Swing-up control of a inverted pendulum by two step control strategy

Though an inverted pendulum is one of the typical examples of nonlinear control systems, it is shown that the inverted pendulum is not feedback linearizable. Saeki proposed a new method to design a backstepping-like controller. This paper presents a swing up controller by combining Saeki´s method with the energy function method. First, we give the control input of the cart to cancel the effect of the pendulum and then design the input that guarantees the convergence of the acceleration of the cart to the desired value. Next, regarding the acceleration of the cart as the input of the pendulum, we design the swing-up control law using a energy function. Moreover, we propose another nonlinear state feedback control law that converges to a homoclinic orbit. Finally, the MATLAB simulations are performed to demonstrate the validity of the proposed control laws.