Design of control laws for rotary inverted pendulum based on LQR and Lyapunov function

Abstract

Abstract In this paper, a new technique for synthesizing control laws of stabilizing rotary inverted pendulum is proposed. The key of the proposed method is combination of linear quadratic regulator (LQR) method and Lyapunov function such that the control system can achieve higher performance. The Lyapunov function-based methods guarantee the globally approximate stability; however, they face to the difficulty of constructing an effective Lyapunov function. On the other hand, the LQR-based methods have been shown the ability to achieve high performance only if the control system has a weak nonlinearity and/or operate around equilibrium point. Combining them may partially deal with their limitations. The effectiveness of the proposed method is examined by experiments on the rotary inverted pendulum and compared with the LQR method. The results show that the proposed method has achieved a better performance.