Modified sliding mode control using a target derivative of the Lyapunov function

This paper presents a modified sliding mode control (SMC) algorithm for vibration control of structures, designed to enhance the control performance of the widely used SMC algorithm. In the modified SMC, the control force is determined so as to meet conditions imposed on the target derivative of the Lyapunov function. A shape function is developed to determine which one of the equivalent and corrective control—which are the two terms comprising the SMC—is the dominant part in controlling structures. Simulation results for linear and nonlinear systems show that the proposed method is able to enhance the control performance of the original SMC. Also, the modified SMC can be applied not only to active control, but also to semi-active control which is suitable for practical application. Moreover, it is observed that the performance is insensitive to the fundamental vibrating period and utilizes less control energy as compared to the original SMC.