Design of an Adaptive Neural Network Controller for Effective Position Control of Linear Pneumatic Actuators

Transcription

1 Researh Artile International Journal of Current Engineering and Tehnology E-ISSN , P-ISSN INPRESSCO, All Rights Reserved Available at Design of an Adaptive Neural Network Controller for Effetive Position Control of Linear Pneumati Atuators Osama. A. Montasser Ȧ* and B. A. El-Sayed Ḃ Ȧ Mehanial Power Engineering, Ain Shams University, Cairo, Egypt, on leave to join the British University in Egypt, BUE Ḃ Sakr Faroty, The Arab Organization for Industrialization (AOI, Cairo, Egypt Aepted 05 Ot 04, Available online Ot 04, Vol.4, No.5 (Ot 04 Abstrat The main target of this work is to design an appropriate position ontroller for a pneumati system using artifiial neural networks. The rod position of a double ating pneumati ylinder, ontrolled by proportional linear valves, was hosen as the present ontrol system. A mathematial dynami model for the pneumati system was derived. The model shows, as it is expeted, that the pneumati system is of highly nonlinear features. This is due to ylinder-piston mehanial frition, the ompressibility feature of air, and nonlinear harateristis of the flow through a valve orifie of variable area. The model shows, as well, that pneumati system is of time varying harateristis. A Proposed Neural Network Controller, PNNC, is designed and implemented. The PNNC is a rule-based ontroller, where both the slope and amplitude of the ativation funtion of eah neuron is adapted to enhane the ontrol system performane. A onsiderable improvement of the system response for different input onditions is ahieved by applying the PNNC on the present ontrol system. The robustness and effetiveness of the proposed ontroller were verified through omputer simulations using MATLAB pakage and SIMULINK toolbox. A omparison with the Conventional Neural Network Controller, CNNC and the typial PID ontroller, assured that the present PNNC is robust and more effiient in terms of both the system stability and speed of response. Keywords: Aurate Position Control, Adaptive Learning Algorithm, Neural Network Controllers, Pneumati Atuators, Sigmoid Ativation Funtion.. Introdution Hydrauli atuators are relatively easy to be positional ontrolled than the pneumati atuators. This is due to the high nonlinearity assoiated with pneumati media flow. A self-tuning fuzzy PID ontroller was suessfully developed and applied to an eletro-hydrauli atuator by (N. Ishak et al,. The proposed ontroller offers promising apabilities to guarantee the position traking auray of their hydrauli system. However, Pneumati atuators are now a reognized alternative tehnology to other hydrauli and eletri ounterparts in areas of high speed, medium power appliations (J. Moore and C. Wong, 000. Pneumati systems are apable of providing suitable power output at relatively low ost, in addition they are lean, of light weight and an be easily servied. Pneumati atuation has been mainly used in the form of logi ontrol systems. Many appliations in industry use pneumati power in open loop ontrol systems where the strokes of the moving parts are usually fixed using mehanial stops. However, many other appliations require the position ontrol of pneumati ylinders suh as, robots, gating systems and *Corresponding author: Osama. A. Montasser CNC mahines. (N. Tillet et al, 997 provided that pneumati systems have been limited to a simple end-stop appliation beause of the diffiulty of providing proportional ontrol of the rod position. This diffiulty stems from the nonlinear nature of air as power transmission medium and non-linearity assoiated with pneumati omponents (M. Shih and M. Ma, 998. (Verseveld and Bone, 997 proposed position ontrolled pneumati atuator. This pneumati system onsists of a double ating ylinder, with low frition option, onneted to a horizontal linear slide. A pneumati brake mehanism is inorporated within the linear slide to lok the atuator firmly in its position one the desired steady state auray is ahieved. Two standard three-way solenoid valves were used. The valves were atuated using a Pulse Width Modulation algorithm, PWM. A PID ontroller with added frition ompensation and position feed-forward is suessfully implemented. As it is well known, PID ontrollers are widely used for proess ontrol beause of their good performane. However, it is very diffiult to self tuning the ontrol parameters of these ontrollers. (K. Fujiwara and Y. Ishida, 995 desribed a method of using neural networks to self-tuning the PID ontrollers for pneumati ylinders. They show simulation and 3498 International Journal of Current Engineering and Tehnology, Vol.4, No.4 (Ot 04

2 experimental results to demonstrate the effetiveness of their model. (M. Shih and M. Ma, 998 have proposed the applying of a fuzzy ontrol tehnology to ontrol the position of a pneumati ylinder. In their work, a modified differential PWM ontrol method was applied. There are numerous works applied artifiial intelligene in the ontrol appliations but few of them are used in pneumati ontrol systems. (X. Cui and K. Shin, 99 used an Artifiial Neural Network Controller, ANNC, to ontrol the middle-point temperature in a thermal power plant. The ANNC was designed to deal with the nonlinearity due to negative effets of long response delays, saturation onditions and proess noise. The ontroller onsists of four-layer, with two hidden layers, pereptrons. Their work introdued a simple algorithm based on the Bak-Propagation, BP, for a lass of nonlinear systems, typified by proess ontrol appliations. The proposed NN ontroller is trained using the system s output errors diretly, with little a priori knowledge of the ontrolled plant. (M. Abdelhameed, 999 introdued an adaptive neural network ontroller for traking a robot of n-degree-offreedom. The learning algorithm is based on the adaptive updating of the weights of the network to minimizing the quadrant traking error and its derivative of eah robot arm. (G. Geng and G. Geary,997 proposed a method whih uses neural networks together with reursive least square algorithm to model nonlinear proesses. (G. Cembrano et al, 997 desribed the use of Cerebellar Model Artiulation Controller (CMAC networks for the adaptive dynami ontrol of an orange harvesting pneumati robot. A neural-network model was preferred sine it provided better approximation apabilities. Finally, it is notied that the appliation of onventional ontrol methods on position ontrol of pneumati systems have some restritions. Furthermore, there are relatively few works related to the appliation of artifiial neural network ontrollers in the field of pneumati atuation systems. It therefore, the main issue onsidered in the present work is to design an appropriate position ontrol system for a pneumati atuator using artifiial neural networks. The Artifiial Neural Network Controller, ANNC was hosen to position ontrol the piston movement of the present pneumati system. This is deided to get the benefits of its intelligene and learning apability needed to ope with the higher inflexibility and nonlinearity of the pneumati systems. A rule based NN ontroller is proposed, tested and found to suessfully ahieve a good traking ontrol performane and is robust to sever hanges in the applied load as well. The present paper is organized as follows. In the following setion, mathematial and state spae models of the present pneumati system are derived. An introdution to the artifiial neural network based ontrollers is reviewed afterward. In the next setion, the Conventional on-line self learning based Neural Network Controller, CNNC, is introdued. The omputational steps used to build a CNNC are listed in subsequent setion. A rule based neural network ontroller is proposed and designed in the following setion, PNNC. Results of the present CNN and PNN ontrollers are onsequently disussed. The onlusions of this study are summarized in the last setion.. Modeling of the present pneumati system In this setion a state spae model of the present pneumati system to be positional ontrolled is derived. Desription of the system is presented and the mathematial model of eah of its omponents is derived... Pneumati system desription Fig. Layout of the present pneumati system The present pneumati system is shown in Figure. It onsists of a double ating ylinder, linear pneumati atuator, ontrolled with two proportional valves, v and v, and arrying an external load M l. Air is disharged from a pressurized air supply to the right hand side of the ylinder through valve, v. The air is disharged from the ylinder to the atmosphere through valve, v. The pressure at the left hand side of the ylinder is held onstant by attahing it with a large aumulator, air pressure in whih, P l, is.9 bar. The funtion of the aumulator is to maintain a reasonable differene of air pressure between right and left sides of the ylinder. This redues the nonlinearity assoiated with large pressure differene between both sides of the ylinder. The value of the supply pressure, P s is fixed at six bar. When v is opened and v is losed, the air flows through v to the right side of the ylinder, whih is initially at fore balane state, to inrease its pressure, P. As P inreases, the piston of the ylinder moves to the left to the desired position, y ref. v is kept opened, as the position of the piston y(t is less than the desired piston position y ref. When the piston position y(t exeeds the desired piston position, y ref, v is losed and valve v is opened to reverse the diretion of the piston motion to the right. The air at the right side of the ylinder disharges to 3499 International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

3 the atmosphere and P thus dereases. This lets the piston moves to the desired position at the right side and when reahed, the valve v is losed... Mathematial modeling In order to derive the governing equation for the motion of the ylinder piston, the momentum equation is onsidered as follows: M y P A P A f y ( l pr l pl Where: P, P l are the air pressure at the ylinder right and left side respetively and A pr and A pl are the ross setional areas of right and left sides of the ylinder respetively, f is the visous damping oeffiient, y and y are veloity and aeleration of the piston rod and M l is the equivalent mass of piston head and the load. The energy equation is applied to obtain a mathematial model for pressure dynamis of the air in the ylinder. Variation in air pressure at the ylinder left side, P l, is ignored sine it is onsidered onstant due to the aumulator effet. Considering the right side of the pneumati ylinder as a thermodynami ontrol volume, the governing equation for air pressure P is obtained by applying the energy equation as follows: d m u m C T m C T dv Q P p p s ( dt dt Where: m and m are the air mass flow rates through valves v and v respetively, Q is the rate of heat transfer aross the ylinder wall, P, V, m and u are pressure, volume, mass and speifi internal energy of air at the ylinder right side, P dv dt is the rate at whih work is done on the moving piston, T s is the supply air temperature and T is the air temperature at the ylinder right side, C m T m T is the enthalpy differene through the p s ontrol volume boundaries and dm u dt is the rate of hange of internal energy of the ontrol volume. Sine the mass transfer through the system is muh faster than the heat exhange through the system boundary, so, Q an be negleted. It was thus reasonably assumed that the system undergoes an adiabati proess. Applying thermodynamis relations for ideal gases, equation ( is redued to: dp dt P dv. V dt R V T m T m Where: is speifi heat ratio, R is the air gas onstant. While opening valve v, the status of air mass flow rate through it, m, hanges from moment to moment. It may be direted to inter the pneumati ylinder, inflow ( m, or may direted to leave it, outflow ( m. This is due to the high dynamis of air pressure at the right side, P, due to whih, it may take a lower or higher value than that of s (3 the supply pressure, P s. Outflow, m, should take a negative sign when it is substituted in energy equation (3. On ontrary, the air mass flow rate through valve v, m is always direted to the atmosphere, sine P never be lower the atmosphere pressure P a. Relations for m and m are onluded as follows: m (4 Av v v Cdv m (5 Av v v Cdv Where: and ρ is the air veloity and density at the valve orifie, A is the partially opened valve orifie area, A varies from 0% to 00% of the orifie area, and C d is the valve disharge oeffiient. Subsripts v or v refers to the valve number. Relations for the air density and veloity, ρ and, through both proportional valves are obtained by applying the ontinuity equation and the thermodynami relations for ideal gases as follows: Proportional valve Two possible onditions for the redued pressure ratio through the valve, P R, are onsidered, namely the subsoni ondition for P R > 0.58 and supersoni ondition for P R Relations for the two onditions are shown as follows: a Subsoni ondition a- Inflow ondition, P < P s, P R = P / P s > 0.58: P v (6 R T ( P s R R / v Ts ( PR ( ( vav / s As (7 a- Outflow ondition, P > P s, (P R = P s / P > 0.58 : Ps v (8 R T ( P R R / v T ( PR ( ( vav / A (9 where: ρ s is the density of supplied air and A s and A are the ross setional areas of the onnetions of air supply and the ylinder with the valve v respetively. b Supersoni ondition For inflow ondition, supersoni flow is possible and the air density relations are derived as follows: b- Inflow ondition, P < P s, P R = P / P s 0.58 : 0.58 Ps v (0 R Ts 3500 International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

4 v R T s ( b- Outflow ondition, P > Ps: Outflow of air from the right side of the pneumati ylinder to the air supply is always subsoni and annot be supersoni sine P s / P never be possibly less than or equal Proportional valve Sine P > P a in all working onditions, flow of air from the ylinder to the atmosphere through valve is always outflow. a Subsoni ondition, P / P a > 0.58: v Pa ( R T ( P R R / v T ( PR ( ( vav / A (3 b Supersoni ondition P / P a 0.58: 0.58 P v (4 R T v R T Where: P a is the atmosphere pressure..3 State spae model (5 The state spae model of the pneumati system ould be derived as follows: Variables x, x, x 3 are defined as: x y, x x y, x3 P (6 From equations, 3 and 6, the following relations are obtained. x (7 y ax3 a a3x x x 3 x 3 P a4 a5 (8 x x Using the previous derived relations to 5, a to a 5 are alulated as follows: Apr a (9 M a a 3 l l Pl Apl (0 M f ( M l a ( 4 a 5. pr 350 International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04. R ( Ts m T m (3 A The model, derived above, shows that dramati hanges always our in the density of air in pneumati systems. This is due to the high ompressibility essential feature of all gases. 3. Artifiial neural network based ontrollers A great attention has been devoted, in reent years, to the artifiial multilayer neural networks, ANNs, whih have proved to be extremely suessful in pattern reognition and ontrol problems. The main feature of the ANNs is their apability of dealing with nonlinear ontinuous funtions. That is why their appliations for ontrolling omplex nonlinear systems have beome an essential matter. In the present work, an ANN ontroller is proposed to be used in positional ontrol of the present pneumati system. Fig., below, shows the arhiteture of an artifiial neural network of one hidden layer. It onsists of three onseutive layers, namely, the input layer, of n dimensions, the neural network hidden layer, of N neurons, and the output layer, of m dimensions. Eah of the input and the output vetors is onneted with eah neuron of the hidden layer through a synapti weight, whih is a real fration number and is alulated aording to an ativation funtion. We, therefore, have two weight matries, n N dimensional matrix for input-neural network layers onnetions and N m dimensional matrix for neural network-output layers onnetions. The neurons are onneted aording to layered feedforward neural networks method, where a layer of neurons reeives input only from neurons of the previous layers. Various methods ould be used to update the weights of the neural network layer, what is so alled training the ANN, so that for a ertain input to the input layer, we an get the desired output from the output layer. One way is to set the weights expliitly using prior knowledge of the system under onsideration, open loop ontrol. The learning ategories are lassified into two distint types, namely the supervised learning and unsupervised learning. In supervised learning, assoiative learning type, the network, whih is alled self-supervised, is trained by providing it with inputs and the mathing outputs patterns. Fig. Arhiteture of an artifiial neural network of one hidden layer

5 Classi appliations of ANN ontrol systems are of supervised learning, open loop type. Reasonable auray of open loop ontrol using ANN ontrollers is attained for a ertain speified initial-desired output error e initial value. This is ahieved through pre-learning the ontroller for the speified value of e initial to get ontrol ations fairly fitting the inputs to the ontroller. Another way is to train the ANN by using a teahing pattern and letting the network sets its weights ON LINE, unsupervised learning. This is arried out aording to some predefined learning rules and an error performane index minimization algorithm. In the unsupervised learning, self-organizing type, the network is trained to respond to lusters of input patterns. Unlike the supervised learning pattern, there is no a priori ategories set, aording to whih the input-output patterns are to be lassified, rather, the system should develop its own representation of the input-output relationships. 4. The onventional on line self learning based NN ontroller, CNNC Reently, the ANN have been used to ontrol many industrial plants. The online learning by ontinuous mapping between the inputs and output fators of the ontroller enables the use of ANN ontrollers in feed-bak ontrol systems. A multilayer pereptron struture with bak propagation, BP, learning algorithm is one of the most effetive online learning algorithms. It an be used to approximate any ontinuous funtion mapping with any desired auray. For ontrol purposes, the ANN based ontroller utilizes the atual system input error to synthesize the ontrol ation. Sine, in ontrol systems, it is pratially to measure the output from the plant, the ontrolled variable y(t, rather than the output from the NN ontroller. It is therefore, the NN based ontrollers utilize the error in the ontrolled variable, the deviation between the desired and the atual output, e(t = y ref - y(t, to synthesize the ontrol ation. The error in plant output, e(t, is used also in training the NNC or in other words in updating the weights of the neural network layers. When designing the NN ontrol system, the major obstale is to train the NNC using the error in the systemoutput, e(t = y ref y(t, rather than the unknown networkoutput s output. (X. Cui and K. Shin, 99 presented a solution for this problem for onventional neural network based ontrollers CNNC. (X. Cui and K. Shin, 99, adopted the basi priniple of multilayer pereptrons with BP to update the weights of eah pereptron. Their formulas for updating the thresholds and the weights from the input to the output layers are utilized in this work to build a onventional neural network position ontroller CNNC. The piston rod position, y(t, of the present pneumati system, shown in Figure above, is ontrolled using a NN based ontroller. A blok diagram for the present position ontrol system is presented in Figure 3. A neural network ontroller, NNC, is asaded with the pneumati ontrolled system. The NNC output, ontrol ation (t, is used to modify the opening ratio, k, of the valves, v and v, to ahieve the desired ontrolled variable, y ref. Fig.3 A blok diagram for the present position ontrol system Figure 4 shows the basi struture of the present artifiial neural network. The hoie of the ANN s inputs should reflet the desired and atual status of the ontrolled variable. Therefore, the inputs of the ANN ontroller is usually the system s traking errors at the urrent time and at two preeding sampling time intervals, t, e(t, e(t - t, e(t - t. Inputs are seleted to onsider the history of the rate of hange of error signal, e(t, to simulate the integral ation in the onventional PID ontroller. Where t is the sampling time interval used in numerial alulations. t was seleted to be as small as possible to overome the numerial instability. Fig.4 Basi struture of the present artifiial neural network The number of the hidden layers depends on the ontrolled plant under onsideration, and is seleted to be two here in this work. The symbols used in Figure 4 are defined as; X: for inputs, I= N for input layer, N=3 in this work, J= N for the st hidden layer neurons, K= N for the nd hidden layer neurons, N and N are hosen to be 4 in this work, and subsripts, and 3 represent st and nd hidden layers and the output layer respetively. We have only one output from the present NNC, O =. 5. Computational steps of the CNNC Computations of the present NN ontroller, presented in Figure 4, are summarized in this setion. The on line self learned CNNC of (X. Cui and K. Shin, 99 are used here as a onventional position NN ontroller. Their 350 International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

6 formulas for updating the thresholds and the weights from the input to the output layers are utilized in this work. The ativation funtion onsidered for eah neuron is of the sigmoid type. The sigmoid ativation funtion has the form: x t O e (4 Where: x(t is the output of a neuron, O(t is its input, the summation of the outputs of previous layer s neurons multiplied by the orresponding weight fators, (t is a threshold value, and is a slope parameter fixed at unity value for the present CNNC, =. Weight fators, W(t, and thresholds, (t, are initially defined and updated as desribed below. A satisfatory ontrol results ould not be attained before seleting the optimum values of the initial values of all the weight fators, W initials, thresholds, initials, learning rates, initials, and gain fators, initials. Learning rates and gain fators are used to update the weight fators and the thresholds. The seletion of these parameters is very tough and takes a very long time beause it depends on trial and error onept. To simplify the proess all members of eah of the above mentioned parameters are given same initial value. The optimum initial value of any of the parameters is obtained as follows; As the values of the other parameters are kept onstant, the value of the parameters under onsideration is hanged and at eah of its values ontrol performane measures are heked. Performane measures are onsidered as the settling time, the steady state error, and the root mean square of the error. The value of the parameters under onsideration whih gives the best ombination of the three performane measures is hosen as the optimum initial value of the parameters taken into onsideration. The same proedure is repeated for all the other parameters to get, at last, their optimum initial values. It is worth noting that there is a narrow range of initial values for eah of the NNC parameters out of whih the ontrol system is unstable. That is why it is very important to arry out the above mentioned seletion proess not only to get optimum ontrol performane but also to avoid system instability. The CNNC is trained to ahieve a ertain ontrol ondition, e initial = y ref - y initial. Computational steps are arried out aording to (X. Cui and K. Shin, 99 as listed in what follows: - For a ertain speified e initial and =, the initial values, W initials, initials, initials, and initials are seleted as mentioned above. - The outputs of the st HIDDEN layer are omputed at the urrent alulation step (t=0. 3- The outputs of the n HIDDEN layer are omputed at (t=0. 4- The output from output layer, ontrol ation, is omputed at (t=0. 5- Weights from the nd HIDDEN to OUTPUT layers are updated for the next alulation step (t = t + t. 6- Weights from the st HIDDEN to nd HIDDEN layers are updated for (t + t. 7- Weights from the INPUT to st HIDDEN layers are updated for (t + t. 8- The thresholds are updated for (t + t. 9- Steps from to 8 are repeated for the next alulation step (t = t + t. The onventional NN ontroller was found to be a single point ontroller and should be set up for eah different e initial value and for eah piston movement diretion. It is therefore it an t be used for traking position ontrol. A most smart ontroller was proposed by this study, so that a wide range of initial error values an be effiiently ontrolled. The Proposed NNC, PNNC, was heked for traking ontrol in both piston movement diretions and found to be suessful. The PNNC is presented in the next setion. 6. The proposed rule based neural network ontroller, PNNC The PNNC is proposed in this study to over a wide range of ontrol points in both piston movement diretions. The same struture, shown in Figure 4, for the CNNC is used. The slope parameter,, of the sigmoid ativation funtion, Equation 4, is fixed at unity value with the present CNNC, =. The slope value affets the degree of nonlinearity of the sigmoid funtion and thus affets the updating of the NNC parameters. It was found that when the value is hanged the optimum e initial of the CNNC is hanged than that at whih the optimum initial values of its parameters are seleted. So the proposed rule based NN ontroller, PNNC, was onstruted to ahieve a suessful traking ontrol as follows: - For forward piston movement and a unity slope parameter, =, a ertain initial error, e initial = y ref - y initial, is defined and for whih, the optimum initial values of the ontroller parameters are seleted as desribed in setion 5. - Keeping the optimum initial values unhanged, the value of the initial error, e initial, is hanged. At eah value of the initial error, the value of the slope parameter,, is hanged to meet the best ombination of the ontrol performane measures, namely, the settling time, the steady state error and the root mean square of the error value. This is arried out utilizing the trial and error tehnique. 3- A fairly good urve fitting, orrelation fator is almost equal to, is onluded for the optimum ( - e initial data for the forward piston movement. The urve fitting is resulted in a polynomial form as: s a i i0 e i initial of the polynomial terms., Where a i are onstants and s is the number 4- Steps from to 4 is repeated but for the piston bakward movement. So that two ( - e initial relations are obtained, one for eah piston movement s diretion. Having the relations the most suitable value of the slope parameter, is alulated at eah initial error value and for any piston movement diretion, and thus satisfatory ontrol results is ahieved International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

7 Displaement, m 7. Results of the present ontrol system The model of the pneumati ontrolled plant is built and all the simulation tests are arried out using MATLAB pakage and SIMULINK toolbox. forward and bakward position ontrol needs a different initial NN parameters seletion. A typial result for the piston bakward movement position ontrol is shown in Figure Results of the CNNC Typial results of the CNNC are shown in Figures 5 and 6. The figures present the ontrol system response with the onventional NN ontroller. Figure 5 shows the response when the initial error, e initial = y ref - y initial, has a value of 4 m for forward piston movement. This value is the value at whih the optimum values of the ontroller s parameters were determined and mentioned in setion 5 above. It is therefore, the system shows satisfatory results as Figure 5 illustrates. Fig.7 Control system response with CNNC set up for e initial = -.5 m 7.. Results of the PNNC 7... Single ontrol point omparison with the CNNC Fig.5 Control system response with CNNC set up for e initial = 4 m Figure 6 shows different results as the system failed to reah the referene position. The reason is that the initial error is hanged to 5.5 m, the value that is different from the value at whih the NN ontroller s parameters were determined. The PNNC showed a suessful ontrol results, as it is expeted, for single ontrol point in both movement diretions. A single universal set up is needed to over a wide range of ontrol point onditions. While the CNNC set up for e initial = 4 failed to over e initial = 5.5 m as shown in figure 6, the PNNC suesses to over multi ontrol onditions as figures 8 and 9, below, show Traking ontrol results for the PNNC Figures 8 and 9 show traking ontrol results of PNNC for two different traking trajetories. In both trajetories, reasonable settling time and steady state error are ahieved. The figures also show that, in both of movement diretions, the piston shows an osillatory movement forward and bakward on his way from its initial position to its referene position. This is beause of the high nonlinearity behavior of the pneumati systems. Y ref Fig.6 CNNC set up for e initial = 4 m failed to over e initial = 5.5 m The CNNC was tested for bakward piston movement and found to be also suessful for single ontrol point. Of ourse for the same e initial absolute value eah of the Time, s Fig.8 Traking ontrol results with PNNC, trak trajetory 3504 International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

8 Displaement, m Load, % of 5.5kg Displaement, m Displaement, m Displaement, m Y ref Time, s Fig.9 Traking ontrol results with PNNC, trak trajetory 7..3Comparison with the results of the onventional PI ontroller The onventional PI ontroller is tested as a position ontroller of the present pneumati system. to be equal to 0.3, above whih the ontrol system beomes instable. Of ourse this leads to a large settling time. The integral effet was found to redue the settling time but it inreases the system instability, and thus it is exluded. Figure 0 shows a typial omparison between ontrol results of both the PNNC and the P ontroller of the largest possible gain, K = 0.3. The P ontroller shows stable results with large settling time, 5 seonds. The PNNC shows small settling time, seonds, with relatively allowable osillations whih are slowly onverged with time, as shown in the figure. The onventional P ontroller does not give satisfatory results when applied to pneumati systems. So, neural network ontrollers are proposed to do the job. 7..4Testing the PNNC against load disturbane The load disturbane effet on the PNNC performane is shown in Figure. The load value hanges in range of about ± 0.90% of a design load of 5.5 kg. The load disturbane is generated using a white noise generator built in faility of the MATLAB-SIMULINK ommerial pakage. The figure shows the robustness of the PNNC to severe flutuation in the applied load and still showing fairly good results. Y ref Time, s Time, s P ontroller, K =0.3 Y ref Time, s s Fig. Effet of external disturbane ± 90% around a design load of 5.5 kg Time, s PNN C Fig.0 Comparison between ontrol results for the PNNC and the P ontroller The proportional gain, K, has to be very small to avoid system instability. This is beause of the high nonlinearity of the ontrolled plant. The largest value of K was found Conlusions A mathematial nonlinear model is derived for a double ating pneumati ylinder plant. A rule based NN ontroller is proposed, PNNC, and applied to positional ontrol the piston movement of the present pneumati system. The robustness and effetiveness of the proposed ontroller were verified through omputer simulations using MATLAB pakage and SIMULINK toolbox. The performane of the present PNNC was tested against the PI and the onventional NN ontrollers. The main onlusions are extrated as follows: 3505 International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

9 The onventional NN ontroller, CNNC, gives satisfatory ontrol performane for a single ontrol ondition. The proposed NN ontroller, PNNC, suessfully ahieves a good traking ontrol performane for a wide range of ontrol point onditions. 3 The PNNC shows a satisfatory ontrol performane for load disturbane of about ±70% of the load design value. Appendix A The pneumati system initial onditions are set as follows: Initial pressure: 3.5 bar Air tank pressure:.94 bar Supply air pressure: 6.0 bar Supply air temperature: 98 K Air inside ylinder initial temperature: 98 K Air tank initial temperature: 98 K External load: 5.5 kg Cylinder diameter:.5 m Stem Diameter:.0 m Supply tube diameter:.0 m Disharge tube diameter:.0 m Piston stroke: 7.0 m Initial piston veloity: 0.0 m/s Gas onstant: 87 J/(kg K Speifi heat ratio:.4 ANN Controller Parameters The value of the ANN ontroller s parameters, W initials, initials, initials, and initials and the slope parameter were obtained as explained in the paper and listed below for both the forward and bakward piston s movement. Forward Piston Movement The seleted parameters are determined at = and for e initial =.50 m, y ref = 3 m and y initial = 0.5 m were: W initials = 0-6 initials = 0-3 initials = 0-3 initials = 0.. The slope parameter -initial error ( - e initial relation is obtained as 6 a i i0 e i initial Where: a 0 = 0.00, a = , a = 0.638, a 3 = , a 4 = -.466, a 5 = , a 6 = Bakward Piston Movement The seleted parameters are determined at = and for e initial = m, y ref = 3 m and y initial = 6.5 m were as follows; W initials =0-6 initials = 0. initials = 0. initials = The slope parameter -initial error ( - e initial relation is obtained as 6 a i i0 e i initial Where: a 0 = -0.6, a = , a = , a 3 =.58, a 4 = -9.93, a 5 = 6.643, a 6 = 0.83 List of symbols A Cross-setional area, m Subsripts C Cylinder inlet onnetion pl Piston left side pr Piston right side S Supply air onnetion v Valve orifie Valve orifie v ANN Artifiial neural network ANNC Artifiial neural network ontroller BP Bak Propagation C d Coeffiient of disharge, valve C d Coeffiient of disharge, valve C p Speifi heat at onstant pressure F Coeffiient of visous frition CNN Conventional Neural Network CNNC Conventional Neural Network Controller e Error signal y ref y(t m Mass flow rate through valve, kg/s m Mass flow rate through valve, kg/s M l External load, kg weight = 9.8 N NN Neural Network U Internal energy of system, J O Sum of node outputs = inputs to next layer nodes P Pressure, Pa/m Subsripts a Atmospheri Cylinder at right side l Cylinder at left side, Tank side R Redued pressure ratio through the valve s Supply air PNNC Proposed Neural Network Controller PWM Pulse width modulation Rate of heat transfer aross the wall of ylinder, Q W R Gas onstant, J/(kg o k t Time, se T Atmospheri Temperature, o K a T Temperature of air inside the ylinder, o K T s Temperature of supply air, o K V Volume of the right side of the ylinder W Weight of ANN node X Output of ANN node y Piston displaement, m y ref Piston referene position, m y initial Piston initial position, m y Piston veloity, m/s y Piston aeleration, m/s Greek letters Speifi heat ratio Slope parameter Air density at right side of ylinder, kg/m 3 s Supply air density, kg/m International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04

10 v Air density after valve, kg/m 3 v Air density after valve, kg/m 3 Bias of ANN Learning rate of ANN Gain of ANN Referenes N. Ishak, M. Tajjudin, H. Ismail, M. Hezri, Y. Sam, R. Adnan, (0, PID Studies on Position Traking Control of an Eletro-Hydrauli Atuator, International Journal of Control Siene and Engineering, (5,pp Moore J. R., Wong C.B., (000, Smart Components-based servo pneumati atuation systems, Miroproessors and Mirosystems, Vol. 4, pp Tillet N.D., Vaughan N.D., Bowyer A., (997, A Non-linear model of a Rotary Pneumati Servo System, Pro. Instn Meh Engrs, Vol., Pert, pp Shih M.C., Ma M.A., (998, Position Control of a Pneumati Cylinder Using Fuzzy PWM Control Method, Int. Journal of Mehatronis, Vol. 8, pp Varseveld R.B., Bone G. M., (997, Aurate Position Control of a Pneumati Atuator Using On-Off Solenoid Valves, IEEE/ASME TRANS. On Mehatronis, Vol. No. 3, pp Fujiwara, K. K., Ishida Y., (995, Neural Network Based Adaptive I-PD Controller for Pneumati Cylinder, SICE, Sapporo, pp Cui, X., Shin, K.G., (99, Appliation of Neural Networks to Temperature Control in Thermal Power Plants, Eng. Appl. Artif. Intell., Vol. 5, No. 6, pp Abdelhameed, M.M., (999, Adaptive Neural Network Based Controller For Robots, International Journal of Mehatronis, Vol. 3, No., pp. -4. G. Geng, G. M. Geary, (997, Appliation of a Neural-Network- Based RLS Algorithm in the Generalized Preditive Control of a Nonlinear Air-Handling Plant, IEEE Trans. On Control Systems Tehnology, Vol. 5, No. 4, pp G. Cembrano, G. Welis, J. Surde, A. Ruggeri, (997, Dynami Control of a Robot Arm Using CMAC Neural Network, Control Eng. Pratie, Vol. 5, No. 4, pp International Journal of Current Engineering and Tehnology, Vol.4, No.5 (Ot 04