Mathematical modelling and fuzzy logic based position control of an electrohydraulic servosystem with internal leakage Mete Kalyoncu * , Mustafa Haydim Department of Mechanical Engineering, Faculty of Engineering and Architecture, University of Selçuk, Alaeddin Keykubat Campus, 42079 Konya, Turkey article info Article history: Received 30 January 2009 Accepted 27 April 2009 Keywords: Mathematical modelling Simulation Position control Electrohydraulic servosystem Fuzzy logic control Leakage abstract This paper describes an application of a fuzzy logic position control to an electrohydraulic servosystem. Mathematical model of the electrohydraulic servosystem is obtained considering the internal leakage within the servosystem. Electrohydraulic servosystems are one of the most commonly used actuators. However, electrohydraulic servosystems are difficult to control due to nonlinearity and complexity of their mathematical models. In this paper, as a first step, the mathematical models of the main compo- nents of the servosystem are obtained. The effect of compressibility, friction, internal leakage in servov- alve, leakage in actuator and inertia are included in the model. Since the system has a complex structure and the system characteristics are time dependent. Fuzzy Logic Control (FLC) is applied to the electrohy- draulic servosystem. The error and change in error are employed in the FLC. The effect of internal leakage on the mathematical model and performance of the position control system is investigated. Numerical simulation results for position control under a square wave reference input are obtained. Results are pre- sented in graphical form. Physical trends of numerical simulation results are discussed. Although leakage is often ignored in dynamic analysis of servosystems, results shown in the paper indicate that the leakage has a significant effect on the mathematical model and performance of the position control system at small spool displacements. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction The control of electrohydraulic systems has drawing many attentions from researchers for many years. The electrohydraulic systems are considered for testing the performance of newly devel- oped control techniques since their highly nonlinear characteris- tics. Also, electrohydraulic components are commonly used in many engineering applications [1–5]. Servovalves are one of the most important electrohydraulic system components that used for controlling the flow direction, volume flow rate, force, pressure, position, speed and acceleration. Torque motor servovalves have very complex structure and they are used in systems in which bet- ter performance of control is needed. Servovalves usually have two stages and there is a complex feedback mechanism between the stages. Servovalves are manufactured with very narrow tolerances, thus the cost and significance of servovalves are higher compared to other electrohydraulic system components. Servovalves are used in control applications where precision and reliability has greater importance such as planes, space vehicles, CNC tools, spe- cial test machines, motion simulators, military equipments. Researches on control of electrohydraulic systems have great significance since new benefits in precision and performance have been achieved as a consequence. A variety of control design tech- niques ranging from linear control to nonlinear control techniques have been employed in the past. Linear control analysis such as classical feedback control is widely applied [6]. But, electrohydrau- lic servosystems exhibit highly nonlinear behaviour to the effect that classical linear controllers, e.g., PD, usually achieve a limited performance. The other techniques such as model based control [7], adaptive control [8], fuzzy logic [9,10] and neural network based control [11], robust control [12], and adaptive wavelet back- stepping control [13] techniques are also used for controlling the hydraulic systems. Zeb [14] employed an analytical method in mathematical modelling of an electrohydraulic position control servosystem and discussed various factors affecting the perfor- mance of a typical position servo and developed expressions for estimating the more important performance factors. Kutlu ve Güner [15] applied a digital PD and a fuzzy logic control in an elec- trohydraulic system with an asymmetric cylinder and results show that the fuzzy logic control is less sensitive to variations in system parameters. Scheidl and Manhartsgruber [16] determined 10th de- gree non-linear model of an electrohydraulic system composed of a servovalve and a hydraulic cylinder and carried out singular per- turbation analysis. Deticek [17] designed a fuzzy PD based self- learning fuzzy controller and used this controller in position con- trol of an electrohydraulic system. Jones et al. [9] designed an adaptive self-learning fuzzy logic controller in order to improve 0957-4158/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2009.04.010 * Corresponding author. E-mail address: mkalyoncu@selcuk.edu.tr (M. Kalyoncu). Mechatronics 19 (2009) 847–858 Contents lists available at ScienceDirect Mechatronics journal homepage: www.elsevier.com/locate/mechatronics