Stabilizing a rotary inverted pendulum based on Lyapunov stability theorem

The stabilization of Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing controls by Lyapunov 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 convergence speed than the usual quadratic function. On this basis, the control of stabilizing rotary inverted pendulum is designed based on the constructed logarithmic function by Lyapunov method. The effectiveness of the designed control is verified by experiments, and is compared with the control designed based on quadratic function.