Comparative Analysis of SMC-LMI and LQR Controllers for Double Inverted Pendulum

Abstract

This paper introduces an innovative method for achieving stability of the highly nonlinear and unstable double inverted pendulum using a combination of linear matrix inequality (LMI) techniques and sliding mode control (SMC). Sliding mode control is a widely used technique for stabilizing the highly unstable and nonlinear double inverted pendulum system. The LMI-based approach is well-suited for handling system uncertainties and constraints, making it a potent tool for robust control design. Compared to other nonlinear control methods, the LMI approach is more computationally efficient and simpler to implement. The controller proposed in this study is evaluated alongside the Linear Quadratic Regulator (LQR) controller to demonstrate its superior performance. The simulation results obtained through the proposed controller demonstrate its effectiveness in stabilizing the double inverted pendulum.