Intelligent IMC-PID Control Using PSO for Ultrasonic Motor

Transcription

1 teratioal Joural of Egieerig ovatio ad Maagemet (0 telliget MC- Cotrol Usig SO for Ultrasoic Motor Shegli MU, Graduate School of Egieerig, Yamaguchi Uiversity, Japa, Kaya TANAKA, Graduate School of Egieerig, Yamaguchi Uiversity, Japa, Abstract: this paper, we propose a ovel scheme of MC- cotrol combied with a particle swarm optimizatio (SO type eural etwork (NN for a ultrasoic motor (USM. this method, the sigle cotrol parameter of MC- is adjusted by the NNs. The weights of NNs are updated by SO algorithm. The proposed method makes it possible to compesate the characteristic chages ad oliearity of USM. O the other had, sice the SO algorithm requires o iformatio about USM beforehad, its applicatio overcomes the problem of the Jacobia estimatio i the covetioal back-propagatio (B method of NN. The effectiveess of the proposed method is cofirmed by experimets usig USM servo system. Key-Words: ultrasoic motor (USM, MC-, eural etwork (NN, particle swarm optimizatio (SO.. troductio Ultrasoic motor (USM is a uique motor which employs frictioal force geerated by high-frequecy mechaical vibratio i piezoelectric elemet as a drive source. t possesses some excellet features, such as lightweight, oiselessess, high torque at low speed rage, high retetio torque, ad o electromagetic oise. Therefore, USM is cosidered as a excellet actuator i may idustrial fields [~3]. However, there are still several drawbacks prevet USM from beig a precise positioig actuator. Firstly, because of USM's frictio drive priciple, it is difficult to get mathematical model of USM based o physical aalysis. Although some plat models for USM have bee proposed, they are too complex to apply moder cotrol theories. Sice advaced cotrol theories are hard to be applied o USM, the cotrol, which has simple architecture ad works well eve without mathematical model, has bee widely used i USM applicatios [4-7]. Ad, the iteral model cotrol (MC- cotrol, which simplifies the tuig of gais, has bee itroduced [8]. Secodly, USM possesses characteristic chages ad oliearity, which are associated with experimetal coditios. Covetioal costat gai MC- cotrol caot solve such problems of USM. Therefore, eural etwork (NN has bee itroduced i recet years [9-]. However, NN has the problem of local miimum. Ad, covetioal back-propagatio (B method i NN requires the Jacobia of USM estimated beforehad [3]. order to solve these problems of NN, we adopt particle swarm optimizatio (SO. SO has bee studied i the field of probability optimizatio i recet years [4-7]. Sice SO is the effective global optimizatio tool, it ca be cosidered as a good tool to overcome problems of the covetioal NN. Therefore, we propose a ovel scheme of MC- cotrol combied with a SO type NN. the proposed scheme, oe parameter of the cotroller is adjusted by NN to compesate the oliearity ad characteristic chages of USM. Learig of NN is carried out by SO istead of the B method. The effectiveess of the proposed method is validated by experimets usig USM servo system. This paper is orgaized as the follows. The covetioal MC- is itroduced i Sec.. The NN ad SO algorithms applied i the paper are preseted i Sec. 3. Sectio 4 itroduces the USM servo system ad experimetal setup. The experimetal results ad discussios are give i Sec. 5. Sectio 6 presets the coclusios i the ed.. Covetioal MC- Cotrol. Cotrol The cotrol is the most widely used cotrol scheme i idustrial fields. Figure shows the scheme of cotrol cosidered i this paper. the scheme, r(, u(, ad y( are the object iput, the iput ad the output, respectively. G (z - is the cotroller. The iput u( is sythesized as u( u( k ( K ( K K K e( k K K e( e( k where K, K ad K are the gais of the cotroller. The error deoted by e( expressed as ( e( r( y( ( Furthermore, the cotroller G (z - ca be deoted as Eq. (3 shows. G K ( z K ( z z K ( z. MC- Cotrol The MC- cotrol requires a mathematical model of the plat. However, the mathematical model of USM is very difficult to derive. Here we adopt a virtual plat model of USM (3 Received: 7, May, 0, Accepted: 9 October 0 Available olie: October 0 Figure Block diagram of cotrol 69

2 Shegli MU, Kaya TANAKA: telliget MC- Cotrol Usig SO for Ultrasoic Motor Figure 3 Block diagram of feedback cotroller Figure Block diagram of MC cotrol where expressed as where ad y( G( z u( (4 b0 z G ( z A( z (5 A ( z az az (6 K K K a ( a a ( b a ( b 0 a Usig above gais, the cotrol iput ca be sythesized as b 0 0 ( u( u( k ( K K K e( (3 ( K K e( k K e( k Figure shows the block diagram of the MC scheme. G MC (z - meas the MC cotroller. G(z - coected to the USM i parallel is the iteral model expressed as the same form i Eq.(5. G(z - ca be divided ito a miimum phase elemet G M (z - ad a leg time z - [8,8,9] expressed as where G( z GM ( z z (7 b0 G M ( z (8 A( z We defie a first-order lag filter as the followig shows. f z ( z where α is a cotrol parameter which ca be decided arbitrary withi the rage of 0 α<. The cotroller G MC (z - ca be expressed as G MC ( z G 0 M az a z b ( z f ( z z (9 (0 3. SO Type Neural Network Sice the covetioal fixed gai type MC- cotroller stated above is difficult to compesate oliearity ad characteristic chages of USM. O the other had, NN is the effective tool to overcome these problems. However, the covetioal NN cotais of the local miimum ad the Jacobia problem. To overcome all problems, we would like to propose the ovel desig scheme of MC- combied with the SO type NN. Figure 4 shows the proposed desig scheme. Fig.4, the system parameter α( is the output from the SO type NN(SO-NN. Weights of NN are tued by SO to compesate the oliearity ad characteristic chages of USM. 3. Neural Network this applicatio, a NN cotroller with a two-layer structure is applied. The structure of the NN cotroller is show i Fig.5. Four euros are set i the iput layer. i ( expressed i Eq.(4 is the iput of NN. i ( { y(, y( k, y( k, u( k } (4 As Fig.5 shows, α( is desiged as the output of the NN ad used as the cotrol parameter i the MC- cotroller. t ca The MC scheme ca be expressed as a feedback cotrol structure as Fig.3 shows. The cotroller G C (z - ca be expressed by Eq.(. G K ( z K c ( z z K ( z ( Figure 4 Block diagram of the proposed scheme 70

3 teratioal Joural of Egieerig ovatio ad Maagemet (0 (WA type SO algorithm expressed i Eq.(8 ad Eq.(9. V V c r ( pbest c r ( gbest X X (8 X X V (9 be expressed as Figure 5 Structure of eural etwork f s ( et (5 ( i where the fuctio f s ( meas the sigmoid fuctio as Eq.(6 shows. The et i ca be calculated as f s ( x (6 x e 4 et i wi ( i ( (7 i where w i ( presets the weights i the coectios. They are desiged to be updated by the SO algorithm i this scheme. 3. article Swarm Optimizatio SO is a global optimizatio algorithm discovered through the simulatio of a simplified social model. Sice it is simple i cocept ad easy to implemet, it is quite attractive i the field of probability optimizatio i recet years [4-6]. Figure 6 shows a example of particle movemet of SO. x i ( meas the positio of the i th particle i the k step, x i (k- ad x i (k+ mea the positio of the (k- step ad the (k+ step, respectively. gbest is the best positio of the whole swarm, ad pbest is the best positio of the particle. v i (, which expresses the positio variace, is the velocity of the particle at the k step. t is related to the best positios as the dash lies show i the figure. NN learig, we defie the value of weights as the positio iformatio cotaied by N particles. The positio of the th particle is defied as X =[w, w, w3, w4]. Ad, the velocity ca be expressed as V =[v, v, v3, v4]. The weights are desiged to be updated by a iertia weight approach Eq.(8, c ad c are two positive costats, r ad r are two radom umbers withi [0,]. Eq.(9, the weight factor which balaces the global ad local search, is calculated as Eq.(0 shows. max mi max episode (0 episode max where episode meas the umber of curret iteratio, episode max presets the max iteratio umber i the searchig. τ max ad τ mi are the weight factor s maximum ad miimum value, respectively. The specificatio of the SO type NN algorithm for experimet is to be itroduced i Sectio USM Servo System this sectio, the USM servo system is preseted. Figure 7 shows the structure of the system. The USM, the ecoder, ad the magetic brake are coected o a commo axis. The positio sigal fetched by the ecoder is iput to the couter board coected to the C. formatio of the cotrol iput calculated from the output ad the object iput i the C is trasferred to the drivig circuit via the /O board. Table shows the specificatios of the USM, the ecoder ad the load. Table shows the specificatios of the drivig circuit. The drivig circuit is show i Fig.8. The phase differece cotrol circuit is costructed by a digital circuit with a shift register. The voltage cotrol ad the voltage cotrol circuit at the fial stage are costructed by a digital potetial meter, a digital operatioal amplifier, ad a booster trasistor. To make stable start, a drivig frequecy is fixed at 36.0 khz Figure 7 USM servo system Table Specificatios of USM, ecoder ad load Rated rotatioal speed: 00 rpm USM Rated torque: 0.39 N m Holdig torque: 0.39 N m Figure 6 Example of particle movemet of SO Ecoder Load Resolutio: deg. 0~0. N m 7

4 Shegli MU, Kaya TANAKA: telliget MC- Cotrol Usig SO for Ultrasoic Motor hase ifferece Cotrol Oscillator ersoal Computer hase verse Cotrol Voltage Cotrol Ultrasoic Motor Figure 8 rive circuit of USM servo system Table Specificatios of the drive circuit rivig frequecy rivig voltage hase differece Resolutio of phase differece Samplig time 36.0 khz 50 V -90~90 deg..406 deg..0 ms which is.0 khz higher tha resoace frequecy of the USM. For the USM drivig, the phase differece cotrol method adopted. The method prevets hysteresis pheomeo ad has a relatively liear relatio betwee iput ad output. The phase differece is adjusted betwee -90 deg. ad 90 deg. by.406 deg. 5. Experimets ad Results 5. Experimetal Setups order to cofirm the effectiveess of the proposed method, a group of experimets are implemeted i the USM servo system. The purpose of the experimets is to validate the performace of this proposed method i reducig the steady-state error i the precise positio cotrol. The object iput r( is a rectagular sigal. The amplitude is set from +45 deg. to -45 deg. The period is 6 sec. this paper, we call the positio, expressed by +45 deg., as clockwise rotatio. The opposite oe, expressed by -45 deg., is the couter-clockwise rotatio. For compariso, a group of covetioal MC- experimets are implemeted. We set a group of optimized system idetificatio parameters for the covetioal MC- cotrol. The value parameters are set as a = , a = , b 0 =0.03, ad α is set as 0.6. ue to differet characteristics of clockwise ad couter-clockwise turig, i the proposed method, two idepedet NNs are assiged to the clockwise ad couter-clockwise rotatios. Two swarms with 0 particles respectively are desiged for the NNs. All the particles are iitialized by radom umbers from - to. Learig of NN, which is the executed by SO, is carried from.0 sec. to.5 sec. after chagig the sig of the object iput. The parameter episode i Eq.(0 varies from to 50, ad episode max is 50. The iertia weight factors τ max ad τ mi are set as τ max =0.9 ad τ mi =0.4, respectively. The positive costats c ad c are set as c =c =.0. The particles are desiged to be evaluated by the followig fuctio fitess, ( f [0, ], usig the real-time error e(=r(-y(. The fitess is updated by each millisecod. Sice the precise resolutio of ecoder makes the fitess variatio isesitive, we elarge e( by 00 times to make fitess respose quickly i the experimets. fitess ( ( 00 e( 5. Results ad Study the experimets, the rectagular wave sigal is set to ru 30 cycles. Figure 9 shows the respose of the last two cycles i the experimet. We ca see that the output follows the object iput almost i a steady state. Figure 0 shows the variatio of α(, the NN output i the first 5 cycles. We ca see that after about 3 cycles learig, the outputs of clockwise ad couter-clockwise NN coverged to differet value. t ca be stated that the USM has the differet characteristic accordig to the rotatory directio, ad that the proposed method is capable to search optimal value for each rotatory directio. Figure ad show the weights updatig of NN, respectively. The weights of the clockwise ad the couter-clockwise coverged to differet values withi 5 cycles. t ca be cocluded that SO is a effective tool to adjust weights of NN. For compariso, positioig errors of covetioal method ad proposed method i the steady state have bee evaluated. The errors were sampled at each 0. secod before directio chagig. Figure 3 shows the histogram of the positioig error with o load of the covetioal MC- method. We ca see that errors are from to deg. i clockwise rotatio ad are from to deg. i couter-clockwise rotatio. t ca be cocluded that the Figure 9 Respose of the proposed method Figure 0 Variatio of the cotrol parameter α( 7

5 teratioal Joural of Egieerig ovatio ad Maagemet (0 Figure Weights of the clockwise turig. Figure Weights of the couter-clockwise turig. idetificatio parameters of covetioal MC- are good at describig the characteristic of the USM. Ad the clockwise performace is better tha the couter-clockwise performace. Figure 4 shows the histogram of the positioig error with o load of the proposed method. Errors distribute from to deg. i clockwise rotatio ad from to deg. i couter-clockwise rotatio. From the results, we ca see that the cotrol performace of the proposed method is superior to oes of the covetioal method. Figure 5 shows the histogram of the positioig error with the load (0.05 N m of the covetioal MC- cotrol. Errors distribute from to 0 deg. i clockwise rotatio ad from to 0.06 deg. i couter-clockwise rotatio. t proves that the covetioal MC- cotrol caot compesate the oliearity ad characteristic chages whe the load is added to USM. The, we ca see the positioig errors of the proposed method show i Fig. 6 shows the histogram of the positioig error with the load (0.05 N m of the proposed method. Errors cocetrate o deg. i clockwise rotatio ad distribute from 0 to deg. i <+45 degree> <-45 degree> Figure 3 ositioig error of the covetioal MC- (o load. <+45 degree> <-45 degree> Figure 4 ositioig error of the proposed method (o load. 73

6 Shegli MU, Kaya TANAKA: telliget MC- Cotrol Usig SO for Ultrasoic Motor <+45 degree> <-45 degree> Figure 5 ositioig error of the covetioal MC- (load: 0.05 N m. <+45 degree> <-45 degree> Figure 6 ositioig error of the proposed method (load: 0.05 N m. couter-clockwise rotatio. We ca see that the positioig error of the proposed method is improved tha oes of the covetioal method obviously. From these experimetal results, the effectiveess of the MC- cotrol with SO-NN has bee cofirmed. 6. Coclusios this paper, a ovel MC- cotrol scheme combied with SO type NN has bee proposed for precise positioig cotrol of USM. The NN is used for optimizig the cotrol parameter of the MC- cotroller ad the SO algorithm is applied i NN's learig. The proposed method overcomes the Jacobia estimate problem of covetioal B type NN. The proposed method ca compesate ot oly the characteristic chages but also oliearity of USM. The effectiveess of the proposed method is cofirmed by experimets usig USM servo system. Refereces: [] T. Kejyo ad T. Sashida: A troductio of Ultrasoic Motor, Oxford Sciece ublicatios, 993. [] T. Maeo, T. Tsukimoto ad A. Miyake: Fiite-Elemet Aalysis of the Rotor/Stator Cotact i a Rig-Type Ultrasoic Motor, EEE Tras. Ultrasoics, Ferroelectrics, ad Frequecy Cotrol, Vol.39, No.6, 99, pp [3] T. Maeo: Ultrasoic Motor, JRSJ, Vol., No., 003, pp.0-4. [4] J.G.Ziegler ad N. B. Nichols: Optimum Settigs for Automatic Cotrollers, Tras. ASME, Vol.64, 94, pp [5]. Hazebroek ad B. L. va der Waerde: The Optimal Adjustmet of Regulators, Tras. AMSE, No.7, 950, pp.3-3. [6] W. A. Wolfe: Cotroller Settigs for Optimum Cotrol, 95, Tras. ASME, No.73, pp [7] C. E. Garcia ad M. Morari: teral Model Cotrol-. A Uifyig Review ad Some New Results, d. Eg. rocess es. & ev., 98, pp [8] J. Li ad K. Taaka: telliget cotrol for eumatic Servo System, JSME teratioal Joural, Series C, Vol.46, No., 003, pp [9] K. Taaka, M. Oka, A. Uchibori, Y. wata ad H. Morioka: recise ositio Cotrol of Ultrasoic Motor Usig Cotroller Combied with NN, EEJ Joural, Series C, Vol., No.8, 00, pp [0] K. Taaka, T. Takeguchi, J. Nakamoto, ad Jihua Li: MC- Cotrol Usig NN for Ultrasoic Motor, EEJ Tras. ES, Vol.3, No., 003, pp [] M. Oka, K. Taaka, A. Nagaawa ad K. Haruyama: recise ositio Cotrol of the Ultrasoic Motor Usig put-output Liear Compesatio Type Cotroller, Joural of AEM, Vol.5, No., 007, pp [] K. Fukuda, T. Kamao, T. Suzuki, T. Yasuo ad H. Harada: High accuracy positioig system with ultrasoic motor usig frequecy ad phase eural etworks, Joural of AEM, Vol.6, No.4, 998, pp [3] K. Taaka, M. Oka, Y. Wakasa, T. Akashi, ad A. Nagaawa: GA Adjustmet Type NN- Cotrol for Ultrasoic Motor, Joural of AEM, Vol.5, No.4, 007, pp [4] J. Keedy ad R. Eberhart: article Swarm 74

7 teratioal Joural of Egieerig ovatio ad Maagemet (0 Optimizatio, roc. EEE t. Cof. Neural Networks, erth, Australia, 995, pp [5] M. Clerc ad J. Keedy: The article Swarm: Explosio, Stability, ad Covergece i a Multi-imesioal Complex Space, EEE Tras. Evolutioary Computatio, Vol.6, No., 00, pp [6] J. Keedy, R.C. Eberhart, Swarm telligece, Morga Kaufma ublishers, 00. [7] M. to ad M. Taaka: A Study of article Swarm Optimizatio for Neural Network Traiig, A publicatio of Electroics, formatio ad System Society, 005, pp [8] K. Taaka, Y. Yoshimura, Y. Wakasa, T. Akashi: Variable Gai Type teral Model Cotrol- Speed Cotrol for Ultrasoic Motor, EEJ Tras. A, Vol.8, No., 008, pp [9] K. Taaka, Y. Yoshimura, Y. Wakasa, T. Akashi, M. Oka, S. Mu: Variable Gai Type telliget Cotrol for Ultrasoic Motor, Joural of AEM, Vol.7, No.3, 009, pp

8 76 Shegli MU, Kaya TANAKA: telliget MC- Cotrol Usig SO for Ultrasoic Motor