Position Control of Shape Memory Alloy Actuators Using Self Tuning Fuzzy PID Controller

Transcription

1 756 Internationa Journa Kyoung of Contro, Kwan Automation, Ahn and Bao and Kha Systems, Nguyen vo. 4, no. 6, pp , December 2006 Position Contro of Shape Memory Aoy Actuators Using Sef Tuning Fuzzy PID Controer Kyoung Kwan Ahn and Bao Kha Nguyen Abstract: Shape Memory Aoy (SMA) actuators, which have the abiity to return to a predetermined shape when heated, have many potentia appications such as aeronautics, surgica toos, robotics and so on. Athough the conventiona PID controer can be used with sow response systems, there has been imited success in precise motion contro of SMA actuators, since the systems are disturbed by unknown factors beside their inherent noninear hysteresis and changes in the surrounding environment of the systems. This paper presents a new deveopment of a SMA position contro system by using a sef-tuning fuzzy PID controer. This contro agorithm is used by tuning the parameters of the PID controer thereby integrating fuzzy inference and producing a fuzzy adaptive PID controer, which can then be used to improve the contro performance of noninear systems. The experimenta resuts of position contro of SMA actuators using conventiona and sef-tuning fuzzy PID controers are both incuded in this paper. Keywords: Fuzzy, PID, rea time, sef-tuning, SMA actuators. 1. INTRODUCTION SMA is smart materia that exhibits shape memory. This occurs through a soid-state phase change by moecuar rearrangement. The two phases that occur in SMA are martensite and austenite. At higher temperatures, the materia is in the austenite phase. As the temperature is owered, the materia changes to the martensite phase and grows unti sufficienty ow temperatures. This unusua characteristic of SMA actuators has a wide variety of appications in contro systems beside conventiona types such as eectric, hydrauic, and pneumatic actuators. Athough the number of appications is increasing [1-4], there has been imited success in precise motion contro since the contro systems are disturbed by unknown factors in addition to the noninear hysteresis effect and changes in the surrounding environment of the systems. These causes ead to inaccuracy and reduce the performance of the contro systems. In order to reach better contro performance for the Manuscript received March 6, 2006; revised Juy 8, 2006; accepted Juy 21, Recommended by Editoria Board member Seung-Bok Choi under the direction of Editor Jin Young Choi. This study was supported by BK21. Kyoung Kwan Ahn is with the Schoo of Mechanica and Automative Engineering, University of Usan, San 29 Muger 2 dong, Namgu, Usan , Korea (e-mai: kkahn@usan. ac.kr). Bao Kha Nguyen is with the Automatic Contro Department, Facuty of Eectrica and Eectronic Engineering, Hochiminh City University of Technoogy, 268 Ly Thuong Kiet, Street, District 10, Hochiminh City, Vietnam (e-mai: nbkha@ hcmut.edu.vn). SMA actuator systems, some contro methods have been proposed to compensate for noninear hysteresis behaviour. Compensation of hysteresis effect for SMA, piezoceramics [5] and eectro magnetics actuators [6] have been addressed in some reports. Most of these works require a precise system mode. This makes the controer synthesis compicated and time consuming. Usuay the Preisach mode of hysteresis based on phenomenoogica nature [7-9] is deveoped. The Preisach mode is aso inverted and then incorporated in an open oop contro system to achieve the desired output [5]. Athough the Preisach mode has found widespread acceptance in managing the major features of the hysteresis phenomena, there have been some restrictions on the accuracy and computation time for impementation of this mode. These restrictions are caused by the imitation of switching points in the Preisach pane, the inaccuracy of data measurement and time consuming data coection from first order transition curves. The hysteresis mode is interpreted in terms of phase shift, and a inear controer is used for hysteresis compensation in this approach [10,11]. The advantage of this method is its simpicity. However, it requires estimation of the frequency range of the system s operation. This paper presents a new deveopment of a SMA position contro system by using a sef-tuning fuzzy PID controer. Fuzzy contro provides a convenient method for constructing noninear controers via the use of heuristic information. The sef-tuning fuzzy PID controer, i.e., the combination of a conventiona PID and fuzzy controer, has been an effective too

2 Position Contro of Shape Memory Aoy Actuators Using Sef Tuning Fuzzy PID Controer 757 for the sef tuning contro of many noninear systems [12-15]. Therefore, it is suitabe for appication in SMA systems with unknown eements and the hysteresis noninearity effect. This contro agorithm tunes the parameters of the PID controer by integrating fuzzy inference and producing a fuzzy adaptive PID controer. This work can be used to improve the accuracy of the dispacement and therefore compensate for the noninearity hysteresis of SMA actuators. Rea time contro using the proposed contro agorithm, and the effect of the contro performance with respect to the input current changes are investigated in the SMA actuator system. The remainder of the paper is organized as foows: The design of sef tuning fuzzy PID controer for SMA actuators is presented in Section 2. The comparison of experimenta resuts of SMA position contro between conventiona PID and the proposed sef tuning fuzzy PID is described in Section 3. Concuding rermarks are provided in Section SELF TUNING FUZZY PID CONTROLLER DESIGN 2.1. Structure of sef tuning fuzzy PID controer The PID controer is widey used in industry due to its simpe contro structure and easy design. However, there are certain probems that are encountered in practica contro systems. The parameters of the conventiona PID controer are not often propery tuned for the noninear pant with unpredictabe parameter variations. For this reason, it is necessary to automaticay tune the PID parameters. On the other hand, fuzzy contro provides a forma methodoogy for representing, manipuating, and impementing a human s heuristic knowedge about how to contro a system. This is aso a convenient method for constructing noninear controers by using heuristic information obtained from experience. Therefore, the advantages of fuzzy and PID controers can be incorporated into a controer in order to achieve high contro performance. The structure of the sef tuning fuzzy PID controer is shown in Fig. 1. The controer has the form of PID structure, but the PID parameters are tuned by fuzzy inference, which provides a noninear mapping from the error signa et ()(the difference between reference signa and system output), and derivation of error de( t ), to the PID parameters Kp, K i, and K d. These parameters are changed within the initia parameter boundaries Appication of sef tuning fuzzy PID controer to the position contro of SMA actuator systems This section presents the impementation of the seftuning fuzzy PID controer for the position contro of Fig. 1. Structure of sef tuning PID controer. Fig. 2. Structure of the fuzzy inference bock. SMA actuators. The structure of the fuzzy inference bock in Fig. 1 is shown in Fig Normaization Suppose that the variabe ranges of K p, K i, and K d are Kpmin, K pmax, Kimin, K imax and Kdmin, K dmax, respectivey. In the position contro probem of SMA actuators, the range of each PID parameter was experimentay determined as foows: Kp [0.1, 10], Ki [0.1, 0.5], Kd [ ]. In order to obtain feasibe rue bases with high inference efficiency, the PID parameters must be normaized over the interva [0, 1] as foows: Kp Kpmin Kp 0.1 K p = =, Kpmax Kpmin Ki Kimin Ki 0.1 Ki = =, Kimax Kimin Kd Kdmin Kd 0.01 Kd = =. K K dmax dmin Therefore: Kp = 9.9K p + 0.1; Ki = 0.4K i + 0.1; K d = 0.09K d (1) (2) (3) Fuzzification In this paper, the inguistic eves assigned to the input variabes e(t) and de(t) are as foows: NB: negative big; NM: negative medium; NS: negative sma; ZO: zero; PS: positive sma; PM: positive medium; PB: positive big. The membership functions of these fuzzy sets are shown in Figs. 3 and 4. The maximum error and the maximum derivation of error ranges are chosen from

3 758 Kyoung Kwan Ahn and Bao Kha Nguyen Fig. 3. Membership functions for error e(t). Fig. 7. Fuzzy contro rue of K p. Fig. 4. Membership functions for derivation of error de(t). Fig. 5. Membership functions for p K and K. d Fig. 8. Fuzzy contro rue of K d. Fig. 6. Membership functions for K i. the specification of SMA actuators. S, MS, M, B are assigned as the fuzzy sets of K p, Kd and K i which are the output variabes, and the membership functions of the fuzzy set are shown in Figs. 5 and 6, respectivey. Fig. 9. Fuzzy contro rue of K i Fuzzy rue and fuzzy inference Using the above fuzzy sets of the input and output variabes, fuzzy rues are composed as foows: Rue i: If et ( ) is A 1 and de( t ) is A 2 then K p is B, K d is C and K i is D, = 1,2,..., m, where m is the number of fuzzy rues, A i is the input fuzzy set in Ui R. The fuzzy sets B, C, D are the output sets is O R, P R, Q R, respectivey, and x = [ x1, x2] = [ e( t), de( t)] U, i T K p O, Kd P, K Q are the input and output inguistic variabes of the fuzzy system, respectivey. For simpicity, ony triange functions are used as the membership functions, denoted by µ, of these fuzzy sets. Generay, the fuzzy rues are dependent on the pant to be controed and the type of the controer. These rues are determined from intuition or practica

4 Position Contro of Shape Memory Aoy Actuators Using Sef Tuning Fuzzy PID Controer 759 experience. In this paper, rues are designed based on the characteristics of SMA actuators, such as sow response or noninear hysteresis effect, and the properties of the PID controer. The rue sets are estabished and shown in surfaces in Figs. 7, 8, and 9. In this paper, the MAX MIN fuzzy reasoning method is used to obtain output from the inference rue and the present input. For given a specific input fuzzy set A in U, the output fuzzy set B in O for K p is computed through the inference engine as foows: m B p = A = 1 A x U 1 µ ( K ) max[sup min( µ ( x), µ ( e( t)), µ ( de( t)), µ ( K ))]. A2 B The output membership functions for are computed simiary. p K d and (4) Defuzzification The centroid defuzzification method is used to convert the aggregated fuzzy set to a crisp output * vaue y from the fuzzy set B in V R. This work computes the weighted average of the membership function or the center of gravity (COG) of the area bounded by the membership function curves: y * = V µ B ( y). ydy. µ ( ydy ) V B K i (5) This system was controed in rea time using the Rea time Windows Target Toobox of Matab. The sef tuning fuzzy PID contro scheme appied to the SMA actuators is shown in Fig. 11. There were two inputs to the fuzzy controer: et ( ) and de( t ). The three outputs of the fuzzy controer were the normaized vaues of the PID parameters. These vaues were denormaized and then appied to the PID reguator. The input current appied to SMA actuator system was obtained from the PID controer shown in Fig. 12. The performance of the proposed contro system was experimentay investigated for different reference inputs. Fig. 13 shows the performance of the contro system with respect to step reference input signa and its contro signa. The system response to step reference input compared with conventiona PID Fig. 10. Experimenta apparatus. We compute the crisp vaue of K p, Kd and K i by using the above expression. 3. EXPERIMENTAL RESULTS To experimentay verify the performance of above controer in the position contro of SMA actuators, an experimenta apparatus using a sma NiTino SMA wire (made by Memory Metae GmbH) was estabished (Fig. 10). The main specifications of SMA wire were: ength: 110mm, diameter: 250µm, heat current: ca.2v/0.85a, gen. force: 8N, dispacement: ca._5mm. This actuator has a one way shape memory effect. The dispacement was measured by a high precision potentiometer and fed to the computer through an A/D Advantech PCI-1711 card. The contro current appied to the SMA wire was obtained from a D/A card and a V/I converter. The samping time was set to 0.01s in a experiments. An extra current source was aso used to simuate the effect of the variation of input current. Fig. 11. Schemetic diagram of sef tuning fuzzy PID controer appied to SMA actuator. Fig. 12. The Structure of PID reguator.

5 760 Kyoung Kwan Ahn and Bao Kha Nguyen Fig. 13. Step response and contro signa. Fig. 15. System response with respect to sine reference input (f = 0.1Hz). Fig. 14. Comparison of step response with and without fuzzy tuning. contro (without fuzzy tuning) is shown in Fig. 14. Figs. 13 and 14 show that the sef tuning fuzzy PID controer achieves better tracking response than the conventiona PID controer without fuzzy tuning. Figs. 15 and 16 depict the performace of contro system to sine reference input with two different frequencies. Steady state error is shown in Fig. 17. Since the SMA actuator is a sow response system, the contro performance is better in the ow frequency tracking. The effect of a sma variation of input current was aso investigated and is shown in Fig. 18. The output dispacement keeps good tracking adaptivey with the desired trajectory even the sma change of the input current. The hysteresis curve between input and output Fig. 16. System response with respect to sine reference input (f = 0.033Hz). Fig. 17. Steady state error.

6 Position Contro of Shape Memory Aoy Actuators Using Sef Tuning Fuzzy PID Controer 761 signa shown in Fig. 16. Fig. 20 shows the neary inear reationship between the desired dispacement (input) and the system output. Consequenty, the sef tuning fuzzy PID contro agorithm proves to be effective for the position contro and hysteresis compensation of SMA actuators. 4. CONCLUSIONS Fig. 18. Effect of the change of input current. Fig. 19. Hysteresis curve obtained from experiment before appying contro agorithm (open oop contro). Fig. 20. Hysteresis curve obtained from experiment after appying contro agorithm (cosed oop contro). reation of a system incuding the SMA actuator and controer before (open oop contro) and after appying the contro agorithm (cosed oop contro) is shown in Figs. 19 and 20, respectivey. The hysteresis curve in Fig. 20 is obtained from the second cyce of the system response with respect to the sine reference In this paper, an adaptive sef tuning fuzzy PID contro agorithm was appied to the rea time position contro of SMA actuators. The experimenta evauation showed that the sef-tuning fuzzy PID controer coud adaptivey achieve good tracking to different references, the sma change of the input current, and therefore coud compensate for the hysteresis phenomenon of SMA actuators. The proposed controer was compared with the conventiona PID controer without fuzzy tuning and performed better. This contro method is effective not ony for SMA actuators but aso for other contro systems. REFERENCES [1] Q. Chang-Jun, M. Pei-Sun, and Y. Qin, A prototype micro-wheeed-robot using SMA actuator, Sensors and Actuators A: Physica, vo. 113, no. 1, pp , [2] T. Raparei, P. B. Zobe, and F. Durante, Design of a parae robot actuated by shape memory aoy wires, Materias Transactions, vo. 43, no. 5, pp , [3] D. D. Shin, K. P. Mohanchandra, and G. P. Carman, Deveopment of hydrauic inear actuator using thin fim SMA, Sensors and Actuators A: Physica, vo. 119, no. 1, pp , [4] M. Vasina, F. Soc, and K. Hoder, Shape memory aoys, unconventiona actuators, Proc. of the IEEE Int. Conf. Industria Technoogy, vo. 1, pp , [5] D. Hughes and J. T. Wen, Preisach modeing of piezoceramic and shape memory aoys hysteresis, Smart Materia Structures, vo. 3, pp , [6] H.-J. Shieh, F.-J. Lin, P.-K. Huang, and L.-T. Teng, Hysteresis compensation in eectromagnetic actuators through Preisach mode inversion, IEEE/ASME Trans. on Mechatronics, vo. 5, no. 4, pp , [7] B. J. Choi and J. J. Lee, Preisach mode of SMA actuators using proportiona reationship of major oop of hysteresis, Proc. of IEEE Int. Conf. Inteigent Robots and Systems, vo. 2, pp , [8] Y. M. Han, S. C. Lim, H. G. Lee, S. B. Choi, and H. J. Choi, Hysteresis identification of

7 762 Kyoung Kwan Ahn and Bao Kha Nguyen poymethyaniine-based ER fuid using Preisach mode, Materias & Design, vo. 24, no. 1, pp , [9] D. Mayergoyz, Mathematica Modes of Hysteresis and Their Appications, Esevier Science, New York, [10] J. M. Cruz- Hernandez and V. Hayward, On the inear compensation of hysteresis, Proc. of IEEE Conf. on Decision and Contro, vo. 2, pp , [11] J. M. Cruz- Hernandez and V. Hayward, Phase contro approach to hysteresis reduction, IEEE Trans. on Contro Systems Technoogy, vo. 9, no. 1, pp , [12] R. Babuska, J. Oosterhoff, A. Oudshoorn, and P. M. Bruijn, Fuzzy sef-tuning PI contro of ph in fermentation, Engineering Appications of Artificia Inteigence, vo. 15, no. 1, pp. 3-15, [13] M. Parnichkun and C. Ngaecharoenku, Hybrid of fuzzy and PID in kinematics contro of a pneumatic system, Proc of the 26th Annua Conf. of the IEEE Industria Eectronics Society, vo. 2, pp , [14] M. Petrov, I. Ganchev, and A. Taneva, Fuzzy PID contro for noninear pant, Proc of the First Int. IEEE Symposium on Inteigent Systems, vo. 1, pp , [15] T. Ahn, Y. W. Kwon, and H. S. Kang, Drive of induction motors using a pseudo-on-ine fuzzy- PID controer based on genetic agorithm, Trans. on Contro, Automation and Systems Engineering, vo. 2, no. 2, pp.85-91, KyoungKwan Ahn received the B.S. degree in the department of Mechanica Engineering from Seou Nationa University in 1990, the M.Sc. degree in Mechanica Engineering from Korea Advanced Institute of Science and Technoogy (KAIST) in 1992 and the Ph.D. degree with the tite A study on the automation of out-door tasks using 2 ink eectro-hydrauic manipuator from Tokyo Institute of Technoogy in 1999, respectivey. He is currenty an Associate Professor in the Schoo of Mechanica and Automotive Engineering, University of Usan, Usan, Korea. His research interests are design and contro of smart atuator using smart materia, fuid power contro, rehabiization robot and active damping contro. He is a Member of IEEE, ASME, SICE, RSJ, JSME, KSME, KSPE, KSAE, KFPS, and JFPS. Bao Kha Nguyen received the B.S. and M.S. degrees from Hochiminh City University of Technoogy in 2001 and 2003, respectivey, a in Automatic Contro Engineering. He is currenty studying Ph.D. Course at University of Usan. His research interests focus on inteigent contro, modern contro theory and their appications, design and contro of smart actuator systems.