Nonlinear Robust Disturbance Rejection

This thesis studies the problem of robust disturbance rejection for nonlinear systems based on three different methods: H∞ control, singular perturbation theory and multiple model adaptive control. Firstly, the disturbance suppression problem for nonlinear systems based on H∞ control is examined. We review the so-called nonstandard mixed sensitivity problem, which introduces an integrator into a selected weight, as well as the linear classical disturbance suppression problem and the linear H∞ disturbance suppression problem. We extend this H∞ problem to the nonlinear case, and present a method to reduce the order of the state feedback Hamilton-Jacobi PDE (Partial Differential Equation) for this nonlinear H∞ problem by extending the concept of comprehensive stability. Finally, we investigate the structure of the output feedback H∞ controller for disturbance suppression, and draw the conclusion that, as in the linear case, there must also be an integrator in the controller. Secondly, a relatively practical method of suppressing the effect of constant disturbances on nonlinear systems is presented. By adding an integrator to a stabilising controller, it is possible to achieve both constant disturbance rejection and zero tracking error. Sufficient conditions for the rejection of a constant input disturbance are given. We give both local and global conditions such that the inclusion of an integrator in the closed loop maintains closed loop stability. The analysis is based on singular perturbation theory. Furthermore, we present some alternative locations for adding an integrator into the closed loop system and extend these methods to deal with Multiple-input Multiple-output nonlinear systems. Finally, we implement our method in the control of a simulated helicopter model. The simulation results show that this method achieves satisfactory performance. In the last part of this thesis, we apply multiple model adaptive control to deal with the robust disturbance rejection problem for an unknown plant. Firstly, a stable multi-estimator for an unstable nonlinear plant is constructed, based on the concept of a stable kernel representation. An example is presented demonstrating the design of a multi-estimator and a multi-controller to ensure constant disturbance rejection as well as constant reference tracking under plant variation. The simulation results indicate that satisfactory performance is achieved. Finally, an efficient way to achieve