This paper presents a multi-objective optimal PID (Proportional-Integral-Derivative) controller with the derivative filter factor as the fourth design parameter. The complete design of the PID controller should involve tuning four parameters instead of three. However, most of the research papers consider only three parameters. The fourth parameter, the filter factor, is assigned to a default value or selected experimentally. In all cases, the choice of this factor filter will alter the closed-loop response’s characteristics that were assumed before inserting the filter in the control loop. Therefore in this study, we include the filter factor in the decision variable space from the early stage of the control system design. Also, we formulate the design problem as a multi-objective optimization problem in order to show all the trade-offs among the system speed of response, percentage overshoot, sensitivity to external load disturbances, and sensitivity to noises impacting the measurements as the four parameters of the PID control are tuned. The optimal trade-offs solutions are then introduced to the decision-maker who can choose any one of them.

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