Sliding Mode Control Of Uncertain Systems With Input Constraints

The existence of some inevitable physical limitations can often make the control input of the actual system nonlinear, such as saturation, dead zone, circle, relay characteristic, etc. It is a hot topic in the control field to analyze and synthesize the system with nonlinear constraint input. The variable structure control with sliding mode is an effective robust control method for the nonlinear control system. The dynamics on the specified sliding surface are insensitive to parameter perturbation, external disturbances and other unknown factors, which are of great attractive for the control system. It has been applied in many fields, including robot, motor control, servo system and space vehicles, etc. Therefore, it is quite significant to design the sliding mode control for the uncertain systems with the control input constraints.This work firstly gives the summary and analysis of some existing works in related field, and then, considers the design problem of sliding mode control for the uncertain system with saturated control input, in which there exists both state matrices uncertainties and control matrix uncertainties. For the case that the system state is measurable, an integral sliding surface is constructed. By using Lyapunov stability theory and linear matrix inequality (LMI) method, the sufficient conditions are derived to guarantee the asymptotic stability of the dynamic sliding mode. A special sliding mode controller is further designed such that the state trajectories can be driven onto the specified sliding surface in spite of the effects of the parameter uncertainties and input saturation. It is well-known that the system states are usually immeasurable in practice due to some physical limitations and cost. Hence, the problem of sliding mode control for the systems with unmeasured states is further considered. A sliding mode controller is designed based on the state observer. The sufficient conditions guaranteeing the asymptotic stability of the sliding mode are obtained, and the reach ability of the specified sliding surface is analyzed. Finally, some numerical simulation results are given to verify the effectiveness of the present algorithms in this work.