The Robust Predictive Control Of Multirate Systems

Predictive control, which is known as an advanced of computer control approach, has been applied successful in industry. However, the model, which is used to describe the dynamics of controlled system, always has some uncertainty. In order to guarantee the specified performance, model uncertainty must be taken into account properly. Robust model predictive control is referred to the predictive control method which can make the performance index within the acceptable range in the presence of model uncertainty. It combines the method of robust control with the moving horizon principle of MPC, and has the capability of handling constraints and optimization over some performance index in a systematic way.Based on the existing theoretical results on model predictive control, this thesis is devoted to the development of the framework of robust model predictive control for uncertain multirate systems. To achieve this goal, the relevant theory and approaches, such as linear matrix inequalities (LMI) and Lyapunov stability theory, robust control, sampled-data control and controllable invariant set and so on, are employed in the research work. The feasibility and robust stability of the closed-loop multirate systems are guaranteed. The main contents of this thesis are stated as follows:(1) the problem of robust predictive control for input multirate control systems is considered , it proposed a robust predictive control algorithm based on H∞performance. The upper Boundγof H∞performance target for the multirate closed-loop system is derived by linear matrix inequality approach, and the condition of the robust stability for the closed-loop system is obtained.(2) The design problem of robust output feedback model predictive controllers is considered which guarantees that the closed-loop system is asymptotically stable and an on-line receding horizon guaranteed cost is minimized for a class of uncertain multirate time-delay systems with I/O constrains. Firstly, the condition for the existence of the output feedback controller is derived by using the receding optimization. The complementary linearization idea is then employed to convert the controller design into a nonlinear programming problem with linear matrix inequality constraints, and a construction of the desired controllers is also provided in terms of feasible solutions to the LMI . (3) A robust predictive control is proposed for multirate uncertain time-delay systems with constrained control input solved in terms of linear matrix inequalities (LMI).Sufficient conditions for stability and a new upper bound on robust preference index are established for time-delay systems.The feedback control law is obtained by convex optimization involving LMI.(4) Computer simulations demonstrate the usefulness of the proposed algorithms in this paper.