Design of an Optimal Controller for a Propeller-Pendulum System using the PSO Technique

Abstract

A new model for the non-linear propeller-pendulum system is derived in this study. The model takes into consideration the effects of external disturbances and the properties of the pendulum elements. Two systems with PID controllers are simulated. In the first system, Simulink is used to implement the system and tune the PID parameters. In the second system, a MATLAB script is used to simulate the system and tune the PID parameters. The scrip uses the Runge-Kutta method for solving the system’s equation and uses particle swarm optimization (PSO) to tune the parameters. Further, both systems were investigated under two disturbance conditions. The performance of these systems is evaluated based on comparing the settling time, the peak overshoot, and the integral of the absolute errors (IAE). The results show that when there is no disturbance, both systems are capable of tracking the desired signal successfully. However, the results also show that the application of disturbances causes the first system to lose its smooth response. In contrast, the second system demonstrates a robust response and effective countermeasures to disturbance effects. The results of unit step disturbance are as follows: the settling time, peak overshoot, and IAE of the first system are 13.16s, 11.6%, and 1.706, respectively. Further, the settling time, peak overshoot, and IAE of the second system are 2.388s, 6.6%, and 0.299, respectively. It can be concluded that Simulink is not recommended to be used for tuning the PID controller in the presence of disturbances.

Keywords

• PID controller
• Non-linear system
• Runge-Kutta technique
• Simulink model
• Integral of the Absolute Errors (IAE)