In this paper, a multi-objective optimization of a time-delayed fractional order damping system is presented. In previous studies, a single objective optimization of this system was based on minimizing the integral of the squared error JISE, integral of the time-weighted squared error JITSE, integral absolute error JIAE, or integral time-weighted absolute error JITAE. However, from the practical point of view other design goals such as those related to system’s response and stability should be also included since an error-based optimized system can result in a system having the smallest error but at the expense of other crucial objectives. Moreover, the one-objective optimization returns only one design option hiding many important details about other possible design preferences. Here, the system under study is optimized by considering three objectives: peak time tp, the percentage overshoot Mp(%), and JISE. The results show that the multi-objective optimization technique provides more information about the system behavior and grants the decision maker different design options, called the Pareto set. In addition, this study investigates the meaning of the aforementioned integral errors within the multi-objective optimization scope.

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