RBF Neural Network PID for Bilateral Servo Control System

Transcription

1 TELKOMNIKA, Vol., No. 9, Septeber 03, pp. 500~509 ISSN: RBF Neural Network PID for Bilateral Servo Control Syste Zhang Jingdong *,3, Wen Guang, Wei Yongqiao 3, Yin Guofu 3 School of Transportation and Autoobile Engineering, Panzhihua University, 0# Airport Road, 67000Panzhihua City, P.R.China, Ph./Fax: School of school of echanical engineering, Panzhihua University, Panzhihua City, China, 0# Airport Road, 67000Panzhihua City, P.R.China, Ph./Fax: School of Manufacturing Science and Engineering, Sichuan University, Chengdu City, China, No.4 South Section, Yihuan Road, Chengdu, P.R.China,, Ph./Fax: *Corresponding author, e-ail: zdzhangingdong@63.co*,3, wenguang973@6.co, scuwyq@63.co, gfyin@scu.edu.cn Abstract Tele-operated bilateral hydraulic servo syste with aster-slave robot at the core can be coplex anipulated in uncertain or extree environent (such as space, seabed, radicalization, battlefield, etc.). In this paper, a novel force feedback bilateral servo syste is presented, based on analysis of bilateral servo syste at hoe and abroad, which adopts tuning PID control algorith with RBF neural network at the sae tie. Fro the siulation results, the novel force feedback bilateral servo syste is presented to verify the effectiveness of the proposed control algorith. The control briefness, fast response, strong robustness, good disturbance reection capability and good adaptive capability can be obtained. It is also revealed fro siulation results that the proposed control algorith is valid for force feedback bilateral servo syste and also provides the theoretical and experiental basis. Keywords: force feedback, bilateral servo control syste, RBF tuning PID, control algorith Copyright 03 Universitas Ahad Dahlan. All rights reserved.. Introduction Since the first Master-Slave tele-operation anipulator was created in the 940s []. After decades of developent, the aster slave tele-control robot [] with the force telepresence has been widely used in soe dangerous environent which has high teperature, high pressure, strong radiation and suffocation, such as the developent of space, underground and underwater, atoic reactor aintenance operations, fire, flood, earthquake and so on. Master-Slave anipulator was an assistance for huan. Many countries have began to study the aster-slave anipulator, such as the United States, Russia, Gerany, Japan and other countries, and achieved good application effect. Its iportant of in technical field was revealed [3]. The bilateral servo control is a key technology in tele-operation control, which can provide the force sence in the operation process for operators, and enhance the operating perforance and speed. Experients show that the operating perforance of tele-operation control with force feedback is doubled to tele-operation control without force feedback [4]. The bilateral servo control tele-operation technology is one of the effective ethods to realize the force sense and visual tele-presence [5]. In this paper, PID control strategy is applied to iprove its perforance in the two-way force servo on the basis of two-way force servo tele-operation technology,taking into account the paraeter characteristics of two-way force servo syste are likely to change in actual working conditions, the traditional PID paraeter tuning ethod already can not satisfy the realtie, accurate control conditions. The PID algorith was done various iproveents. Eerging selective control PID-PD, control PID control and adaptive PID control algorith [6], especially in recent years with the research of the intelligent control and developent of the so-called intelligent PID controller was fored fro cobining intelligent control and conventional PID control, the controller has caused widespread concern and great interest and has been successfully applied [7], scholars has researched soe intelligent PID algorith and controllers, Received February 7, 03; Revised June 7, 03; Accepted June 9, 03

2 TELKOMNIKA ISSN: such as paraeter fuzzy PID controller [8, 9], PID controller based on genetic algorith [0, ], neural network PID controller [, 3], PSO-PID controller [4], Iune PID [5] and so forth, and achieved good control effect. Radial basis function neural network is a forward neural networks with good perforance, it has a good ability of generalization and Sall aount of calculation, its learning speed is also uch faster than the other algoriths, so it has been widely used in syste identification and paraeter estiation [6]. In this paper, a novel force feedback bilateral servo syste is presented, based on analysis of bilateral servo syste at hoe and abroad, which adopts tuning PID control algorith with RBF neural network.it uses a selftuning ethod of PID control paraeters based on RBF neural network, cobining theneural network with PID, on the basis of conventional PID perforance, using the adaptive capacity of neural network to fine-tune the control paraeters of the syste, so that a stable PID controller with self-tuning capability was Construct to adapt the changes of work paraeters of the bilateral force servo control, to get better control effects. Scene experients show that the proposed ethod can achieve better tracking results.. New Type Servo Syste Matheatical Model.. Brief Introduction to the Bilateral Servo Control Syste At present, the coonly used control systes are force feedback directly type (Figure ), Parallel Control Strategy Diagra (Figure ), syetrical position type (Figure 3), deviation of force feedback type (Figure 4) and so on. A variety of aster-slave servo control ethod, each have advantages and disadvantages of four double servo control systes, as shown in Table, copared with four kinds of control syste, the ost coonly used and the ost effective one is the force-location type, however, this control strategy exists spring effect, which akes the operator have the feeling of anipulation of heavy even when no-load operation [7-9]. Therefore, it needs a new way to solve the proble. Table. Contrast Analysis of Four Bilateral Control Systes Types of control Sensor Advantages Disadvantages Force feedback directly type Deviation of force feedback type Torque sensor Torque sensor Siple ipleent Less influence by ain hand More influence by ain hand and large influence when fetching the higher stiffness obect Large influence when fetching the higher stiffness obect Syetrical position type bilateral type Displaceent sensor Force and displaceent sensors Siple ipleent,realize the force feedback on displaceent difference Ease the feedback force ipact on the oystick Affected by the syste tie delay Obviously, the Following features of Follower institutions influence on oystick goes weak + - F Position Index F s Master Syste X Slave Syste X s Figure. Diagra of Force Feedback Directly Type Figure. Iproved Parallel Control Strategy Diagra RBF Neural Network PID for Bilateral Servo Control Syste (Zhang Jingdong)

3 A A 50 ISSN: Figure 3. Diagra of Syetrical Position Type Figure 4. Deviation of Force Feedback Type.. A Novel Bilateral Servo Control Syste The principle of the iproved parallel force bilateral hydraulic servo control syste is shown as Figure 5. The control strategy that the slave echanis always follows the anipulator has been used internationally, but it is not very idea for the force telepresence fro the control effect. The iproved parallel control strategy presented by this paper cobines the advantages of force error and parallel bilateral servo control, uses the error between the operating force of the anipulator and the working resistance of the slave echanis as the control signal to control the aster s otion. The feedback force is related to the force error between the aster and the slave, the slave driving force is related to the difference force between the aster and the slave and the displaceent difference between the aster and the slave. So it iproves the probles exist in the existing control ethod that the ipact force is too large when the slave contacts the obect with big rigidity, and that the aster-slave position following characteristics is bad. 3. Description of Syste 3.. Structure of Construction Robot The construction robot is based on the boo of the excavator, the bucket is replaced by an single degree of freedo end-effector to for an four-dof series oint type anipulator, as shown Figure 5. The end-effector opens and closes to grasp the obect by a pair of esh gear, and there are in sections on the tooth surface to enhance the reliability of grasping the obect. In order to bear greater working load, the ar of the construction robot are driving by hydraulic power, four cylinders are used to control the four-dof of the robot. The hydraulic syste are coposed of hydraulic station, oil circuit, electronic-hydraulic controlled proportional reversing valves and their controllers and cylinders. The proportional reversing valves and their controllers are the core of the electro-hydraulic control subsyste, which realize the flow control of the cylinders, naely speed control and reversing control. Figure 5. 4 DOF Engineering Robot Structure Chart 3.. Tele-operation Robot Syste In a tele-operated anipulation syste, the operator needs not only a visual representation but also a force representation of a syste existing in a reote place. Those TELKOMNIKA Vol., No. 9, Septeber 03:

4 TELKOMNIKA ISSN: devices of sense of force, at present, have probles, such as insufficiencies in the display functions and coplications in their constitutions. Figure 6. Master-slave Syste for Reote Control A conceptual illustration of a tele-operated anipulation syste for this study is given in Figure 6. The figure shows that the syste is constructed as a aster-slave syste and that both anipulators for the aster and the slave consist of 4-DOF type actuators. Moreover, it is illustrated that a achine tool for grinding is ipleented at the end-effecter of the slave anipulator. In a tele-operated aster-slave syste as shown in Figure5, the aster has to play two roles, firstly as a reference input device to the slave, and secondly as a sense of force device. Here, the ter sense of force eans a function that allows the operator to feel a force that is fed back to hi fro the slave [0-]. 4. Control Algorith 4.. Radial Basis Neural Network Setting PID Control Strategy The Radial Basis Function(RBF) is a neural network which was put forward by J.Moody and C.Darken in the late 980s, it is a three layer feed forward network with single hidden layer, is a kind of local approxiation of the neural network. The network s characteristic is that to enter a local area of the space only a handful of connection weight affect the output of the network, so that the local approxiation network has the advantage of fast learning. RBF learning ethods include k-eans ethod, the OLS (Orthogonal Least Squares) and gradient descent ethod, etc. In the process of practical application, the obect features and odels are changing frequently, ust changing slowly. Setting and well optiized PID paraeters ay no longer have a very good control effect after a period of tie. In order to ake the production process always keep a good control effect, the paraeters of PID controller need to be adusted and optiized online. To eet this requireent, a neural network intelligence PID controller has the characteristics arises at the historic oent. The neural network intelligence PID controller can identify the odel and features of the controlled obect through identifier; and on the basis of identification, it can realize PID paraeters online adustent and optiization through the neural network controller. 4.. The PID Control based on RBF Neural Network [3-5] There are any function for of RBF neural network, Gauss function was selected in this article as the hidden layer node function according to its unique advantages : Gauss function : f x exp x c b () RBF Neural Network PID for Bilateral Servo Control Syste (Zhang Jingdong)

5 504 ISSN: The structure of RBF neural network was showed as below. Figure 7. The Structure of RBF Neural Network In the structure of RBF neural network, r(k) is input of network, h=[h,h,,h]t is the radial basis vectors of network, h is the Gauss function,which showed as forula : h exp b r k C () Where eans,,, B is the base width paraeters based on node, b is greater than zero, C is the the center vector of -th node of the network, C eans [c,,c]t, B eans [b,,b]t. The weight vector of network as follows: W [ w,, ] w T (3) The network input of RBF was showed in forula 3: u n k h w h w h w (4) Where is the counts of hidden layer neurons of RBF neural network. The law of control was shows as below: u k u k u k p n The perforance indicator of Neural network adustent was showed in forula 5: (5) E n k u k uk (6) In the current applications of RBF neural network, soe paraeters should be deterined, such as the counts of hidden layer neurons, a center vector of RBF, the width of the base function b and each connection weight w fro hidden layer to output layer. In this article, d is selected as the center distance. Base width is b d L. The weight of output unit is calculated by the gradient descent. The iteration algorith of output weight w, node center c and node base width b for the RBF neural network is given as follows: w kw k y ky kh w k w k (7) TELKOMNIKA Vol., No. 9, Septeber 03:

6 TELKOMNIKA ISSN: c b c i i c yk y k w k b k b b k b k k c k c c k c k i i x b i i i (8) (9) (0) b X C yk y k w h 3 b () Where is the learning rate, is oentu factor. Because the gradient descent ethod is easy to fall into local optial value, slow convergence speed, aiing at this proble, this paper adopts an iproved algorith, which is the variable step size gradient descent ethod. So an appropriate learning rate is a ain factor affecting the control results. In order to avoid the instability of network initial training value, ake the training weights up out the local optiu, this paper presents a variable step gradient descent ethod. k k e e ek k k ek ek () (3) 4.3. Paraents of Controller based on the BRF Tuning PID The PID control syste (Figure8) based on RBF network can be obtained by increental PID controller. Figure 8. PID Control Syste based on RBF Network The control error is given as following: e k r k y k (4) The three inputs of PID is given following as : ek ek xc (5) xc xc ek 3 e k ek ek (6) (7) Control algorith is given as: RBF Neural Network PID for Bilateral Servo Control Syste (Zhang Jingdong)

7 506 ISSN: u( k) u( k) k ( e( k) e( k )) k e( k) k ( e( k) e( k ) e( k )) p i d (8) The tuning index of neural network is selected as: E k e k (9) The gradient descent ethod is used for adustent of kp, ki, k d : alost equal to E E y u y kp ek xc k y u k u p E E y u y ki ek xc k y u k u i E E y u y kd ek xc k y u k u d p i d y Where, can be obtained by the identification of neural network. The u k y u k k y y u k u c x w h b u k, and x x is a one diensional vector of the u, then. u w w h k exp k uk uk x So we can obtain: y u k k y u x c b w h b k c wh k b x c x (0) () () y k u k (3) (4) is 5. Syste Siulation and Analysis Coparison The bulk odulus of liquid is selected as 700MPa. Liquid density is selected as 855kg/3. Piston diaeter of Hydraulic cylinder is selected as Piston diaeter of Hydraulic cylinder is selected as Flow coefficient of the valve port is selected as Load viscous daping coefficient is selected as 8KN/(/s), Aplifier gain is selected as 50A/V. Coefficient of proportional valve is selected as 3X0-6/A. The natural frequency of the hydraulic cylinder is selected as 4.6rad/s. Relative daping coefficient is selected as There can be derived the open-loop transfer function of syste according to the paraeters above: TELKOMNIKA Vol., No. 9, Septeber 03:

8 TELKOMNIKA ISSN: Ys ( ) 5894 Gs () Us () ss ( 74.4s 34596) (5) In the RBF tuning of PID control, the three paraeters of PID control were given as follows: Kp is 30, Ki is zero, Kd is 0.3. Take the Sapling tie as s, network weights learning paraeter η as 0.5 and α as The network structure is 3-4-, take rando nubers between zero and one as the Network initial weights w, take paraeter values of the Gaussian function C as [-3-3]T and B as [ ]T. Figure 9. The Displaceent and Force Curve of Force Feedback Directly Type (PD) Figure 0. The Displaceent and Force Curve of Iproved Parallel Control Strategy Diagra (PD) The siulation results show in figure 9-0. A result of using PID control ethod is shown in Figure 9, results of the RBF tuning PID control strategy is shown in Figure. Fro in the Figure 9, there exists the position error when the aster hand with force feedback bilateral servo control strategy follows the slave hand, which the ain hand lags fro hand. Force feedback signal has local shock relative to operator anipulates, affects the stability of the syste. It can be seen fro Figure 0, with the iproved parallel bidirectional control strategy, due to the salve controlling signal was controlled by the deviation of the position and the force existed between aster and slave force, it akes the slave follow the aster s oveents synchronously, the syste response speed was greatly iproved. Fro the Figure, the active anipulator is better than the slave anipulator overall at displaceent of the following features. The active anipulator can follow the slave RBF Neural Network PID for Bilateral Servo Control Syste (Zhang Jingdong)

9 508 ISSN: anipulator well. But for the reason of RBF neural network with learning tie delay itself and uncertainty of control syste, syste is not stable or shock at part. Local displaceent oscillation phenoena can be found out clearly in the process of location to follow fro this figure. Figure. The Displaceent Curve and Force Curve of RBF Tuning PID 6. Conclusion Through analyzing the previous side-by-side type bilateral servo control strategy, then we propose the RBF tuning PID control strategy, which can ake the BRF neural network optiize by the three paraeters of PID, and achieve the ai about dynaic perforance of initiative hand with follower hand. Results of the siulation indicate that the control eans and the control principles raised by testing syste can achieve the ai of following features. In addition, the arithetic is siple and reliable, fast constriction, Good real-tie, strong robustness and fast response. In the eantie, it offers the basis of theory and experient about father studying side-by-side type bi-directional servo control strategy. Acknowledgents The authors wish to thank the helpful coents and suggestions fro y colleagues. This work is supported by the study fund of Sichuan province science and technology support proects at Chengdu (No.0GZX0065). References [] Junren Gu. Tele-operation aster-slave anipulator. Atoic Energy Press. 98 [] Hirokuni BEPPU. Tele-operation of hydraulic excavator with aster-slave syste. Hosei University Graduate School of Engineering Bulletin. 005; 46. [3] Hitoshi Kino, Shigeru Yabe, Ryo Hurutani, Sadao Kawaura. Developent of Force Display Syste using Serial-link Structure driven by Parallel-wire Mechanis. Reports of the Electronics Research Laboratory, Fukuoka Institute of Technology. 003; 0: [4] Kaereier P, Kron A, Hoogen J, Schidt G. Display of holistic haptic sensations by cobined tactile and kinesthetic feedback. Presence: Teleoperators and Virtual Environents.004; 3(): 5. [5] Petzold B, Zaeh M, Faerber B, Del B, Egereier H, Schilp J, Clarke S. A study on visual, auditory, and haptic feedback for assebly tasks. Presence: Teleoperators and Virtual Environents. 004; 3(): 6. [6] Li Shiyong, Fuzzycontrol neurocontrol and intelligent cybernetics. Harbin The Press in Harbin Institute of Technology. 996 [7] Tao Yonghua, Yin Yixin, GeLusheng, Novel PID control and its application. Beiing MechanicalIndustry Press. 998 [8] Karasakal Onur, Guzelkaya Mude, Eksin Ibrahi,Yesil Engin, Kubasar Tufan. Online tuning of fuzzy PID controllers via rule weighing based on noralized acceleration. Engineering Applications of Artificial Intelligence. 003; 6(): TELKOMNIKA Vol., No. 9, Septeber 03:

10 TELKOMNIKA ISSN: [9] Li Liang, Xie Jian, Huang Jianzhao. Fuzzy adaptive PID control of large erecting syste.journal of Theoretical and Applied Inforation Technology. 03; 47(): [0] Yin ialin. Rsearch on the optiization PID paraeters based on genetic algorith. Journal of Convergence Inforation Technology. 0; 7(): [] Hultann Ayala, Helon Vicente, Dos Santos Coelho Leandro. Tuning of PID controller based on a ultiobective genetic algorith applied to a robotic anipulator. Expert Systes with Applications. 0; 39(0): [] Shi Yong, Qi Zi-Da, Zhang Lian-Yu, Zhang Hong-Guang. Application of CMAC neural network coupled with PID controller on speed control of diesel generating set. Transactions of CSICE (Chinese Society for Internal Cobustion Engines). 0; 30(6): [3] Lu Wei, Yang Jianhua, Liu Xiaodong. The PID controller based on the artificial neural network and the differential evolution algorith. Journal of Coputers (Finland). 0; 7(0): [4] Gharghory Sawsan, Kaal M, Hanan A. Adaptive utation PSO for optiu design of PID controller in robotic ar. Mediterranean Journal of Measureent and Contro. 0; 8(4): [5] Daogang Peng, Hao Zhang, Conghua Huang, Jiaun Lin, Hui Li. Study of Iune PID Networked Control Syste Based on True Tie. Journal of Networks. 0; 6(6): [6] Xiaofan li. Design of PID Controller Based on RBF Neural Network.Ordnance Industry Autoation. 009; 8(): [7] Gong Mingde, Zhao Dingxuan. Research of Electro-hydraulic Position Servo with Force-feedback. Transactions of the Chinese Society for Agricultural Machinery. 003; 34(): [8] Wen Guang, Zhao Dingxuan. Bilateral hydraulic servo control syste based on force sense for teleoperated engineering robot. Journal of Jilin University. 006; 36(6): [9] GC Burdea. Force and Touch Feedback for Virtual Reality. Wiley-Interscience. New Yowk [0] Takagi T, Sugeno. Fuzzy identification of syste s and its application to odelling and control. IEEE Trans, Man and Cybern. 985; 5(I): 6-3. [] J Ware, YJ Pan. Realisation of a bilaterally teleoperated robotic vehicle platfor with passivity control. IET Control Theory & Applications. 0; 5(8): [] E Slawinski, VA Mut, P Fiorini, LR Salinas. Quantitative Absolute Transparency for Bilateral Teleoperation of Mobile Robots Systes. Man and Cybernetics. Part A: Systes and Huans. IEEE Transactions on. 0; 4(): [3] S Kudoi, H Yaada, T Muto. Developent of a hydraulic aster-slave syste for tele-robotics haptic-display device for usage of a hydraulic servo-syste. Proc. of st FPNI-PhD Syp. Haburg 000: [4] S Kudoi, H Yaada, T Muto. Developent of a Hydraulic Parallel Link Force Display Iproveent of Manipulability Using a Disturbance Observer and its Application to a Master-slave Syste. Joural of Robotics and Mechatronics. 003; 5 (4): [5] Wei Gao, Zhirong Guo. Speed Sensorless Control of PMSM using Model Reference Adaptive Syste and RBFN. Journal of Networks. 03; 8(): 3-0. RBF Neural Network PID for Bilateral Servo Control Syste (Zhang Jingdong)