‖σ‖ . (13)Therefore if k > 0 and Lyapunov function is negative,can stable sliding mode controller.B. Design of VSS observerThis section discusses the design of the VSS ob-server. The continuous time system presented asx˙(t) = Ax(t) + Bh(t) + Bu(t),y(t) = Cx(t). (14)where, h is a nonlinear term or uncertainty parameter.Since (C,A) is observable, constant matrix L exists,and configuring to complex plane half, left side of thefollowing equation, Ao can stable eigenvalue,Ao = A− LC. (15)Therefore, there isPA0 + AT0 P = −Q, (16)satisfying P > 0 for Ao and positive matrix Q > 0,and F can be defined asFC = BTP. (17)State estimate error e is defined bye(t) = xˆ(t)− x(t). (18)and F estimate error α is defined byα = F{yˆ(t)− y(t)}. (19)Main Routine Timer InterruptSTARTENDStep 3Step 4Step 6Step 5Step 2Step 1STARTStep 7Initializingmicro computerDisplayingopening messageWaitingtimer interruptt < 10sYes NoDecidingcontrol inputEstimatingstate valuesDisplayingmeasured valueFig. 6 Control algorithm.where, xˆ(t) and yˆ(t) are the estimated value of x(t)and y(t). Using these, the design of the VSS observercan as follows.˙ˆx(t) = A0xˆ + Ly + Bu + Bδ,δ(t) ={ − α‖α‖ρ for α = 0,0 for α = 0.(20)where, ρ is a constant. The following error equationcan be obtained by differentiating Eq. (18).e˙ = ˙ˆx− x˙= A0xˆ + Ly + Bu + Bδ − Ax−Bh−Bu= A0e + Bδ −Bh={A0e−B α‖α‖ρ−Bh for α = 0,A0e−Bh for α = 0. (21)It selects to Lyapunov function as following equa-tion.Vo =12eTPe. (22)By differentiating Vo with respect to t, we haveV˙o =12e˙TPe +12eTP e˙, (23)where, by substituting Eq. (19), FC = BTP ,eTCT FT = αT , and |αT h| ≤ ‖α‖ρ,α = 0V˙o(t) = 12eT (PA0 + AT0 P )e−eTPB α‖α‖ρ− eTPBh= −eTQe− eTCTFT α‖α‖ρ− eTCTFT h= −eTQe− ‖α‖ρ− αT h≤ −eTQe− ‖α‖ρ + ‖α‖ρ = −eTQe, (24)α = 0V˙o(t) = 12eT (PA0 + AT0 P )e− eTPBh= −eTQe− αTh≤ −eTQe, (25)which obtains e(t) → 0(t →∞) for V˙o.Fig. 7 Configuration of USM.Fig. 8 Micro computer and drive circuit.IV. EXPERIMENTAL RESULTS AND DISCUSSIONA. Micro computer algorithmMicro computer used in this research is SH7125of SH/Tiny series. It uses development environmenttool HEW(High-performance Embedded Workshop)of Renesas Technology Corp, and is written in C.Features of SH7125 are PWM mode, timer interrupt,and phase number count mode of MTU2. Using thesefeatures, we implemented sliding mode controller forthe USM.The control algorithm is shown in Fig. 6, and thesteps are given as following.STEP1 Initialize micro computer.STEP2 Display opening message.STEP3 Wait for timer interrupt.STEP4 Determine the setting time.STEP5 Decide the control input.STEP6 Estimate the state values.STEP7 Display the measured value.B. Experimental resultsUSM experimental set up is show in Fig. 7, and themicro computer and the drive circuit are shown in Fig.8. Here, control cycle is 1 ms, data sampling time is20 ms, reference position of USM is sinusoidal wave,reference position frequency is 0.2 Hz, drive frequencyf is 41 kHz, initial position is y = 0.0 rad and they areimplemented digitally. Control parameters are shownin Table. 2.Experimental results by using the proposed slidingmode controller are shown in Figs. 9, and 10. Figs.9(a), and 10(a), provide good control both for no loadand applied load. Figs. 9(d), and 10(d), provide goodTable 2. Control parameters.S [−1.1× 104 8.8×103 147.7 3.2]Kf 3.3k 0.1F 1ρ 0.1L [0.3 1.4×10−9 −7.1× 10−5]Tζ 0.2ωn 2200.8position estimation. Figs. 9(f), and 10(f) provide thatestimated speed is reduced in quantization error.Therefore, it can be said from the discussion ofthe experimental result that the proposed sliding modecontroller has robustness, provide effective to controlthe USM with unknown dead-zone.V. CONCLUSIONSThe USM has an excellent performance and manyother useful features. However, dead-zone occurs incontrol input with applied torque. In this paper, weproposed robust position control of the USM usingthe VSS observer. The VSS observer is nonlinearobserver, achieved to reduce quantization error and toprovide good position estimation. The sliding modecontroller is nonlinear controller, achieved to robustposition control for USM. Then, the dead-zone effectis reduced by the sliding mode controller using theVSS observer. Experimental results demonstrated goodtracking performance and robustness of the proposedcontrol and estimate scheme.REFERENCES[1] T. Kenjyo, and T. Sashida, “An Introduction of Ultrasonic Motor”,Oxford Science Publications, 1993.[2] Tomohiro Yoshida, Tomonobu Senjyu, Mitsuru Nakamura, Atsushi Yona,Naomitsu Urasaki, and Hideomi Sekine, “Position Control of UltrasonicMotors using Two-control Inputs H∞ Controller”, Electric Power Com-ponents and Systems, vol. 35, pp. 741-755, 2007.[3] Tomonobu Senjyu, Mitsuru Nakamura, Naomitsu Urasaki, HideomiSekine, and Toshihisa Funabashi, “Mathematical Model of UltrasonicMotors for Speed Control”, Electric Power Components and Systems,vol. 36. pp. 637-648, 2008.[4] Bin Wang, Xinghou Yu, and Guanrong Chen, “ZOH discretization effecton single-input sliding mode control systems with matched uncertain-ties”, Automatica, vol. 45, pp. 118-125, Jun. 2009.[5] Yi-feng Chen, and Tsutomu Mita, “Adaptive Sliding Mode Control”, T.IEE Japan, vol. 113-C, pp. 203-210, 1993.[6] Brice Beltran, Tarek Ahmed-Ali, and Mohamed EI Hachemi Benbouzid,“Sliding Mode Power Control of Variable-Speed Wind Energy Conver-sion Systems”, IEEE Trans. Energy Conversion, vol. 23, pp. 551-558,2008.[7] Yi-feng Chen, and Tsutomu Mita, “Sliding Mode Control with AdaptiveVSS Observer”, T. IEE Japan, vol. 111-C, pp. 514-522, 1991.[8] Liping Guo, John Y. Hung, and R. M. Nelms, “Digital Implementation ofSliding Mode Fuzzy Controllers for Boost Converters”, Applied PowerElectronics Conference and Exposition(APEC’06), pp. 1424-1429, 2006.[9] Pasquale Corsonello, Stefania Perri, Paolo Zicari, and Giuseppe Co-corullo, “Microprocessor-based FPGA implementation of SPIHT imagecompression subsystems”, Microprocessors and Microsystems , vol. 29,pp. 299-305, 2005.[10] Tomonobu Senjyu, Satoru Yokoda, and Katsumi Uezato, “A Study onHigh-Efficiency Drive of Ultrasonic Motors”, Electric Power Compo-nents and Systems, vol. 29, pp. 179-189, 2001.-1 0 1 0  1  2  3  4  5  6  7  8  9  10Time[s]Rotor Position θ[rad]yer(a) Reference position and measured position.-0.2-0.1 0 0.1 0.2 0  1  2  3  4  5  6  7  8  9  10Time[s]Position error e  [rad]θ(b) Position error.-90-45 0 45 90 0  1  2  3  4  5  6  7  8  9  10Time[s]Control input φ[deg](c) Control input.-1 0 1 0  1  2  3  4  5  6  7  8  9  10Time[s]yeyEstimate position θ[rad](d) Measured position and estimate position.-0.2-0.1 0 0.1 0.2 0  1  2  3  4  5  6  7  8  9  10Time[s]Estimate error e  [rad]θ(e) Estimate position error.-1 0 1 0  1  2  3  4  5  6  7  8  9  10Time[s]Estimate speed ω[rad/s]ωe ω(f) Measured speed and estimate speed.Fig. 9 Experimental result with sliding modecontroller(τL=0.0Nm).-1 0 1 0  1  2  3  4  5  6  7  8  9  10Time[s]Rotor Position θ[rad]yer(a) Reference position and measured position.-0.2-0.1 0 0.1 0.2 0  1  2  3  4  5  6  7  8  9  10Time[s]Position error e  [rad]θ(b) Position error.-90-45 0 45 90 0  1  2  3  4  5  6  7  8  9  10Time[s]Control input φ[deg](c) Control input.-1 0 1 0  1  2  3  4  5  6  7  8  9  10Time[s]yeyEstimate position θ[rad](d) Measured position and estimate position.-0.2-0.1 0 0.1 0.2 0  1  2  3  4  5  6  7  8  9  10Time[s]Estimate error e  [rad]θ(e) Estimate position error.-1 0 1 0  1  2  3  4  5  6  7  8  9  10Time[s]Estimate speed ω[rad/s]ωe ω(f) Measured speed and estimate speed.Fig. 10 Experimental result with sliding modecontroller(τL=0.2Nm).

Robust position control of ultrasonic motor using VSS observer

https://biblio.ugent.be/publication/2974081/file/2974090

Robust position control of ultrasonic motor using VSS observer

Abstract

Similar works

Full text

Available Versions

Ghent University Academic Bibliography