Optimal Control of the Double Inverted Pendulum on a Cart: A Comparative Study of Explicit MPC and LQR

Abstract

This paper proposes the use of explicit model predictive control (eMPC) method for the stabilising control of the nonlinear underactuated double inverted pendulum on a cart system. To access the effectiveness of the proposed method, a linear quadratic regulator (LQR) was used as a benchmark. The study showed that the proposed eMPC can provide significantly better performance than LQR under various conditions of the system. This superior performance is especially significant in terms of the system outputs peak values reduction. Nonetheless, it was pointed out that there is a need to consider other eMPC methods that lead to further reduction of the number of critical regions and more efficient exploration of the parameter space for the stabilising control of the double inverted pendulum system.

Keywords

• double inverted pendulum
• explicit model predictive control
• linear quadratic regulator
• stabilising control