OUTPUT FEEDBACK STABILIZATION AND REGULATION FOR A CLASS OF UNDERACTUATED NON-MINIMUM PHASE BENCHMARK NONLINEAR SYSTEMS

Abstract

In this thesis, the problem of output feedback stabilization and regulation for a class of underactuated benchmark nonlinear systems is considered. The proposed method utilizes an extended high gain observer (EHGO)-based sliding mode control (SMC) technique to control a class of nonlinear systems which may have unstable zero dynamics. Starting with Lagrangian model of the system and using a suitable coordinate transformation, a generalized normal form representation is derived which decouples the system into its internal and external dynamics. The internal dynamics is utilized to derive an auxiliary system and the full-order EHGO thus obtained is used for estimation of derivative(s) of the system output that are further used in design of an output feedback control law. It is shown that the proposed output feedback controller stabilizes the system and convergence of estimated states is demonstrated with suitable selection of observer parameters. The proposed stabilizing control scheme is applied to two of the benchmark nonlinear systems, namely Inertia Wheel Pendulum (IWP), and Translational Oscillator with Rotational Actuator (TORA), in order to demonstrate the effectiveness of the technique by simulation. The technique is extended to further solve for the servomechanism (output regulation) problem for the class of under actuated non-minimum phase nonlinear systems under consideration. Towards this end, the control design is modified to include a ‘conditional servo compensator’ in order to track reference signals as well as reject disturbances while achieving stabilization and steady-state accuracy with a desired transient performance. The conditional servo compensator is utilized to regulate the controllable states by using SMC while neglecting the internal states initially. The uncontrollable states of the system are estimated using an EHGO and the error signal is then used to synthesize a control input to stabilize the internal states by incorporating it in the sliding surface of the SMC design. The proposed control scheme is then applied to the Translational Oscillator with Rotational Actuator (TORA) system to validate the efficacy of the technique.