A Neural Based Position Controller for an Electrohydraulic Servo System

A Neural Based Position Controller for an Electrohydraulic Servo System ŞAHĐN YILDIRIM and SELÇUK ERKAYA Mechatronics Engineering Department Erciyes University Erciyes University, Engineering Faculty, Mechatronics Engineering Department Kayseri/Turkey TURKEY sahiny@erciyesedutr, ĐBRAHĐM UZMAY Mechanical Engineering Department Erciyes University Erciyes University, Engineering Faculty, Mechanical Engineering Department Kayseri/Turkey TURKEY MENDERES KALKAT Mechanical Engineering Department Nigde University Engineering Faculty, Mechanical Engineering Department Nigdei/Turkey TURKEY Abstract: - This paper proposes a neural network based controller for controlling the position of an electrohydraulic servo system Feedforward network structure, which consists of an input and output layer with one linear neuron, a hidden layer with two nonlinear neurons, is used for the related controlling, and backpropagation algorithm (BP) is implemented for the learning process Du to the adaptability and robustness, the neural network based model reference adaptive control scheme gives very successful control results The simulation gives that the proposed adaptive neural controller has better control performance than that of the standard PID controller This kind of neural controllers could be utilized in experimental investigation of electrohydraulic servo systems Key-Words: - Model reference control, Adaptive control, Electrohydraulic servo system, Neural networks Introduction Since the electrohydraulic systems provide large torque and higher speed of response with fast motion to the plant, these systems are widely used in the industrial applications, especially in automobile industry and heavy-duty machine However, due to the fluid compressibility, highly nonlinear and parameter uncertainties, flow-pressure relationship and internal leakage, the control of the electrohydraulic system using well-known control scheme is not always optimum [] In addition to this, adaptive control techniques are very useful for such systems A novel Variable Structure Control (VSC) with a time-varying switching gain, a second-order relation between sliding surface and uncertainties, and a boundary layer for the sliding surface, has been employed by Hwang and Lan [] to deal with the position control of the electrohydraulic servomechanism which has been subjected to parameter uncertainties and external disturbances In addition, the robust stability of the system has been verified by a Lyapunov stability criterion An accurate and robust tracking performance of the system has been achieved by using the proposed approach For the digital implementation, the discrete existence conditions of sliding mode have ISBN: 978-960-474-83-7 3

been introduced to adapt the Integral Variable Structure Control (IVSC) to the discrete systems by Chuang and Shiu [3] The system equations have also been extended to more general forms Experimental results show that the discrete integral variable structure control has the robustness to against the parameter derivations and disturbances Position control of an electrohydraulic servo system under both large inertia variations and substantial external loads has been studied by Chin et al [4] Time Delay Control (TDC) has been applied to the servo system and a stability analysis has been made Knohl and Unbehauen [5] have summarized the adaptive position control of an electrohydraulic servo system, which consists of a 4/3 way proportional valve, a differential cylinder and a variable load force, using artificial neural networks Yanada and Furuta [6] has studied online parameter estimation of an electrohydraulic servo (EHS) system Natural frequency of the EHS system has been investigated using pressure sensors based on the equation of motion and equation of continuity, and the estimate of the natural frequency has been utilized to enhance the robustness of the EHS system combined with a parallel feedforward compensator (PFC) A non-linear model reference adaptive control technique has been as used by Trajkov et al [7] for the vibration suppression of a smart piezoelectric mechanical structure In the study of Herrmann et al [8], a discrete non-linear, adaptive neural network (NN) element has been introduced to make the performance of a track following controller in a hard disk drive improve for its disturbance rejection Davliakos and Papadopoulos [9] have developed a novel modelbased controller for a six Degree-of-Freedom electrohydraulic Stewart Gough platform Dynamic models of low complexity have been employed that describe the salient dynamics of the main electrohydraulic components Rigid body equations of motion and hydraulics dynamics, including friction and servovalve models have been used Simulations with typical desired trajectory inputs have been presented and a good performance of the controller has been obtained Yıldırım [0, ] has proposed a recurrent neural network control system to control a four-legged walking robot Neural Network (NN), which was three layers, has been employed as an inverse controller of the robot The reason to use a hybrid layer was that the robot s dynamics consists of linear and nonlinear parts The results show that the neural-network controller can efficiently control the prescribed positions and trajectory of the four-legged walking robot Milic et al [] have investigated the use of the techniques based on linear matrix inequalities for robust H position control synthesis of an electro-hydraulic servo system A nonlinear dynamic model of the hydraulic cylindrical actuator with a proportional valve has been developed For the purpose of the feedback control an uncertain linearized mathematical model of the system has been derived By considering the structured (parametric) perturbations in the electro-hydraulic coefficients, H controller extended with an integral action has been proposed An observer has been designed to estimate internal states of the electro-hydraulic servo system Developed control algorithms have been tested experimentally in the laboratory model of an electro-hydraulic servo system The objective of the present study is to construct a robust and adaptive neural controller for controlling the electrohydraulic servo mechanism Theory of Electrohydraulic Servo System A typical position controlled electrohydraulic servo system consists of a power supply, flow control valve, linear actuator, displacement transducer, and controller The controller compares the signal from the feedback displacement transducer with an input demand to determine the position error, and produces a command signal to drive the flow control valve The control valve adjusts the flow of pressurized oil to move the actuator until the desired position is obtained: a condition indicated by the error signal falling to zero The electrohydraulic servo system is outlined in Fig ISBN: 978-960-474-83-7 3

Fig Schematic representation of electrohydraulic servo system Characteristic values of the dominant roots are also given in Table Table Dynamic parameters of electrohydraulic servo system Parameter Description Value ω Natural frequency of first stage 68 ω Natural frequency of second stage 4396 ζ Damping ratio of first stage 005 ζ Damping ratio of second stage 005 τ Characteristic constant value 00 Dynamic behaviour of the servovalve and actuator can be expressed in the following equation, ( ζτω 0) ω τ ω D( t) = t τ e ω τ τ ω ( ζ τω ) ω ( τω ζ ω 0τω 0ζ ω) ζ tω ω e ( τ ω ζ τω ) ( ω t ζ ) cosh ( t ) ( ) ζ τωω ω ζτωω 0ω sinh ω ζ ω τω ζ ω 0τω 0ζ ω ζ ω τω ζ ω 0τω 0ζ ω t ω e ζ ω τ ω ζ τω ζ ( ) () where ω and ω are natural frequency of first and second stage, respectively ζ and ζ are also damping ratio of first and second stage, respectively τ is characteristic constant value of system Also, the position variation (G(s)) of the proposed electrohydraulic servo system can be given in transfer function form as follows, ( ) ( ) 3 0s ζ s τ s τω ωζ ω 0ω s τωω ζ ω ζ ω s G( s) = ω ω ω ( ωω ) ωω () 3 Standard Control Systems Many simple control problems can be handled very well by PID control, provided that the requirements are not too high The PID algorithm is packaged in the form of standard regulators for process control and is also the basis of many tailor-made control systems The textbook version of the algorithm can be given in the following form [3], t u( t) = K p e( t) e( s) ds T T i 0 d de dt (3) ISBN: 978-960-474-83-7 33

where u is the control variable and e is the error defined as e=u d -y, where u d is the desired value, and y is the process output Block diagram of PID PID Controller control system for position control of electrohydraulic servo mechanism is given in Fig Q d (s) Desired Flow rate u d y - e K p Ti s Td s Control Input Electrohydraulic Servo System Q a (s) Actual Flow rate Fig PID Control System The used algorithm actually comprises several modifications It is standard practice to let the derivative action operate only on the process output It may be advantageous to let the proportional part act only on a fraction of the desired value The derivative action is replaced by an approximation that reduces the gain at high frequencies The integral action is modified so that it does not keep integrating when the control variable saturates Precautions are also taken so that there will not be transients when the regulator is switched from manual to automatic control or when parameters are changed The essential parameters to be adjusted are Proportional term (K p ), Integral time (T i ) and Derivative time (T d ) The tracking time constant is typically s fraction of the integration time T i 4 Model Reference Neural Control (MRNC) System Neural network (NN) is a parallel distributed information processing system This system is composed of operators interconnected via one-way signal flow channels NN stores the samples with a distributed coding, thus forming a trainable nonlinear system It includes hidden layers between the inputs and outputs The main idea of the NN approach resembles the human brain functioning Therefore, NN has a quicker response and higher performance than a sequential digital computer Many NN models use threshold units with tangent hyperbolic activation function and gradient descent learning algorithm The MRNC is an adaptive control approach in which the desired performance is given in terms of a reference model which is chosen based on some prior information concerning the plant (system) The reference model gives the desired response to a command signal Block diagram of the proposed controller is described in Fig 3 ISBN: 978-960-474-83-7 34

Reference Model - Control Error (e c) Q d (s) Desired Flow rate u r - y s e s NN Controller Control Input (u c) Prediction Electrohydraulic Servo System NN Plant Model - Q a (s) Actual Flow rate Model Error (e m ) Hidden Layer Hidden Layer w ij w jk w ij w jk e s Input Layer Output Layer u cnn u cnn Input Layer Output Layer y NN : Nonlinear neuron : Linear neuron :Feedforward connection Fig 3 Proposed model reference neural control system The MRNC scheme has two neural networks; one is to work as the controller network while the other works as the plant identifier network The system also has an ordinary feedback loop composed of the process and the controller and another feedback loop that changes the controller parameters The parameters are changed on the basis of feedback from the control errors (e c ) between the system outputs and reference model outputs [4] One important question is how small we can make the error e c This depends both on the model, the system, and the command signal If it is possible to make the error equal to zero for all command signals, the perfect model is achieved for optimal control [5] Reference model of the system for MRNC is selected in the following form, s 0,64s 400 G ( s) = (9) s 5,643s 664, Some simulations are carried out on the MATLAB software to demonstrate the adaptability and robustness of MRNC scheme and performed on a PIV processor with a CPU speed of 3MHz and 04Mb Ram [6] Simulations are divided in two subsections In the first subsection, the results of standard PID controller are given and analyzed In the second subsection, the results of MRNC scheme are analyzed 5 Simulation I In this section, standard PID controller is used to control the electrohydraulic servo system The gain parameters (K p, T i, and T d ) are empirically selected These parameters are set to K p =50, T i =5 and T d =0 The results of standard PID controller are given in Fig 4 5 Simulation Results ISBN: 978-960-474-83-7 35

Fig 4 System response with PID controller As shown, the deviations between input and output values are very high Therefore, the obtained result for this case is not acceptable 5 Simulation II The proposed MRNC scheme is designed by using a feedforward neural network The weight parameters of the neural network are adjusted by using BP learning algorithm Numbers of hidden elements in nonlinear parts of the neural network are set to two, and the activation functions are selected as hyperbolic tangent type Fig 5 shows flow rate variations as an input to the system, amplitude as a response of the hydraulic system, amplitude error variations as a NN model errors and amplitude as a NN system responses 35 Hydraulic System Input Hydraulic System Output Flow rate (m 3 /s) 3 5 5 Amplitude (mm) 5 05 05 0 0 0 30 40 50 NN Model Error 0 0 0 0 0 30 40 50 NN System Output Amplitude (mm) 0 0-0 Amplitude (mm) 5 05-0 0 0 0 30 40 50 0 0 0 0 30 40 50 Fig 5 Variations MRNC for system input, System response, error and NN output Training and testing data RMSE variations are given in Fig 6 Results of reference model response and system output are also outlined in Fig 7 ISBN: 978-960-474-83-7 36

Fig 6 Error measure of neural system using mean square error 5 Reference Model Output System Output Amplitude (mm) 5 05 0 0 5 0 5 0 5 30 35 40 45 50 Fig 7 Reference model and system response 6 Conclusion and Discussion In this study, a model reference neural position controller using neural networks for an electrohydraulic servo valve system is proposed From the simulation results, it is seen that the model reference adaptive control system with a feedforward neural controller produces the best performance while the PID control system yields poor control A reason for strong performance of neural based MRAC system is the fast learning and robustness of the neural network This facilitates the training of the neural controller, and the nonlinear neurons could readily learn the linear part of the electrohydraulic servo system The results show that the model reference neural controller has a superior performance than that of the conventional PID controller for controlling the position of an electrohydraulic servo system In the next study, the optimal number of the nonlinear neuron in hidden layer will be determined to decrease the position error for the proposed control structure References: [] Merrit, H E, Hydraulic Control System John Wiley, New York, 976 [] Hwang, CL, Lan, C, The position control of electrohydraulic servomechanism via a novel variable structure control Mechatronics, Vol4, No4, 994, pp 369-39 [3] Chuang, CW, Shiu, LC, CPLD Based DIVSC of hydraulic position control systems Computers and Electrical Engineering, Vol30, 004, pp 57 54 [4] Chin SM, Lee, CO, Chang, PH, An experimental study on the position control of an electrohydraulic servo system using time delay control Control Engineering Practice, Vol, No, 994, pp 4-48 [5] Knohl, T, Unbehauen H, Adaptive position control of electrohydraulic servo systems using ANN Mechatronics, Vol0, 000, pp 7-43 [6] Yanada, H, Furuta, K, Adaptive control of an electrohydraulic servo system utilizing online estimate of its natural frequency, Mechatronics, Vol7, 007, pp 337 343 [7] Trajkov, TN, Köppe, H, Gabbert, U, Direct model reference adaptive control (MRAC) ISBN: 978-960-474-83-7 37

design and simulation for the vibration suppression of piezoelectric smart structures Communications in Nonlinear Science and Numerical Simulation, Vol3, 008, pp 896 909 [8] Herrmann, G, Ge, SS, Guo, G, Discrete linear control enhanced by adaptive neural networks in application to a HDD-servosystem Control Engineering Practice, Vol6, 008, pp 930 945 [9] Davliakos, I, Papadopoulos, E, Model-based control of a 6-dof electrohydraulic Stewart Gough platform Mechanism and Machine Theory, Vol43, No, 008, pp 385-400 [0] Yıldırım, Ş, A proposed hybrid neural network for position control of a walking robot Nonlinear Dynamics, Vol5, 008, pp 07 5 [] Yıldırım, Ş, Design of a proposed neural network control system for trajectory controlling of walking robots Simulation Modelling Practice and Theory, Vol6, 008, pp 368 378 [] Milic, V, Situm, Z, Essert, M, Robust H position control synthesis of an electrohydraulic servo system, ISA Transactions, Vol49, 00, pp 535-54 [3] Aström, KJ, Wittenmark, B, Adaptive Control, Addision-Wesley Press, 989 [4] Ge, SS, Lee, TH, Harris, CJ, Adaptive Neural Network Control of Robotic Manipulators, Singapore-World Scientific Publishing Co Pte Ltd, 998 [5] Yıldırım, Ş, Erkaya, S, Uzmay, Đ, Design of neural controller system for concorde aircraft Journal of Automatic Control and Computer Sciences, Vol38, No3, 004, pp 53-63 [6] MATLAB, 006, The MathWorks Inc, 3 Apple Hill Drive, Natick, MA 0760-098 ISBN: 978-960-474-83-7 38