Stabilization Control of Rotary Base Inverted Pendulum by Combination of Lyapunov-base controller and Linear PD controller

In this paper a control scheme for rotary base inverted pendulum is developed in order to stabilize system. The mathematical model is obtained by Euler-Lagrange equations and some considerations are taken. The control scheme is divided into three steps: first, a linear control law for angle's base is proposed for tracking trajectory problem. Then, the desired trajectory in angle position is used as artificial control input and some auxiliary controllers are developed in order to express the dynamics as a pendulum on a cart system. The last step consist in propose a Lyapunov-based controller for stabilization problem. Numerical simulations are shown into two scenarios: with external disturbances and without external disturbances to observe the effectiveness of control scheme proposed.