Consider Parameter Uncertainty And External Disturbance The Acrobot Robust Control Design

The underactuated two-link maninupulator Acrobot operating in a vertical plane is a typical underactuaed mechanical system with non-holonomic constraints. It consists of one joint each at the shoulder and elbow with a single actuator at the elbow. The control objective is to swing it up from a stable downward equilibrium position to the unstable straight-up equilibrium position and balance it there.In the practical control design for acrobot, there may exist lots of uncertainties such as the parameter uncertainties and exogenous disturbance because acrobot is a class of high-nonlinear underatucated system. In order to derive a practical control method, it is important to investigate the robust stability issue under the existence of the uncertainties of parameters as well as disturbances.This thesis focuses on the robust control problem of the acrobot, and a robust control strategy is proposed, which not only has the robustness to the parameter uncertainties, but also can suppress the influence of the disturbances.First, the dynamic model of the acrobot is obtained based on Lagrange equation, and some inherence structure characteristics of the acrobot are analyzed. Moreover, two kinds of uncertainties including the parameter uncertainties and the exogenous disturbance are ascertained, which is necessary for the following robust controller design.Second, the whole motion space is redefined as the swing-up area and the balance area. The swing-up area is again divided into two subspaces: the stage of energy pumping and free rotation. The swing-up controller mainly for the energy pumping, which has the robustness to the parameters, is designed based on the ideal of increasing the system energy with each swing until it reaches to the max potential energy at the up-right position. Then, in the balance area, a sufficient condition of existence of a H_∞robust state feedback controller is deduced based on linear matrix inequality (LMI), and a controller is designed by solving a term of linear matrix inequalities.Finally, a control design method of robust stabilization and disturbance attenuation for the acrobot, in which uncertainties of the parameters and exogenous disturbance exist, is presented. The swing-up controller contained a compensator to suppress the influence of disturbance is obtained so that the system energy can still increase monotonically. Then, a robust controller is designed for the balance area to guarantee the quadratic stability of the control system. It employs an uncertain linear model of the manipulator. The design problem is transformed into a standard H_∞control problem, and a sufficient condition of existence of a H_∞robust state feedback controller is deduced using the LMI approach.