CONTROL OF A BASE-EXCITED INVERTED PENDULUM WITH 2 DEGREES OF ROTATIONAL FREEDOM

The purpose of this paper is to develop a method that can be used to s tudy the control and stability of a base-excited inverted pendulum wit h multiple degrees of rotational freedom. The stabilization of such an inverted pendulum is achieved by. applying appropriate control torque s at the base point. The inclusion of base point motion leads to a con trol system with time varying parametric excitation which makes the co ntrol task challenging. The pendulum studied in this paper has two deg rees of rotational freedom and the base point moves freely in the vert ical direction with the only restriction being that the acceleration m ust be continuous. First, a piecewise continuous feedback control is d esigned to determine the stabilizing torques. Such a control law makes the control system non-smooth, which does not meet the requirement of all classical theories on the existence and uniqueness of solutions. Thus, the existence and uniqueness of the solution to the proposed con trol system are studied using the solution concept developed by Filipp ov. Lyapunov's second method and LaSalle's invariance principle are th en employed to prove the global and asymptotic stability of the contro l system. The robustness of the controller with respect to the physica l parameter variations and measurement errors is also investigated and the control system stability is shown to be largely insensitive to th is class of uncertainties. In order to reflect the actual implementati on scenario, the discontinuous terms in the control law are approximat ed by continuous functions. Such an approximation makes the stability analysis highly challenging. Tt is proven that the pendulum can be sta bilized in a controlled region around the upright position using the g eneralized Lyapunov analysis concept in which a quasi-lyapunov functio n is constructed. Simulations are performed to support the theoretical analyses presented in this study. Copyright (C) 1996 Published by Els evier Science Ltd