Optimal Sliding Mode Control For Linear Time-Delay Systems With Sinusoidal Disturbances

Sliding mode control, as a nonlinear control, is different from other general control methods. The fundamental difference is the discontinuity of sliding mode control, which uses an especial control fashion and drives the state variable to the expected point along man-set trajectory. As the given trajectory is independent of control object parameters and external disturbances, systems have more predominant invariability when moving on the sliding mode surface. Because the arithmetic of sliding mode control is simple and easy to be implemented in engineering, it provides a preferable solution for complex industry control problems. Sinusoidal disturbances and time-delay exist in many systems such as industry, aerospace and ocean engineering, the existence of time-delay can seriously influence the stability and performance of systems. Therefore, the research of optimal sliding mode control for linear time-delay systems with sinusoidal disturbances is significant both in theory and in practice. The main results of this dissertation are shown as follows.1. First, the research actuality and development tendency of sliding mode control theory is introduced, and the main methods to design sliding surfaces and eliminate chattering are summarized.2. The variable structure control for linear discrete systems with control delay is considered. First, the original discrete system with control delay is simplified to a linear discrete system without time-delay. Then we develop a new chattering-free sliding mode control strategy for the discrete system simplified. The control algorithm makes the control process divide into two phases. For the system's trajectory is out of some given neighborhood, the conventional reaching control law is used such that the trajectory is driven monotonically toward the switching surface. And for the trajectory is in the neighborhood, the chattering-free control law drives the trajectory reaches the switching surface precisely in one step. This control algorithm eliminates chattering of the sliding mode caused by discontinuity for discrete systems. The numerical simulation results verify the validity of the proposed approach.3. The optimal sliding surface and variable structure control are developed for linear time-delay systems with sinusoidal disturbances. In the optimal sliding surface designing process, by using the successive approximation approach (SAA), the two-point boundary value (TPBV) problem with both time-delay and time-advance terms is transformed into a sequence of linear TPBV problems without delay and advance terms. The obtained sliding mode controller ensures that the state trajectories reach the sliding surface in finite time and remain on it thereafter. The stability of the sliding mode is proved. A numerical simulation is employed to verify the effectiveness of the proposed approach.4. The presented techniques in this dissertation employ the sliding mode control and optimal control together to promote the performance of the motion over the sliding surface. Based on the SAA, the optimal sliding mode surface is designed and also the control law is obtained, which ensures the state trajectory to reach the sliding surface and maintain on it thereafter. And the performance of the sliding motion is ensured to be optimal.5. Summarize the main work in this paper and point out the investigation aspects for the future.