Sliding mode control of high order systems using a constant nonlinear sliding surface on a transformed coordinate axis

Sliding mode control allows insensitivity to bounded parameter variations, and rejection of disturbances. However, this property is valid only in the sliding phase. Therefore, various studies have been performed with the aim of improving system performance by minimizing, or even removing, the time needed to reach the sliding phase. Sliding surface design is one method of achieving this aim. In this study, a new approach to the design of nonlinear sliding surface for high order systems, which relies on defining a new coordinate axis, is proposed. A constant and nonlinear sliding surface is presented in this newly defined coordinate axis. Next, the control law for the proposed method is derived, and it is seen that the equivalent control term is composed of the equivalent control term of the conventional sliding mode controller and an additive signal, which is a nonlinear function of the system state error vector and conventional sliding surface design parameters. In order to set these design parameters, various performance evaluations are conducted. Simulations are then performed with these design parameters, using a third order nonlinear system model. The results of the new design methodology are compared with both a conventional sliding mode controller and an alternative sliding mode controller that also uses an additive term in the control law to minimize the reaching time. It is shown that the proposed method improves the system performance in terms of reaching time, magnitude of control input, robustness to disturbances, and smoothness in error state behavior issues.