Robust tracking of an inverted pendulum via a new linear exact model matching technique

In this paper a new approach to the robust asymptotic output tracking of an inverted pendulum is presented. The inverted pendulum is described by a third order nonlinear system. The proposed approach is as follows: First, we determine a static state feedback control law which solves the linear exact model matching (LEMM) problem resulting in an input-output (i/o) linearized closed-loop system. Second, in case where there exists a parameter uncertainty in the inverted pendulum model, we design a robust output tracking controller for the perturbed i/o linearized closed-loop system. The LEMM problem is solved using a new LEMM technique. This technique reduces the problem of finding the control law to that of solving system of first order partial differential equations. Based on these equations, the general analytical solution for the feedback control law is derived. The robust design consists in determining the input signal of the perturbed i/o linearized closed loop system as a function of the state vector based on the construction of an appropriate Lyapunov function.