Optimal tuning of a linear quadratic regulator for control of an inverted pendulum using a whale optimization algorithm Available to Purchase

This paper proposes an efficient optimization technique-based controller for nonlinear systems such as the Inverted Pendulum (IP), which requires control of the pendulum’s angle to keep it steady in the vertical position as the cart within the system moves to the required position. The IP system is thus a benchmark challenge in control engineering. In this study, a controller for an IP system was designed using a Linear Quadratic Regulator (LQR). The construction of LQR parameters is based on weight matrices, and the most difficult part of designing LQR controllers is determining how to adjust the weight matrices parameters. These are commonly calculated by trial and error; however, this method consumes a great deal of time and effort. A Whale Optimization Algorithm (WOA) was thus applied in this work to adjust the weighting matrices of the LQR controller to identify the best options for these matrices, reducing the difficulty in predicting the optimum matrices and providing for their self-adjustment. Integral Square Error (ISE) was used as the objective function for both the angles and positions, and the simulation results confirmed the robustness and effectiveness of a WOA-based LQR controller.