<div>In this thesis work, a novel approach for the design of a fractional order proportional integral</div><div>derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller</div><div>to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The</div><div>voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a</div><div>derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is</div><div>left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to</div><div>take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains</div><div>a fast system response and signi?cantly reduces the voltage spike at the controller output. The time-varying</div><div>FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm</div><div>(GA) to ?nd the optimum constants and time-varying parameters. The improved control performance is</div><div>validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID</div><div>controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created</div><div>for comparison with all three PID gain constants replaced by the optimized time functions. The simulation</div><div>results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage</div><div>spike at the controller output but also is also able to keep approximately the same characteristics of the system</div><div>response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation</div><div>block between the controller output and the plant still performs best according to system overshoot, rise time,</div><div>and settling time.</div>