Identification and Position Control of Marine Helm using Artificial Neural Network

Transcription

1 Identfaton and Poston Control of Marne Helm usng Artfal Neural Network Hu ZHU Yannan RUI College of Mehanal & Eletr Engneerng, Soohow Unversty Suzhou, Jangsu,, Chna ABSRAC If nonlneartes suh as saturaton of the amplfer gan and motor torque, gear baklash, and shaft omplanes- just to name a few - are onsdered n the poston ontrol system of marne helm, tradtonal ontrol methods are no longer suffent to be used to mprove the performane of the system. In ths paper an alternatve approah to tradtonal ontrol methods - a neural network referene ontroller - s proposed to establsh an adaptve ontrol of the poston of the marne helm to aheve the ontrolled varable at the ommand poston. hs neural network ontroller omprses of two neural networks. One s the plant model network used to dentfy the nonlnear system and the other the ontroller network used to ontrol the output to follow the referene model. he expermental results demonstrate that ths adaptve neural network referene ontroller has muh better ontrol performane than s obtaned wth tradtonal ontrollers. Keywords: Neural Network Controller, Identfaton, Poston ontrol system, Nonlnearty, Marne helm. INRODUCION Usually, the tradtonal PID (Proportonal-Integral-Dervatve) ontroller an be used to mprove the ontrol performane suessfully when poston system of marne helm s regarded as a lnear system. However, n fat, the real system s nonlnear when saturaton of the amplfer gan and motor torque, gear baklash, and shaft omplanes are onsdered[]. Baklash of deelerator gear, for example, s a ommon nonlnear fator n mehanal onneton of the follower system. Owng to restrton on mahnng auray and assembly, baklash s hard to avod. In addtonal, ths knd of nonlnearty an not be lnearzed. herefore, PID ontrol method s not suffent to deal wth nonlnear stuaton. An alternatve approah to tradtonal ontrol methods - a neural network referene ontroller - s proposed to establsh an adaptve ontrol system for the poston of the marne helm to aheve the desred desgn ondtons. Wth the development of artfal ntellgent tehnology, neural network ontrol have been appled very suessfully n the dentfaton and ontrol of dynam systems[] [3][4][] nstead of tradtonal PID ontrol n order to have muh better ontrol performane than s obtaned wth tradtonal ontrollers, suh as less maxmum overshoot, less settlng tme, less steady error and so on. Sne the neural network has powerful unversal approxmaton apabltes of the multlayer pereptron, t should be a good hoe to dentfy nonlnear system and ontrol nonlnear system based on neural network. he goal of ths researh s to evaluate a nonlnear adaptve neural network referene ontroller, n whh a neural network model of a plant s used to dentfy the poston system of marne helm and a neural network ontroller s used to ontrol the output (atual poston of marne helm) to aheve ts desred value.. POSIION CONROL SYSEM OF MARINE HELM Dagram of Poston Control System Fgure llustrates the blok dagram of poston ontrol system of marne helm. In the fgure : -Preamplfer -Power amplfer wth urrent feedbak 3-DC motor 4-Gear tran -Load 6-ahometer - -Desred poston -Atual poston he objetve of the ontrol system s to have the output of the system followed the nput. In ths ontrol Fgure Blok dagram of the poston ontrol system of marne helm proess, a number of ontrol performane suh as overshoot, settlng tme, steady error - just to name a few - have to be evaluated and ontrolled. herefore, It s rather mportant to determne orret ontrol approah to make the ontrolled varable reah ts set pont. In the orgnal ontrol system whh s shown n fgure, the urrent feedbak an ompensate for the devaton aused by load urrent of motor and the poston feedbak an ompensate for the devaton aused by dsturbane or upset suh hange of parameter of system, ambent ondtons and et. 6 6 SYSEMICS, CYBERNEICS AND INFORMAICS VOLUME 6 - NUMBER ISSN: 69-44

2 .636 bak-emf Clok XY Graph In sensor Saturaton -K- Preamp Power amplfer.3s+ urrent/emf 9.s+. orque onstant /(Js+B) s. IntegratorBaklash Gear rato Out. Current feedbak Fgure ransfer funton blok dagram of the poston ontrol system Sope he transfer funton blok dagram of the system s shown n fgure. Applyng K=6, a omparson of two poston outputs, of whh wth and wthout saturaton of the amplfer and gear baklash n the poston ontrol system of marne helm, s shown n fgure 3. One s a plant model neural network and another ontroller network. hey both are dsplayed n the Fgure 4. Referene Model NNI. X Y Plot NNC Learnng algorthm Controlled plant Y Axs... X Axs Fgure 3 Output response of system wthout nonlnearty (urve ) and wth nonlnearty (urve ) In fgure 3, urve shows the output response assumng the system s lnear whle urve shows the poston response assumng the system has nonlneartes of saturaton and baklash. he smulatng result demonstrates that the output of the system an not follow the ommand nput aurately when nonlnearty s onsdered. It s obvous that the output s tremblng. 3. NEURAL NEWORK CONROL SYSEM Control arhteture he objetve of neural network ontroller s to dentfy the nonlnear system and ontrol the output of the system to trae the desred nput value aurately. At the same tme, the ontrol system must have satsfatory dynam performane. In ths paper, two neural networks are nluded. Eah network has three layers,.e. nput-lay, hdden-layer and output-layer. he ontrolled plant s dentfed by plant model neural network frst, and then the neural network ontroller s traned so that the plant output follows the referene model output. System Identfaton we selet two delayed plant outputs and two delayed plant nputs as the nputs of the neural network plant model. Sze of hdden layer s seleted to ten. he sample data reated by a random sgnal are used to tran the plant-model neural network that an be represented the forward dynams of the marne helm poston system. he predton error between the plant output and the neural network output s used as the neural network tranng sgnal. he neural network plant model uses prevous nputs and prevous plant outputs to predt the future values of the plant output. We use Levenberg-Marquardt algorthm[6] as tranng funton. When the performane funton has the form of a sum of squares, the Hessan[7] matrx an be approxmated as H = J J () and the gradent an be omputed as g = J e () where s the Jaoban matrx that ontans frst dervatves of the network errors wth respet to the weghts and bases, and e Fgure 4 Control model wth neural network J s a vetor of network errors. he Jaoban matrx an ISSN: SYSEMICS, CYBERNEICS AND INFORMAICS VOLUME 6 - NUMBER 7

3 be omputed through a standard bakpropagaton tehnque[8]. he Levenberg-Marquardt algorthm uses ths approxmaton to the Hessan matrx n the followng Newton-lke update: x = x [ J J µ I J e (3) k + k + ] When the salar µ s zero, ths s just Newton's method[9], usng the approxmate Hessan matrx. When µ s large, ths beomes gradent desent wth a small step sze. Newton's method s faster and more aurate near an error mnmum, so the am s to shft towards Newton's method as qukly as possble. hus, µ s dereased after eah suessful step (reduton n performane funton) and s nreased only when a tentatve step would nrease the performane funton. delayed referene nput, two delayed plant outputs, and one delayed ontroller output. Bak-propagaton reated by generalzng the Wdrow-Hoff[] learnng rule to multplelayer networks and nonlnear dfferentable transfer funtons s the algorthm of the network. In ths way, the performane funton wll always be redued at eah teraton of the algorthm. For nonlnear poston ontrol system of marne helm, the tranng result, whh demonstrates that the model neural network an dentfy the plant suessfully, s shown n fgure. - Input Error -.4 tme (s) Plant Output - - NN Output - - tme (s) Fgure 6: ypal learnng urve for model network. Mean squared error s used as performane measure. A set of tranng patterns are presented every tranng epoh. We an estmate the mean square error by usng the squared error at eah teraton. Input vetors and the orrespondng target vetors are used to tran a network untl t an approxmate a funton, assoate nput vetors wth spef output vetors, or lassfy nput vetors n an approprate way. Networks wth bases, a sgmod layer, and a lnear output layer are apable of approxmatng any funton wth a fnte number of dsontnutes. Referene Model Input Fgure estng result for Neural network Mdl Durng the tranng we observed four dfferent attrator states dependng on the ntal settngs, three of whh produed equally good performane (MSE <. on test set). A typal urve of onvergene to the fnal value s presented n Fgure 6. Obvously onvergene s not unform.e. the weght spae has a omplex struture. Referene model For ths poston ontrol system, sne the eletral tme onstant s muh smaller than the mehanal tme onstant, we an perform a rude approxmaton by negletng the armature ndutane. herefore ths thrd-order system an be regarded as a seond-order system. We use a well-defned seond-order system whh has good performane as a referene model. hs referene system must at mnmum satsfy the three bas rtera of stablty, auray, and a satsfatory transent response (eg. Overshoot, settlng tme). Neural network ontroller we desgn the neural network ontroller whh has fve nputs n nput-layer, thrteen neurons n hdden-layer and one output n output-layer. he nputs to the ontroller onsst of two tme (s) Fgure 7 Comparson of referene model output (grey) and neural network output (blak) 8 SYSEMICS, CYBERNEICS AND INFORMAICS VOLUME 6 - NUMBER ISSN: 69-44

4 After tranng the neural network ontroller, we get the omparson of referene model output and neural network output as followng fgure 7. Results Let the ommand nput be a unt-step funton. We nvestgate three responses to three dfferent ontrol approahes. he smulaton results are shown n Fgure 8. follow the ommand poston aurately wth good dynam performane. he fgure 9 llustrates the smulatng result. X Y Plot Y Axs X Axs Fgure 9 Response to unform random number sgnal Curve : Controlled poston varable Curve : Desred poston output Fgure 8 Smulaton results of output response he output response of poston ontrol system wthout saturaton of the amplfer and gear baklash by usng tradtonal PID ontroller ( urve); he output response of atttude ontrol system wth saturaton of the amplfer and gear baklash by usng tradtonal PID ontroller (urve ); he output response of atttude ontrol system wth saturaton of the amplfer and gear baklash by usng referene neural network ontroller ( urve 3). From the smulaton of output response, we get the followng results: ) When the system s smplfed to a lnear system that saturaton of the amplfer gan and motor torque, gear baklash, and shaft omplanes have all been negleted, we an mprove the system performane by modfyng the parameter of ontroller, usng lag-phase ompensaton, ahead-phase ompensaton and lag-ahead-phase ompensaton. ) When the nonlnearty of system s nluded, the output wll may be osllaton that make output not be able to follow the referene objet. PID ontroller s not suffent to mprove ontrol performane of poston system.. 3) when the neural network ontroller, whh we developed here, s adopted, the output response of the system wth nonlnearty an trae the referene model better than tradtonal ontrollers. he overshoot dereases from 4% to 6%, whle the response approahes to steady state rather qukly. When we use a unform random number sgnal, whose mnmum s set to -, maxmum and sample tme., as a ommand nput of the neural network ontroller, the output response smulaton shows that ontrolled varable an also 4. DISCUSS A method sutable for a poston ontrol of nonlnear marne helm has been proposed. he method s based on the applaton of a neural network referene ontrol approah that norporates the nonlnear saturaton and baklash poston ontrol. Nonlnear propertes are aqured durng a learnng phase hough just prelmnary results are gven n ths paper the potental of neural networks to apture nonlnearty exhbted n poston ontrol system ould be learly demonstrated. A network was traned to model a plant wth ts nonlnearty. hs tranngs proess has to be explored further to smplfy the employed network struture and to guarantee onvergene to an aeptable performane measure. Suessvely we utlzed ths traned neural network wthn a referene ontroller approah to ontrol helm poston to follow a desred target sequene aurately.. CONCLUSION In prate, most system s nonlnear for large varatons about the operatng pont, and lnearzaton s based on the assumpton that these varatons are suffently small. But ths annot be satsfed, for example, for systems that nlude relay, saturaton, dead-band, baklash, hysteress and frton et. the analyss and desgn tehnques dsussed n lassal ontrol theory are no longer vald, sne the prnple of superposton does not apply to nonlnear system. Worse, there s no general equvalent tehnque to replae them. Instead, a number of tehnques exst, eah of lmted purpose and lmted applablty. he desrbng funton tehnque, for example, s a response method, and ts man use s n stablty analyss. t s dffult to analyse, dentfy, desgn and ontrol the system wth nonlneartes. For those more omplex ases, t wll be more dffulty to dentfaton and ontrol the system usng tradtonal methods. In ths paper the applablty of neural network referene ontrol to a poston problem ould be demonstrated. In the ISSN: SYSEMICS, CYBERNEICS AND INFORMAICS VOLUME 6 - NUMBER 9

5 ontext of the marne helm ths approah may prove to be valuable as t naturally extends to multdmensonal problems. Results show that ths approah an make the system output follow the ommand poston aurately as well as suessfully dentfy the nonlnear poston system of marne helm. In addton to poston, some other parameters, suh as speed, urrent and power et., are mportant for optmzng system. hs study demonstrates that neural network referene ontrol may prove valuable as a tool n poston ontrol system. 6. REFERENCE [] Atnerton, D.P.. Nonlnear Control Engneerng. Van Nostrand: Ren-Hold Company Lmted. 97 [] Hu Zhu Knut Möller Ventlator Control Based on a Fuzzy-Neural Network Approah he nd Internatonal Conferene on Bonfomats and Bomedal Engneerng 8. IEEE, Shangha, Chna, pp , 8 [3] Hagan,M.. and H.B. Demuth, "Neural Networks for Control," Proeedngs of the 999 Ameran Control Conferene, San Dego, CA, pp [4] Murray, R., D. Neumerkel, and D. Sbarbaro, "Neural Networks for Modelng and Control of a Non-lnear Dynam System," Proeedngs of the 99 IEEE Internatonal Symposum on Intellgent Control, pp [] Ca Zxn, Xu Guanyou. Artfal ntellgent and applaton. Bejng: Qng Hua Unversty Press. 3 [6] Hagan, M.., and M. Menhaj, "ranng feedforward networks wth the Marquardt algorthm," IEEE ransatons on Neural Networks, vol., no. 6, pp , 994. [7] Ma W J, Wu M, Hseh J and Chang S L Level statsts of Hessan matres: random matres wth onservaton onstrants he nd APCP and 6th awan Internatonal Symposum on Statstal Physs, May, ape, awan [8] Rumelhart, D. E., G. E. Hnton, and R. J. Wllams, "Learnng nternal representatons by error propagaton,", n D. E. Rumelhart and J. L. MClelland, eds. Parallel Data Proessng, vol., Cambrdge, MA: he M.I.. Press, pp , 986. [9] Battt, R., "Frst and seond order methods for learnng: Between steepest desent and Newton's method," Neural Computaton, vol.4, no., pp. 4-66, 99 [] Wdrow B. and S. D. Sterns, Adaptve Sgnal Proessng, New York: Prente-Hall 98 3 SYSEMICS, CYBERNEICS AND INFORMAICS VOLUME 6 - NUMBER ISSN: 69-44