Robust adaptive output feedback control of nonlinear systems

In this thesis we design a robust adaptive output feedback control to solve the tracking problem for a class on nonlinear systems. We consider a single-input-single-output minimum phase system represented globally by an nth order differential equation. We start by designing a state feedback control to achieve tracking error convergence. The control uses a Lyapunov based adaptation to estimate uncertain parameters. Then, we saturate the control over a compact set of interest to prevent peaking and design a high-gain observer to estimate the unmeasured states. We show that this control guarantees the boundedness of all the state variables of the closed-loop system and achieves tracking of a given smooth reference signal without requiring persistence of excitation. We show robustness to small bounded disturbances. If the bound on the disturbances is not small but known, we go one step further by designing a robust control component that ensures the boundedness of all signals and makes the mean-square tracking error of the order $Oe+m$ where $e$ and μ are design parameters. We pick the induction motor as an application candidate to demonstrate the applicability of our technique. We design a robust control that uses an adaptive observer to estimate the rotor resistance. The design guarantees the boundedness of all closed-loop signals and makes the mean-square speed tracking error of the order O(μ) where μ is design parameter. We show some experimental results. The design is tested experimentally and the experimental results are in good agreement with the theory.