Time-varying sliding-coefficient-based terminal sliding mode control methods for a class of fourth-order nonlinear syste
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O R I G I N A L PA P E R
Time-varying sliding-coefficient-based terminal sliding mode control methods for a class of fourth-order nonlinear systems Husnu Bayramoglu · Hasan Komurcugil
Received: 5 October 2012 / Accepted: 29 March 2013 © Springer Science+Business Media Dordrecht 2013
Abstract This paper presents a decoupled terminal sliding mode control (DTSMC) and a nonsingular decoupled terminal sliding mode control (NDTSMC) method for a class of fourth-order nonlinear systems. First, the nonlinear fourth-order system is decoupled into two (primary and secondary) second-order subsystems. The sliding surface of each subsystem was designed by utilizing time-varying coefficients, which are computed by linear functions derived from the input–output mapping of the one-dimensional fuzzy rule bases. Then the control target of the secondary subsystem was embedded to the primary subsystem by the help of an intermediate signal. Thereafter, the DTSMC and the NDTSMC methods were utilized separately to ensure that both subsystems converge to their equilibrium points. The inverted pendulum system was used in the simulations and results were given to show the effectiveness of the proposed methods. It is seen that the proposed methods exhibit a considerable improvement in terms of a faster dynamic response and lower IAE and ITAE values as compared with the existing decoupled control methods in the literature.
H. Bayramoglu · H. Komurcugil () Computer Engineering Department, Eastern Mediterranean University, via Mersin 10, Gazi Magusa, Turkey e-mail: [email protected] H. Bayramoglu e-mail: [email protected]
Keywords Decoupled sliding-mode control · Fourth order nonlinear functions · Nonsingular terminal sliding-mode control · Sliding-mode control · Terminal sliding-mode control
1 Introduction Sliding mode control (SMC) has received much attention due to its major advantages such as guaranteed stability, robustness against parameter variations, fast dynamic response and simplicity in implementation and, therefore, has been widely applied to control nonlinear systems [1–3]. The design of a SMC consists of two steps: design of a sliding surface and design of a control law. Once a suitable sliding surface function and a suitable control law are designed, the system states can be forced to move toward the sliding surface and slide on the surface until the equilibrium (origin) point is reached. Despite the very well-known advantages of SMC, it suffers from the constant (timeinvariant) coefficient utilized in the linear sliding surface, which slows the convergence rate of the system. Although the convergence rate can be made faster by adjusting this coefficient, again the system states in the sliding mode cannot converge to equilibrium in finite time. In order to achieve finite time convergence of the system states, a terminal sliding mode control (TSMC) method has been firstly proposed by Zak [4]. Authors in [5–7] developed the first-order TSMC approach for
H. Bayramoglu, H. Komurcugil
the control of second
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