This paper introduces the simple cell mapping (SCM) method for the multi-objective optimal time domain design of feedback controls for linear systems with or without time delay. The SCM method is originally developed for the global analysis of nonlinear dynamical systems, and is extended to the multi-objective optimal design problem of feedback controls in this paper. We consider two feedback control design problems to demonstrate the method: a linear quadratic regulator based approach with the weighting matrices as design parameters, and a direct optimization with feedback control gains as design parameters. The Pareto set and Pareto front consisting of the peak time, overshoot and integrated absolute tracking error are obtained for two linear control systems, one of which has a control time delay. It is interesting to note that for the second order linear system, we have found a structure of the Pareto front, which has been very difficult to obtain using stochastic search algorithms. This study suggests that the SCM method is an effective
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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