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1. Introduction
Electrohydraulic control systems are widely used in industry, due to their unique features of small size to power ratio, high nature frequency, high position stiffness, and low position error [1]. However, the dynamics of hydraulic systems is highly nonlinear in nature. The systems may be subjected to nonsmooth nonlinearities due to control input saturation, friction, valve overlapping, and directional changes of valve opening. A number of robust and adaptive control strategies have been proposed to deal with such problems [2–4], but modeling and identification of control systems remain an important and difficult issue in most real-world applications.
Linear models of electrohydraulic control systems are simple and widely used, but they assume that the hydraulic actuator always moves around an operating point [5, 6], which does not accord with most real-world cases where the actuator moves in a wide range with hard nonlinearities. In the literature, Wang et al. [7] analyzed the nonlinear dynamic characteristics of hydraulic cylinder, such as nonlinear gain, nonlinear spring, and nonlinear friction force. Jelali and Schwarz [8] identified the nonlinear models in observer canonical form of hydraulic servodrives. Kleinsteuber and Sepehri [9] used a polynomial abductive network modeling technique to describe a class of hydraulic actuation systems which were used in heavy-duty mobile machines. Yousefi et al. [10] proposed the Differential Evolution algorithm to identify the nonlinear model of a servohydraulic system with flexible load. Yao et al. [2] also pointed out that there were many considerable model uncertainties, such as parametric uncertainties and uncertain nonlinearities. As we can see, modeling and identifying the electrohydraulic control system as a flexible nonlinear black-box or grey-box are more appropriate for real-world applications.
In the field of nonlinear system identification, the Hammerstein and Wiener (H-W) models are widely used [11]. Kwak et al. [12] proposed two Hammerstein-type models to identify...