Multi-objective optimal tuning and performance comparison of the LQR controller for an underactuated motion control system with GA, ABC, VPS, and BB-BC algorithms

The presented study is organized to provide details on the design and performance analysis of multi-objective optimization of LQR controller parameters for an underactuated motion (pendulum type gantry crane) system. The objective of the optimization is to design an LQR controller to eliminate pendulum oscillations caused by the motion of the system. In line with this objective, a new multi-objective function has been designed by considering the important parameters of control responses. The VPS and BB-BC algorithms have been utilized for the first time in the design and development of motion control for single pendulum gantry systems and compared with traditional GA and ABC algorithms. The six different populations or particle size values of GA, ABC, VPS, and BB BC algorithms were examined over 100 iterations to achieve the most successful optimization results. Furthermore, the configurations of the GA, ABC, VPS, and BB-BC algorithms yielding the best control performance were compared amongst themselves and against conventionally designed LQR controllers. Preliminary design findings indicated the elimination of steady-state error in the pendulum cart system, along with a considerable improvement of 51.54\% in settling time. Additionally, a substantial enhancement of up to 67.57\% was achieved in the settling time of the pendulum angle.