State feedback and LQR controllers for an inverted pendulum system

In this paper, a control problem of a nonlinear pendulum is considered. The control problem contains two stages. First, swing up the pendulum by a nonlinear control to bring the pendulum from pendant to a limited region near of upright position. Secondly linear state feedback controller is used to stabilize pendulum at the upright position. Energy based control is used for swinging up task. The stabilizing pendulum at upright position task is achieved by two linear state feedback controllers namely pole placement and linear quadratic regulator LQR. The closed loop stability is achieved by Lyapunov method. The performance of the closed loop system is discussed.