Research On Optimal Tracking And Disturbance Rejection For Linear Systems

The study on optimal tracking and disturbance rejection has been broadly applied in modern control engineering. Recently, fruitful results have been achieved on the study of optimal tracking on linear systems and disturbance rejection problems based on state feedback. However in engineering practice, when tracking the expected output, control systems are always disturbed by various external signals; and not all of the state variables can be easily measured referred to the disturbing systems. Therefore, the research on optimal tracking control of the disturbing systems and disturbance rejection based on output feedback has important theory and application value. The main contents of the thesis are generalized as follows.1. The optimal output tracking control problems of linear systems with sinusoidal signal disturbances are investigated. By principle of the minimum, the finite horizon and infinite horizon optimal feed-forward feedback output tracking control laws, which can make the linear quadratic index minimum, are obtained for the linear systems with sinusoidal signal disturbances. A reduced order observer is also designed so that the optimal tracking control law is easily realizable. The simulation results validated the effectiveness of the control law.2. The optimal output tracking control problems of linear systems with deterministic signal disturbances are considered. By principle of the minimum, the finite horizon and infinite horizon optimal feed-forward feedback output tracking control laws, which can make the linear quadratic index minimum, are gained for the linear systems with deterministic signal disturbances. Reduced order observers for the state of disturbing system and reference input system are also designed so that the optimal tracking control law is easily realizable. The simulation examples show that the effect of the feed-forward feedback control is better than the state feedback control.3. The problems of disturbance rejection for linear systems based on output feedback are discussed. For a class of systems with disturbances which are depicted by linear systems, the infinite horizon optimal output feedback control law, which can make the linear quadratic index minimum, has been presented by constructing an augment system and using LMI approach. Simulation examples show that the optimal output feedback control law can make the quadratic index minimum and therefore inhibits the disturbance.