Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function

Abstract

The stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. A logarithmic function is constructed as the Lyapunov function and is compared with the usual quadratic function theoretically. The comparative results show that the constructed logarithmic function has higher numerical accuracy and faster convergence speed than the usual quadratic function. On this basis, the control law of stabilizing Rotary Inverted Pendulum is designed based on the constructed logarithmic function by Lyapunov control method. The effectiveness of the designed control law is verified by experiments and is compared with LQR controller and the control law designed based on the quadratic function. Moreover, the system robustness is analyzed when the system parameters contain uncertainties under the designed control law.