By integrating the orthogonal-functions approach (OFA), the hybrid Taguchi-genetic algorithm (HTGA) and a robust stabilizability condition, an integrative method is presented in this paper to design the robust-optimal active vibration controller such that (i) the flexible mechanical system with elemental parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-horizon integral performance index for the nominal flexible mechanical system can be minimized. The robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal flexible mechanical feedback dynamic equations. By using the OFA and the LMI-based robust stabilizability condition, the robust-finite-horizon-optimal active vibration control problem for the uncertain flexible mechanical dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition; thus greatly simplifying the robustoptimal active vibration control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust-optimal active vibration controllers of the uncertain flexible mechanical systems. Two design examples are given to demonstrate the applicability of the proposed integrative approach.
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