Real-time Evaluation of Ant Lion Optimizer tuned Linear Matrix Inequalities based State Feedback Controller for the Control of an Under-actuated System

Abstract

The stabilization and trajectory tracking control problem of the classical benchmark Under-actuated cart-inverted pendulum system is addressed. In the Linear Matrix Inequality (LMI) based State Feedback Controller (SFC), the LMI regions are selected by cumbersome trial and error methods where optimal results are not always guaranteed. Hence in this work, the optimization algorithms are proposed to tune the LMI region in the LMI based SFC. The Ant Lion Optimizer (ALO) is proposed to tune the LMI regions of the SFC for the control problem. The ALO algorithm finds the optimal LMI region from the solution of the inequality problem, which results in the optimal state feedback gain, minimising trajectory tracking error while stabilising the pendulum in the unstable upright position. The performance of the proposed ALO tuned LMI based SFC is presented and compared with the LMI based SFC without optimization and APSO tuned LMI based SFC scheme. The suggested controller's real-time viability is demonstrated by incorporating it in Quanser's IP02 benchmark Cart-inverted pendulum system and the results show a 41.97 percentage reduction in Integral Square Error (ISE) of trajectory tracking with improved transient response while stabilizing the pendulum in the unstable position when compared to the controllers in comparison.