Nonlinear control of swing-up and stabilization of an inverted pendulum

In this paper an effective method of control for swing-up and stabilization for an inverted pendulum system 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 by the coordinate change and input transformation via the Lie theoretic approach and to apply a kind of equivalent linearizations 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.