Recently, we have proposed the simple cell mapping method (SCM) for global solutionsof multi-objective optimization problems (MOPs). We have applied the SCM method to the multi-objective optimal time domain design of PID control gains for linear systems to simultaneously minimize the overshoot, peak time and integrated absolute tracking error of the closed-loop step response. The SCM method can efficiently obtain the Pareto set and Pareto front globally, which represent the optimal control gains and performance measures, respectively. The Pareto set and Pareto front contain a complete set of control designs with various compromises in the tracking performance, and give the system designer a much wider range of choices and flexibility. Furthermore, we have discovered a fine structure of the Pareto front of the MOP solution, which was notseen before in the literature. In this paper, we further examine the implication of the fine structure with regard to the vibration control design and expected performance of the controller, and compare our findings with the dominant method in MOP studies, i.e. the genetic algorithm.

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