Controller design for inverted pendulum stabilizing on equilibrium manifold based on vector field

Abstract

In general, mechanical systems are stabilized on their equilibrium point. Equilibrium point is often not unique and they are continuously connected, which is an equilibrium manifold. To stabilize the mechanical system on an equilibrium manifold will enable optimal control including the selection of the stabilizing position. In this paper, we propose a controller design method that stabilizes a mechanical system on an equilibrium manifold based on vector field. The equilibrium manifold is derived from dynamic equations, and by setting an appropriate evaluation function, (1) an optimal equilibrium point from arbitrary initial value is calculated, (2) a trajectory, input and vector field are derived based on linear control theory, (3) a controller is designed using functional approximation. Simulations show that different initial values are stabilized to different equilibrium points, and experimental results show the effectiveness of the proposed method.