백스테핑 설계 방법과 L2-게인 분석을 이용한 불확실성을 가진 비선형 시스템의 강인 제어기 설계

Abstract

Hinf control theory for nonlinear systems has been developed, which is based on the concept of the energy dissipation. A nonlinear Hinf controller using the energy dissipation is designed in the sense of L2-gain attenuation from a disturbance to performance and it is essential to find the solution of the Hamilton Jacobi equation (or inequality) for application. However, it is difficult to obtain its solution in general. In this thesis, the nonlinear dynamics is transformed to a affine form to express the Hamilton Jacobi inequality as a more tractable form, i.e., a nonlinear matrix inequality, and its approximated solution is obtained from the fact that the terms in the matrices which describe nonlinear dynamics can be bounded. Using the proposed nonlinear Hinf control design method, robust control is designed for nonlinear cascaded systems with uncertainties, which can be decomposed into two subsystems, that is, a series connection of two nonlinear subsystems. A backstepping design method is used for such a system generally. The backstepping design procedure is constructive and contains two steps. In first step, a fictitious robust controller for first subsystem is designed as if the subsystem had an independent control. When the fictitious control is designed, the proposed nonlinear Hinf control design method is used. In second step, the actual robust control is designed recursively by Lyapunov’s second method. The designed robust control is applied to a robotic system with flexible joints, in which physical control inputs are not the torque to robot links but the torque to the motors. Another systematic method for the robust control of cascaded system is developed in this thesis. The system dynamics are transformed to state error dynamics and the proposed nonlinear Hinf control is designed for the state error dynamics to compensate for the model uncertainties. Conceptually the design method is similar to integrator backstepping design methodologies. However, unlike some of the previous works which used the Lyapunov’s second method, this work introduces L2-gain analysis based on the concept of energy dissipation and a stability analysis using the passivity. State error dynamics are derived and the terms including model uncertainties are regarded as disturbance. The disturbance is overcome by the robust control, which is designed to satisfy the L2-gain condition for the disturbance attenuation. This method permits a decoupled design using state error dynamics and direct consideration of model parameter uncertainties in designing the robust control. The proposed design method is applied to a electrohydraulic system with a mechanical subsystem.