Servo Actuating System Control Using Optimal Fuzzy Approach Based on Particle Swarm Optimization

Transcription

1 Servo Actuatng System Control Usng Optmal Fuzzy Approach Based on Partcle Swarm Optmzaton Dev Patel, L Jun Heng, Abesh Rahman, Deepka Bhart Sngh Abstract Ths paper presents a new optmal fuzzy approach based on partcle swarm optmzaton (PSO) evolutonary algorthm for controllng the servo actuatng system. It s clear that attanng the maxmum stablty margn s the promnent goal n control desgn of servo actuatng systems. To reach the control goal, two man steps of desgn are requred; an approprate dentfcaton method and a controller development. Hence, the nonlnear system s frst dentfed by the fuzzy algorthm. Then, the controller parameters and the algorthm s weghtng functons are tuned through the Partcle Swarm Optmzaton algorthm. The objectve functon of optmal control strategy s such that the mnmum error between the actual and the dentfed data s attaned. The effectveness of the proposed approach comparng to the conventonal fuzzy control wth regular parameter tunng s llustrated and analyzed n the smulatons. Keywords Optmal control, fuzzy control, Partcle Swarm Optmzaton, servo system, evolutonary algorthm. I. INTRODUCTION The servo actuators are wdely useful and applcable n ndustres, control, automaton area, and manufacturng processes [1]. Consderng that these systems have nonlnear dynamcs and parameter varatons, t s dffcult to desgn a proper controller for them. Varous control methods have been used on these systems n the prevous researches lke real tme teratve learnng control, adaptve control, neural network control, etc [2-4]. Regular certan mathematcal models have been used for representng the servo systems nonlnear models. They have been used based on the nonlnear control theory. The basc method n these algorthms s to lnearze the exact system through the nonlnear state feedback. Although usng the certan mathematcal models, some mportant factors such as payload varatons and mass flow parameters uncertantes are beng neglected n the model. To overcome ths ssue, fuzzy approaches are beng wdely used for servo actuators control. Extensve research works have been done n the dentfcaton area of servo systems n the past. Actually the nonlnear servo systems are assumed to be presented by local models through fuzzy algorthms. One of the famous fuzzy methods used before s the Takag & Sugeno fuzzy model, n whch smoothed pecewse lnear models are used to analyze and synthesze the nonlnear system. In fact, fuzzy controllers are very smple to mplement on servo systems, also they buld an effcent nonlnear fuzzy controller for extensve range of applcatons [5], [6], [7]. Fuzzy approaches and neuro-fuzzy control methods are known to be very effcent for applyng on servo actuators and varous researchers appled fuzzy algorthms to desgn the controller or to dentfy the nonlnear system based on fuzzy methods. In mplementng the fuzzy algorthm, choosng approprate weghts s of great mportance. Several evolutonary algorthms have been used n order to choose the best parameters for the fuzzy structure [8]. The objectve n the optmal algorthm s to mnmze the error between the actual and dentfed model such that hgh performance and robustness of the system are acheved properly. In order to mplement the fuzzy functons and fuzzy controllers, an approprate programmng envronment s needed to be chosen. The fuzzy toolbox of MATLAB has been chosen n ths work snce t s convenent, smple to be used and very detaled. Ths paper work s focused on dentfyng the nonlnear servo actuator system n the frst stage through the fuzzy structure. In the second stage, he parameters of the fuzzy structure and the weghtng functons of the algorthm are then tuned and set based on the Partcle Swarm Optmzaton (PSO) algorthm. However Genetc Algorthm (GA) s very famous n tunng the controller s parameters, PSO s proved to operate faster n such applcatons snce ts calculatons are smpler than GA. As a matter of fact, PSO s one of the most effcent technques for adaptng parameters of fxed order controllers [9]. The lterature n [9] s effectvely used n ths work as the work have appled PSO on H nfnty loop shapng controller desgn for the mechancal beam system. Thus, by PSO optmzaton algorthm the optmum parameters and the weghtng functons for desgnng the fuzzy control desgn are attaned. The am s to mnmze the objectve functon ncludng the errors between the actual and dentfed models. The smulatons results proved the effcency and the effectveness of the proposed algorthm. The paper s organzed as follows. The system dynamcs and ts detals are represented n secton II. Secton III descrbes the chosen fuzzy control desgn approach. Secton IV gves the Partcle Swarm Optmzaton (PSO) algorthm descrpton used n the proposed technque. Then, the results of the approach on the servo actuatng system and ts comparson to the conventonal method results are shown n secton V, and the last secton gves the concluson as well. II. DYNAMIC MODELING OF SERVO ACTUATING SYSTEM The system under consderaton s a servo actuator or a servo drve as Fg. 1.

2 ths controller, frst the part of the system that can be lnearzed s lnearzed. The lnearzed equaton for the system would be as (2). x 1 = x 2 x 2 = x 3 x n = f(x 1,, x n ) + g(x 1,, x n2 )u(t) + d(t) y = x 2 (2) Fg. 1: Servo actuatng system The man components of the system are the cylnder, valve, load, actuator, also the fuzzy controller s to be added to the structure n the next part. The valve controls the flow rate of the compressed ar. The poston of the cylnder s beng controlled by the valve. The poston of the valve s used to control the spool movement, whch controls the ar flow rate of the cylnder and also controls the velocty and poston of the cylnder. The mathematcal model of the servo actuatng system s attaned by physcs laws. The descrptve model of the system a nonlnear model of order fve. The advantage of ths model s that t consders the mass flow rate, the pressure dynamcs, the frcton, the moton dynamcs. Hence, the state space equatons are stated as (1). x = v 1 v = ( M + m )(A 1P 1 A 2 P 2 F frcton + mg snθ) P 1 = (ε/a(l + x))(cf(p 1, u) A 1 P 1 v h) P 2 = (ε/a(l x))( Cf(P 2, u) A 2 P 2 v h) (1) where v s the velocty, x s the poston, and P 1 and P 2 are the absolute pressure of cylnder. M and m are the pston and load mass respectvely. Also, A 1 and A 2 are the areas of the chambers. l s the length of cylnder, F frcton s the force from frcton, g s the gravty acceleraton, ε s the coeffcent, and C s the constant. III. FUZZY CONTROL DESIGN The controller s model chosen for ths system s an adaptve fuzzy controller from lterature [5]. To mplement Note that the functons f and g are unknown functons. Usng the control sgnal, the system parameters θ are tuned. The feedback controller s desgned by Mamdan fuzzy system as [5]. By tunng the parameters vector θ, the unknown functons f and g are estmated as f and g. The objectve s to track the desred output trajectory n order to mnmze the trackng error. If-then fuzzy rules are used to estmate the functons f and g. The fuzzy rules are desgned based on the nput-output behavor of the system. The parameter vector θ s also splt nto two dfferent vectors θ f and θ g for the functons estmaton through the algorthm. Thus the control sgnal can be stated as (3). u = ( 1 g (x,θ) ) [ f (x, θ f ) + y n + K T e] (3) Note that the error vector e n the above equaton s the dfference between the system output and the desred output trajectory. Therefore, the followng stages are ntroduced to mplement fuzzy control strategy on the system: Step 1: The nput output behavor of the system s consdered by the P number of the nput fuzzy sets and the q number of output fuzzy sets. Step 2: The f then statements are bult base on the system s nput output behavor. Worth mentonng that the level of f then fuzzy rules accuracy s related to the human knowledge of the system. The f then statements are as follows: f x s A, then f (x, θ f ) s a member of B. For estmatng f and g functons, sngleton fuzzfer s used and the adaptve law for estmatng fuzzy functons would be as: f (x, θ f ) = θ f T ε f (X) g (x, θ f ) = θ f T ε f (X) (4) Consder that the type of fuzzy approach s the ndrect adaptve fuzzy method. The membershp functons are pcked from the MATLAB fuzzy toolbox as Fg. 2 (the trangular-shaped membershp functons (trmf of fuzzy toolbox) are used for the nputs and the outputs of the system).

3 Fg. 2: Membershp functons and Mamdan nference engne n Fuzzy toolbox Also, the membershp functons (MF1 to MF10) for one of the nputs s shown as Fg. 3. Fg. 5: f-then fuzzy rules wndow n the toolbox Choosng the P matrx as 10 3 I also the block dagram of the fuzzy structure s as follows [5]: Fg. 3: Membershp functons for the fuzzy system nput The output membershp functon (MF0 to MF13) s also supposed as Fg. 4. Fg. 6: Fuzzy control structure Fg. 4: Membershp functons for the fuzzy system output The f then fuzzy rule created are also from the followng wndow n Fg. 5. Usng the algorthm and the fuzzy strategy the controller s man structure s defned. In the next step, the structure s parameters are optmzed based on the PSO optmzaton algorthm (Partcle Swarm Optmzaton). The closed loop dagram of the fuzzy controller and the system s llustrated n Fg. 7.

4 v k+1 = wv k + c 1 rand(p x k ) + c 2 rand(p g k x k ) (5) x k+1 = x k + v k+1 (6) Fg. 7: The closed loop system of the servo actuatng system and the fuzzy controller IV. PSO OPTIMIZATION ALGORITHM Partcle Swarm Optmzaton (PSO) s a generalzed optmzaton technque based on the nsects socal nteractons [10]. The followng dagram shows step by step of the PSO algorthm. n the above equatons, v k s the partcle s velocty at teraton k and the v k+1 s the partcle s velocty at teraton k+1. The other parameters are the nerta weght, partcle and swarm constant coeffcents, partcle s ndvdual best and global best. In fact, for each optmzaton algorthm lke PSO there exsts a stoppng crteron to recognze where to stop the teratons; the teratons stop where the convergence s attaned n the strategy. In fact, the man use of PSO n fuzzy control desgn s for choosng the scalng gans, the controller structure settngs, determnng the membershp functons of the nputs and outputs, fuzzfer and defuzzfre, etc. Therefore, PSO s used manly to fnd the optmum fuzzy controller for the specfc system. It s worth mentonng that PSO s smlar to Genetc algorthm (GA) n nature; snce these two algorthms are populaton base, however GA s more tme consumng compared to PSO whle used for nonlnear problems. Ths s the man reason here PSO (not GA) s recommended n desgnng fuzzy model. V. SIMULATION RESULTS In ths secton, the smulaton results of usng the proposed fuzzy method based on PSO are represented. Also for evaluatng the results, the conventonal fuzzy control desgn method wthout optmzaton process s used on the system. Fg. 9 shows the results usng the classc fuzzy control on servo actuatng system and Fg. 10 shows the results of mplementng the proposed method. Comparng Fg. 9 and Fg. 10, the velocty trackng error usng the proposed PSO fuzzy controller s recognzably lower than the trackng error usng the conventonal fuzzy controller. As t can be seen from Fg. 9, the trajectory starts from 10 and ends wth less than 15, however the desred trajectory starts from 9 and ends n more than15. Regardng Fg. 10, the estmated trajectory perfectly follows the desred trajectory. Fg. 8: Partcle Swarm Optmzaton algorthm flowchart In PSO, each partcle has ts own poston and the velocty of the partcles are beng updated based on an algorthm that determnes the drecton and velocty of the movement of each partcle. Each poston partcpates n evaluatng the ftness (objectve) functon. After each teraton, new canddate partcles are created wth the am to attan the optmum pont n the ftness functon. The velocty and the poston of each partcle s updated based on equatons (5) and (6) respectvely.

5 the model structure. The parameters of the controller are then tuned base on PSO optmzaton strategy. PSO s chosen as the optmzaton approach because t s computatonally effcent and smple for nonlnear problems. The objectve of the optmzaton algorthm s such that the mnmum trackng between the actual model output and the estmated model output s attaned. The smulaton results proved the effectveness and effcency of ths hybrd approach n the servo system control desgn. Moreover, to strongly emphasze the superorty of the new method, the outcomes of the conventonal fuzzy algorthm are llustrated and compared to the results from the proposed approach. Fg. 9: System velocty trajectory regardng the desred trajectory usng classc fuzzy control REFERENCES [1] B. W. Anderson, The analyss and desgn of pneumatc systems, New York, London, Sydney: Wley, [2] Xu, J., Panda, Sanjb Kumar, Lee, Tong Heng, Real-tme Iteratve Learnng Control Desgn and Applcatons (Advances n Industral Control), [3] H. Wenme, Y. Young, and T. Yal, Adaptve neuron control based on predctve model n pneumatc servo system, [4] K. Harbck, S. Sukhatme., Speed control of a pneumatc Monopod usng a neural network, [5] R. En and S. Abdelwahed, Indrect Adaptve fuzzy Controller Desgn for a Rotatonal Inverted Pendulum, 2018 Annual Amercan Control Conference (ACC), Mlwaukee, WI, USA, 2018, pp do: /ACC [6] J. Espnosa, J. Vandewalle & V. Wertz, Fuzzy Logc, Identfcaton and Predctve Control, London: Sprnger, [7] R. Jang, MATLAB - Fuzzy Toolbox - The MathWorks, Inc. Revson: 1.12, Date: 2000, 15. [8] T. Gulrez, A. Hassanen, Advances n Robotcs and Vrtual Realty (Vol. 26, Intellgent Systems Reference Lbrary). Berln, Hedelberg: Sprnger Berln Hedelberg, [9] R. En, Flexble Beam Robust H-nfnty Loop Shapng Controller Desgn Usng Partcle Swarm Optmzaton. Journal of Advances n Computer Research, 5(3), Quarterly pissn: x eissn: , [10] M. Coucero, P. Ghams, Fractonal Order Darwnan Partcle Swarm Optmzaton (Sprnger Brefs n Appled Scences and Technology). Cham: Sprnger Internatonal Publshng, Fg. 10: System velocty trajectory regardng the desred trajectory usng PSO fuzzy control VI. CONCLUSIONS Ths paper proposed a new a new fuzzy approach based on Partcle Swarm Optmzaton algorthm for control desgn of a servo actuatng system. Snce the system descrptve model s nonlnear, fuzzy dentfcaton s used as the controller and