PSO-Optimized LQR Control for Anti-Sway and Positioning of Rotary Cranes

This paper proposes a Linear Quadratic Regulator (LQR) parameter optimization method based on Particle Swarm Optimization (PSO) to enhance the grab attitude controller for rotary crane systems, with the objectives of improving positioning accuracy and suppressing load swing. Lagrange’s equations are first used to create a nonlinear dynamic model of the rotary crane, which is then linearized around an operational point to produce a fourth-order state-space representation. Based on this representation, a dual-objective fitness function is created, employing the Integral of Time multiplied by Absolute Error (ITAE) as the performance index and assigning the swing angle error more weight. The important parameters of the LQR weight matrix are optimized using the PSO algorithm. A dedicated novel pre-compensation gain algorithm is then developed to solve the pseudo-inverse of an augmented matrix, thereby removing steady-state error. According to simulation results, the PSO-optimized controller greatly improves the anti-sway performance and positioning accuracy of the system by reducing the peak swing angle and settling time by 33.9% and 55.9%, respectively, as compared to the traditional LQR control.