Remote Control of an Inverted Pendulum System for Intelligent Control Education

Transcription

1 Remote Control of an Inverted Pendlm System for Intelligent Control Edcation Sel Jng Intelligent Systems and Emotional Engineering Laboratory Department of Mechatronics Engineering Chngnam ational University, Daeeon, , Korea and Jae Koo Ahn Intelligent Systems and Emotional Engineering Laboratory Department of Mechatronics Engineering Chngnam ational University, Daeeon, , Korea ABSTRACT This paper presents a remote control tas of an inverted pendlm system for intelligent control edcation The inverted pendlm moving on the gided rail is reired to maintain balancing while it follows the desired traectory commanded remotely by a oystic operated by a ser Position commands for the inverted pendlm system are given by a oystic throgh the networ The inverted pendlm system is controlled by a neral networ control method The corresponding control reslts are confirmed throgh eperimental stdies Keywords: Inverted pendlm system, remote control, intelligent control edcation 1 ITRODUCTIO Recently, control edcation has become more important in a control engineering field since the state-of-the art technologies demand more sophisticated control algorithms It is tre that proportional-integral-derivative (PID) controllers have been dominantly sed in manfactring indstries for their simplicity and stability However, as technologies develop rapidly, advanced control methods are gradally demanded for reglating sophisticated and complicated control systems to satisfy highly specified performances For effective edcation of advanced control methods to stdents, control theories shold be eplained along with eperimental demonstration Eperimental stdies will help stdents to nderstand control theories with ease and can compensate for the lac of simlation stdies for advanced control applications since real world has to deal with many ncertain problems The inverted pendlm systems have been dominantly sed as a control system test-bed since they have several particlar characteristics Firstly, a single inpt controls two otpts, an angle and a position, which is considered as a single-inpt mltiple otpt system One single inpt has to control two variables, angle and position to satisfy desired position tracing while balancing Ths, sitable combinations between angle control and position control provide sccessfl performances Secondly, the inverted pendlm system is also a nonlinear system, bt can be linearized Lastly, the system is costly effective that can be easily implemented A single motor and necessary hardware along with a inverted pendlm body are reired Cost of eperimental apparats for edcation is mostly concerned since many copies of the same system are reired These characteristics lead to enormos interest of sing it as a prototype control system in the control edcation class Particlar reasons are to illstrate the concept of nonlinearity and challenge of control In addition, the control concept of balancing mechanism can be applied to many other control applications sch as control of balancing hmanoid robots, two wheeled mobile robots, single wheeled mobile robots, and other balancing systems Many control algorithms have been proposed and applied to varios modified types of the inverted pendlm system since its challenging characteristics are evolving Recently, endowing intelligence to the control systems has been vastly increased along with growing of hman desires One control sbect called an intelligent control area has been enormosly epanded and has drawn attention of many researchers as technologies develops fast and systems become more complicated Two feasible candidates for intelligent control applications are fzzy logic and neral networ Fzzy controllers are poplarly sed in commercial prodcts sch as consmer appliances and mechatronics systems Recently, neral networ is gaining many interests since its strctre is similar to hman brain whose fnctions are learning and adaption capabilities that system learns and adapts environment gradally by reinforcement Many researches on control of inverted pendlm system have been presented in the literatre [1-8] Fzzy controllers are sed to control the nonlinear systems [1, 2] Rotational inverted pendlm systems have been presented [4] Inverted pendlm systems with two or three lins have been presented [7, 8] ISS: SYSTEMICS, CYBERETICS AD IFORMATICS VOLUME 9 - UMBER 4 - YEAR

2 Fig 1Teleoperation of an inverted pendlm system The aim of this paper is to apply neral networ to intelligent control edcation In the framewor of neral networ control edcation, two edcational goals, intelligent control and remote control are presented althogh time delay isse is not considered in this paper [9] Radial basis fnction (RBF) neral networ is implemented as a neral controller for controlling an angle and a position of the inverted pendlm system at the same time Bac-propagation learning algorithm for the neral networ is presented and embedded on the hardware to achieve real-time control Position of the inverted pendlm system is commanded by a oystic as the desired position A ser controls the oystic to command the movements of the inverted pendlm system remotely Then the inverted pendlm follows the position command while it maintains balance of the angle Eperimental environment of remote control of the inverted pendlm system by the oystic is bilt as shown in Fig 1 Eperimental wors of sing a neral networ controller along with a PID controller are demonstrated and their reslts are compared 2 PID COTROL SCHEME The PID control method is sed in controlling an angle and a position The balancing angle error of the inverted pendlm system is defined as e, (1) = d - where is the desired angle vale which is 0 and is the d actal angle The angle error passes throgh the PID controller where d Fig 2 PID control strctre is the desired position vale received from the oystic and is the actal position The detailed PID controller otpt becomes e + e + e dt, (4) p where,, are controller gains p d i d Each controller otpt is added together to generate a force inpt to the system The total control inpt is i ò = + (5) The PID control bloc diagram for the inverted pendlm system is shown in Fig 2 The oystic command is considered as the desired traectory after an appropriate filtering process d 3 RBF EURAL ETWORK STRUCTURE eral networ has a massive parallel processing strctre which reires a fast processor to perform many calclations in on-line The radial basis fnction (RBF) networ among many neral networs is sed since it has a linear otpt sch that nonlinear fnction is not sed in the otpt layer There are no weights between the inpt layer and the hidden layer which is a different strctre from the mlti-layered perceptron (MLP) networ The RBF networ also ses the Gassian fnction as a nonlinear fnction However, the nmber of weights to be pdated is 4 which is same as the one layered MLP networ The RBF strctre is shown in Fig3 The Gassian fnction sed in the hidden layer is e + e + e dt, (2) p d i ò 2 e - m y ( e) = ep( - ) 2 2s (6) where,, are controller gains p d i The position error of the inverted pendlm system is defined by e =, (3) d - where e is the inpt vector T e = [ e 1e2 e n ] which is the error vector, m is the center vale vector of the th hidden nit, and s is the width of the th hidden nit The forward th otpt in the linear otpt layer can be calclated as a sm of otpts from the hidden layer 50 SYSTEMICS, CYBERETICS AD IFORMATICS VOLUME 9 - UMBER 4 - YEAR 2011 ISS:

3 Fig 4 RCT neral networ control bloc diagram Fig 3 RBF neral networ strctre M f = åy w + b (7) =1 where y is th otpt of the hidden layer in (6) and w is the weight between the th hidden nit and th otpt, and b is the bias weight In the RBF networ, the nmber of pdated weights is 4 sch as m, s, w, and b 4 EURAL ETWORK COTROL SCHEME Reference Compensation Technie(RCT) PID controllers are dominantly sed and wor for balancing angle control Bt they have the difficlty of control desired position at the same time especially when distrbances are present Ths, the proposal is to add a neral networ along with PID controller to improve tracing performances nder oter distrbances eral networ has the capability of compensating for nonlinear ncertainties in the system When neral networ is sed as a controller, development of an on-line learning algorithm is the most important technie to be solved One of neral networ control algorithms is the reference compensation technie (RCT) Fig 4 shows the concept of RCT that has neral networ at the inpt traectory level [3,6,10,11] The idea of the RCT scheme is for neral networ to locate at the inpt traectory level to compensate for ncertainties in the system as shown in Fig 4 The reference inpt r is added to the neral networ otpt f to generate modified the errore The modified error e is different from the otpt error e = r-y The modified error is given by where r is the desired inpt, and f is from the neral networ otpt After passing the controller, we have = K e + f ) (9) ( Define the training signal to be minimized as v = Ke Then (9) becomes the closed loop error eation given below v = f - Kf, (10) where f is the system dynamic eation and K is the controller gain For deriving learning algorithm, we define the obective fnction to be minimized as 1 v 2 E = 2 (11) The bac-propagation algorithm is reired to calclate the gradient fnction below E Dw( t) = -h w f = hkv w (12) where h is the learning rate Then weights are pdated at each sampling time as w( t + 1) = w( t) + Dw( t) (13) Therefore, in the learning algorithm point of view, the RCT control scheme becomes eventally same as the feedbac error learning control scheme ecept controller gain [12] However, compensation at the oter control loop withot bothering the internal control strctre is one of most important advantages Reference Compensation Technie for Inverted Pendlm e = r - y + f = e + f (8) According to the previos RCT control scheme [6,13], the detailed PID controller otpts for the inverted pendlm system are described as ISS: SYSTEMICS, CYBERETICS AD IFORMATICS VOLUME 9 - UMBER 4 - YEAR

4 Position(m) n Fig 5 eral networ control strctre p ( e + f1) + d ( e + f2 ) + i ( ò e dt + f3 ) n p( e + f4) + d( e + f5) + i( ò edt + f6) where f is the ith neral networ otpt i The control inpt to the system is where, n n (14) (15) = + (16) =, d i v + F + F v = c +, c pe + e + ò e dt c pe + d e + i ò e dt F f + f +, F f + f + p 1 d 2 if3 The training signal v is defined as p c, 4 d 5 if6 Angle(rad) Time(ms) (a) position Time(ms) (b) Angle Fig 6 Simlation reslts v = - F + F ) (17) ( To minimize the error v, the obective fnction defined in (11) is minimized The detailed bac-propagation algorithm reires differentiating (11) with respect to the weight vector w as E E v v F F = = v = -v( + ) (18) w v w w w w The detailed neral networ control strctre for the inverted pendlm system is shown in Fig 5 Delayed errors are inpts of neral networ and neral networ otpts are added to each component of PID controllers The internal PID controlled bloc has the oter loop of compensating for ncertainties to form the closed loop controlled system pendlm system is reired to move to 05 m while balancing Fig 6 shows the simlation reslts We see that the balancing angle and the cart position are well reglated Eperimental setp 6 EXPERIMETS Control environment of the inverted pendlm system has been setp as shown in Fig 7 The system is composed of an inverted pendlm actated by a dc motor, a compter, a oystic, and control hardware The pendlm moves on the gided rail At the end of gided rail, limit switches are attached to protect movement beyond the allowable distance 5 SIMULATIO Position and angle control of the inverted pendlm system are simlated by sing a neral networ control method Initial angle is 018radian and position is 0 m Then the inverted 52 SYSTEMICS, CYBERETICS AD IFORMATICS VOLUME 9 - UMBER 4 - YEAR 2011 ISS:

5 performance of the inverted pendlm system by the oystic movements sch that the pendlm follows the desired position while balancing Fig 7 Eperimental setp The positional command from the oystic can be obtained from a PC and the PC sends it to a DSP throgh serial commnication Then, the DSP performs control algorithms, PID and neral networ to generate a control inpt tore signal A FPGA board generates PWM signal and send it to the motor driver to drive a dc motor Control hardware bloc diagram is shown in Fig 8 Main processors are a DSP and an FPGA There are two encoders, one for the position and another for the angle The FPGA processor receives two encoder data, conts them, and commnicates with the DSP to generate a plse-widthmodlation (PWM) signal to the motor driver Fig 9 Balancing control eperiment at the beginning Fig 10 Joystic command control for inverted pendlm Fig 8 Overall strctre Eperimental reslts Position tracing control eperiments of the inverted pendlm system are condcted Initially, the pendlm balances itself as shown in Fig 9 Then a ser moves the oystic to generate desired position commands Figre 10 shows the control ISS: SYSTEMICS, CYBERETICS AD IFORMATICS Figre 11 shows the corresponding plots of eperimental reslts Figre 11 (a) shows the desired traectory commanded by the oystic and filtered commands Since the command from the oystic is not smooth and rogh, it is reired to be filtered ot to generate smooth traectory command for the pendlm to follow Figre 11 (b) shows the actal tracing reslts with desired commanded traectory In Figre 11 (b), the inverted pendlm maintains balancing withot the oystic command at the beginning, and then it follows the oystic commands of twice oystic operations of psh and pll Each psh and pll oystic operation taes abot 7 seconds Althogh there are small tracing errors, the pendlm sccessflly follows the desired traectory while balancing It is tre that faster movements of the oystic cannot satisfy position tracing performances since the bandwidth of the inverted pendlm is low compared with that of hman movements VOLUME 9 - UMBER 4 - YEAR

6 Position(mm) Desired Filter performance and stdent evalations on this test-bed will be investigated ACKOWLEDGEMET This paper has been presented in World Mlti-conference on Systemics, Cybernetics and Informatics(WMSCI 2010) and recommended for the sbmission to Jornal of Systemics, Cybernetics and Informatics This research was financially spported by Korea Research Fondation (KRF) throgh the basic research program (R ) Position(mm) Time(s) (a) Joystic command traectory Position Desired Time(s) (b) Enlarged position tracing reslt for the oystic command Fig 9 Position tracing performance 7 COCLUSIOS The remote position control of the inverted pendlm system is presented Remote control test-bed is developed and integrated for intelligent control edcation based on neral networ control application eral networ along with PID controllers is sed and implemented on the hardware to control the angle and the position simltaneosly in on line fashion The reference compensation technie control algorithm is sed for the RBF networ is to improve performances of the cart position of following the traectory commanded by the oystic remotely The test-bed can be sed for eperimental stdies of stdents who tae an intelligent control sbect Althogh remote control of the inverted pendlm system is sccessfl, time delay isse which is the most important problem in the remote control applications is not considered in this research Frther improvement on intelligent control REFERECES [1] T H Hng, M F Yeh and H C L, A PI-lie fzzy controller implementation for the inverted pendlm system, Proc of IEEE Conference on Intelligent Processing Systems, 1997, pp [2] M E Magana and F Holzapfel, Fzzy-logic control of an inverted pendlm with vision feedbac, IEEE Trans on Edcation, vol 41, no 2, 1998, pp [3] S S Kim and S Jng, Hardware implementation of a real time neral networ controller with a DSP and an FPGA board, IEEE ICRA, 2004, pp [4] M W Spong The swing p control problem for the acrobat, IEEE Control Systems Magazine, 15, 1995, pp [5] W White, and R Fales, Control of doble inverted pendlm with hydralic actation : a case stdy, Proc of the American Control Conference, 1999, pp [6] S Jng and H T Cho, "Decentralized neral networ reference compensation technie for PD controlled two degrees of freedom inverted pendlm, International Jornal of Control, Atomations, and Systems, vol 2, no 1, 2004, pp [7] H Fer and D Enns, An application of dynamic inversion to stabilization of a triple inverted pendlm on a cart, IEEE Conf on Control Applications, 1996, pp [8] J Shen, A K Samyal, Chatrvedi, D Bernstein, and H McClamroch, Dynamics and control of a 3 D pendlm, IEEE Conf on Decision and Control, 2004, pp [9] H J Choi and S Jng, eral networ-based Smith predictor design for the time-delay in a tele-operated control system, Artificial Life and Robotics, vol 14, no 4, 2009, pp [10] G H Lee, J S oh, and S Jng, "Decentralized Implementation and eperiment of neral networ controllers for intelligent control system edcation International Jornal of Fzzy Logic and Intelligent Systems, vol 7, no 4, 2007, pp [11] D H Song, G H Lee, S Jng, eral networ compensation technie for standard PD-lie fzzy controlled nonlinear systems, International Jornal of Fzzy logic and Intelligent Systems, vol 8, no 1, 2008, pp68-74 [12] M Miyamoto, M Kawato, T Setoyama, and R Szi, "Feedbac error learning," eral etwors, vol 1, 1988, pp [13] S Jng, H T Cho, and T C Hsia, " eral networ control for position tracing of a two-ais inverted pendlm system: Eperimental stdies, IEEE Trans on eral etwors, pp SYSTEMICS, CYBERETICS AD IFORMATICS VOLUME 9 - UMBER 4 - YEAR 2011 ISS: