Optimal design of adaptive and proportional integral derivative controllers using a novel hybrid particle swarm optimization algorithm

Controlling of a rotational inverted pendulum is considered as a challenging problem, mainly due to the system's inherent nonlinear and unstable dynamics. In fact, the goal of this control is to maintain the pendulum vertically upward regardless of external disturbances. This paper aims to optimally design a model reference adaptive proportional integral derivative (PID) control for rotary inverted pendulum system based on a novel hybrid particle swarm optimization algorithm, combining sine cosine algorithm and levy flight distribution. Evaluation of the performance quality of the proposed adaptive controller is accomplished based on the stabilization and tracking control of rotary inverted pendulum system. In addition, two other PID controllers are designed to get a better understanding of the performance and robustness of the proposed controller. To make a complete comparison, the performance of the hybrid particle swarm optimization algorithm is examined against two other optimization techniques known as simple particle swarm optimization and whale optimization algorithm. Finally, the obtained simulation results demonstrate that the proposed optimal adaptive controller is superior to the other controllers, especially in terms of the transient response characteristics and the magnitude of control output signal.