Abstract
In this paper, a novel approach for the design of a fractional order proportional integral derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains a fast system response and significantly reduces the voltage spike at the controller output. The time-varying FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm (GA) to find the optimum constants and time-varying parameters. The improved control performance is validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created for comparison with all three PID gain constants replaced by the optimized time functions. The simulation results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage spike at the controller output but also is also able to keep approximately the same characteristics of the system response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation block between the controller output and the plant still performs best according to system overshoot, rise time, and settling time.
Highlights
A traditional proportional integral derivative (PID) controller is one of the most used type of controller in industrial applications, because it provides stability and rapid responses, for a wide range of operating conditions [1]
The TVD-fractional order proportional integral derivative (FOPID) controller has a timevarying derivative gain which is achieved via an optimized time function
The proposed TVD-FOPID controller has the ability to mitigate the derivative kick by reducing voltage spike at the controller output by a stunning value of 80% while keeping the system overshoot, settling time and rise time on par with the regular FOPID controller
Summary
A traditional proportional integral derivative (PID) controller is one of the most used type of controller in industrial applications, because it provides stability and rapid responses, for a wide range of operating conditions [1]. The FOPID controller using extra parameters does provide better control of the DC motor speed, the derivative kick exists whenever a sudden change to the setpoint occurs [5], [40], [41]. Time-varying fractional order PID controllers are developed with a purpose to mitigate the derivative kick which exhibits at the controller output in the form of a voltage spike.
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