Abstract
In this paper an effective method of control for swing-up and stabilization of an inverted pendulum is established without resorting to any approximation of each nonlinear terms appearing in the mathematical models. The key idea is to derive the partially linearized system due to the coordinate change and input transformation via the Lie theoretic approach and to apply a kind of equivalent linearization to the resulting linear system with nonlinear output injection. Based on the linearized system, the control law is established performing both swing-up and stabilization of the pendulum. The effectiveness of the proposed control method is examined by numerical simulations and tested by experiments.
