Sensitivity Analysis of Disturbance Accommodating Control with Kalman Filter Estimation

The design of controllers that can automatically compensate the effects of uncertain disturbances in a system has become an important topic in modern control engineering. The general theory of disturbance accommodating control provides a method for designing feedback controllers which automatically detect and minimizes the effect of waveformstructured disturbances. This approach has been applied on linear systems with small modeling errors and uncertainties. Based on the disturbance accommodating control theory, a control technique for nonlinear systems with time-varying modeling errors and uncertainties is presented in this paper. This control approach exploits an Extended Kalman Filter for the simultaneous estimation of the system states and the uncertain disturbances. Validity of this control approach is verified by implementing the proposed technique on a highly nonlinear wing-rock system. The simulation results indicated that the closed-loop stability of the controlled system is extremely sensitive to the user selected process noise covariance value. A Lyapunov stability analysis is conducted on a controlled linear system, which reveals a lower bound requirement on the process noise covariance norm to facilitate the asymptotic stability of the closed-loop system. This lower bound on the process noise covariance norm depends on the model uncertainties, external disturbances and the amount of noise associated with the measurements.