Stabilization of inverted pendulum system using intelligent Linear Quadratic Regulator controller

TLDR: Simulation results showed that the proposed method is efficient in determining the weighting matrices of LQR and minimizes time-to-solution in comparison with the conventional trial-&-error approach.

Abstract: One of the classical problem in dynamics and control theory, which has being widely used as a benchmark for testing control algorithms, such as Linear Quadratic Regulator (LQR) is the balancing of inverted pendulum. The performance of LQR depends largely on the design choice of state and control weighting matrices (Q & R). However, these matrices are usually selected by the designer through a trial and error iterative process which might not guarantee robustness and may increase computational time. To overcome this, we propose a new approach for the optimal determination of the LQR weighting matrices based on weighted artificial fish swarm algorithm (wAFSA). The designed controller is then used to obtain an optimal controller for a dynamic nonlinear Quadruple Inverted Pendulum (QIP). In this paper, we first introduce an approach called inertial weight into the standard Artificial Fish Swarm Algorithm (AFSA) to adaptively select its parameters (visual & step sizes) thereafter, the modified algorithm was used to determine the optimize values of LQR weighting matrices randomly. The optimized values of the weighting matrices were also determined using the standard AFSA and the standard Artificial Bee Colony (ABC) algorithm. This was then used to stabilize the QIP system. Simulation results showed that the proposed method is efficient in determining the weighting matrices of LQR and minimizes time-to-solution in comparison with the conventional trial-&-error approach.