Multi-Objective Optimal Design of Four-Parameter PID Controls

Abstract

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.

Three‐time scale multi‐objective optimal PID control with filter design

“…Following this approach, we will have five parameters to design, namely, k p , k i , k d , 𝜀 1 , and 𝜀 2 . This problem has been solved in Sardahi and Boker [19] with 𝜀 1 = 1 using multi-objective optimization technique. In Sardahi and Boker [19], the problem was solved in one shot by optimizing the controller parameters to achieve a number of conflicting objectives.…”

“…The term dependent on e s 0 in (19) is regarded as bias since e s 0 is a 'frozen' parameter in this time scale. Consequently, to remove this bias from ( 18)-( 19), we employ…”

“…This work proposes a method that designs the PID controller with a measurement derivative filter through solving a multi-objective optimization problem in a systematic and computationally efficient way. It avoids solving the optimization problem in one shot thus improving the result reported in [26], where four tuning parameters need to be optimized at the same time. The key idea in our work is to exploit the fact that the integrator dynamics are typically slower than the system dynamics while the filter dynamics are typically faster.…”

“…As the measurement noise is usually dominated by higher frequencies [17], a low-pass filtering is required for the derivative part of the PID controller to limit the high-frequency gain [18]. The work by Sardahi and Boker [19] proposed a second-order PID controller, which requires tuning of four parameters including the derivative filter factor, and it was shown in that the derivative filter factor must be taken into account while optimizing the PID controller. This was a departure from the practice of designing commercial controllers as the filter gain is usually kept constant or totally ignored due to its noise amplification characteristics [20], especially when input disturbances are considered.…”

Multidisciplinary Optimal Design of an Active Control System and State Estimator for an Aircraft Wing

“…However, the computational cost can be justified if a more accurate solution is desired, and the optimization is conducted offline. The most widely used multi-objective optimization algorithm is the NSGA-II (Sardahi, Y. and Boker, A., 2018). It yields a better Pareto front as compared to SPEA2 (strength Pareto evolutionary algorithm) and PESA-II (Pareto Envelope based Selection Algorithm).…”