Optimal Disturbance Rejection Methods For Systems With Control Delay

In this paper, the problem of optimal disturbance rejection for linear systems and nonlinear systems with control delays is considered. The present studies include aspects as followings:1. The approach named model transformation for time delay systems is introduced. The linear systems with control delay or with both state delay and control delay are transformed into equivalent nondelayed systems. The optimal disturbance rejection control law which is derived from Riccati equation is combined by control memory term and state memory term, which compensate for the effects of the control delay and the state delay, respectively.2. For the nonlinear systems, the linearization approach is used to design the optimal disturbance rejection control law. By linearizing the system about the desired equilibrium point, a state feedback controller is designed for the linearization system under disturbances. The Lyapunov function for the closed-loop system in the neighborhood of the origin is used to estimate the region of attraction and its stability is proved.3. The feedforward and feedback control and the internal model-based control are applied to the disturbance rejection problem. For the disturbances with known dynamics and unknown initial conditions, the feedforward and feedback control law is designed, of which the feedforward control term compensates for the effects of disturbances. A disturbance state observer is constructed to make the feedforward control physically realizable. And a high-gain disturbance observer is constructed to eliminate the effects of modeling errors and nonlinear factors while guaranteeing it physically realizable. For the sinusoidal disturbances of known frequency, but unknown amplitude and phase, or other unmeasurable persistent disturbances, based on the internal model principle, the internal dynamic compensator is designed to reject disturbances with zero steady-state errors perfectly.4. The designed control laws are applied to the numerical simulations on vibration control for offshore platform. And the simulations results demonstrate the easiness and the convenience of the model transformation approach. The characteristics of the feedforward and feedback control law and the internal model control law are compared by the simulations. Therefore, the effectiveness of the method for designing the optimal disturbance rejection is verified.