In this paper, two optimization methods are used to adjust the gain values for the cascade PID controller. These algorithms are the butterfly optimization algorithm (BOA), which is a modern method based on tracking the movement of butterflies to the scent of a fragrance to reach the best position and the second method is particle swarm optimization (PSO). The PID controllers in this system are used to control the position, velocity, and current of a permanent magnet DC motor (PMDC) with an accurate tracking trajectory to reach the desired position. The simulation results using the Matlab environment showed that the butterfly optimization algorithm is better than the particle swarming optimization (PSO) in terms of performance and overshoot or any deviation in tracking the path to reach the desired position. While an overshoot of 2.557% was observed when using the PSO algorithm, and a position deviation of 7.82 degrees was observed from the reference position.

In this paper, there are two contributions: The first contribution is to design a robust cascade P-PI controller to control the speed and position of the permanent magnet DC motor (PMDC). The second contribution is to use three methods to tuning the parameter values for this cascade controller by making a comparison between them to obtain the best results to ensure accurate tracking trajectory on the axis to reach the desired position. These methods are the classical method (CM) and it requires some assumptions, the genetic algorithm (GA), and the particle swarm optimization algorithm (PSO). The simulation results show the system becomes unstable after applying the load when using the classical method because it assumes cancellation of the load effect. Also, an overshoot of about 3.763% is observed, and a deviation from the desired position of about 12.03 degrees is observed when using the GA algorithm, while no deviation or overshoot is observed when using the PSO algorithm. Therefore, the PSO algorithm has superiority as compared to the other two methods in improving the performance of the PMDC motor by extracting the best parameters for the cascade P-PI controller to reach the desired position at a regular speed.

In this paper, two contributions are presented. the first is to design two cascade controllers to control the velocity and position for two Permanent Magnet DC motors (PMDC) working together at the same time for use in many applications such as CNC machines, robotics, and others. Furthermore, the cross-coupling technique is used to connect these motors and adjust the precise synchronization of their movement on the axes. The second contribution is the use of the butterfly’s optimization algorithm (BOA) with the objective function Integral Time Absolute Error (ITAE) to extract the optimal parameter values for the two cascade controllers and the synchronization controller in order to obtain the best accurate results. The simulation results showed high accuracy to reach the desired position at a regular velocity of both the PMDC motors with accurate synchronization and tracking trajectory on the axes. In addition, a very small position deviation of 0.021 rad was observed, and the system returned to a steady-state after 2 seconds of applying the full load.