Mixed H₂/H_∞ Fault-tolerant Control For Delta Operator Uncertain Systems

In the actual industrial control systems, due to the environmental and other factors, the control system components will appear damaged, the system will generate uncertainty which can reduce the stability of control system. As an important performance of the control system, the robustness of systems which is studied has the practical significance. Delta operator is a kind of new discretization method, which can avoid ill-conditioned problems caused by the conventional shift operator when the fast sampling is used. Delta operator method in control system, broadband communications and signal processing and other fields have a good development prospect. At present, the Delta operator to its unique advantage has become the modern control theory research hot spot.The main contributions of this thesis are as follows:(1) The H2, control for delta operator uncertain systems is studied. In terms of linear matrix inequality (LMI), the designed method of H2 stste feedback controller for delta operator systems with controller gain variation is given. The sufficient condition of delta operator system controller can be presented via linear matrix inequality. The problem of H2 control for delta operator uncertain systems with parameter uncertainty is considered. And a sufficient condition of the state feedback H2, controller is derived by using linear matrix inequality. A numerical simulation shows the feasibility of the proposed method.(2) The problem of H2/H∞robust fault-tolerant control for delta operator uncertain systems with model parameter uncertainty and the model of actuator continuous fauilure is studied. A sufficient condition of the robust H2/H∞fault-tolerant state feedback controller for delta operator uncertain systems are derived by using linear matrix inequality approach, the state feedback control law of the system is equivalent to the feasible solutions problem of a group of linear matrix inequalities. Finally, a corresponding convex optimization problem solving with Matlab toolbox is given. An example simulation shows the availability of the proposed method.