Design of robust-stable and quadratic finite-horizon optimal active vibration controllers with low trajectory sensitivity for uncertain flexible mechanical systems using an integrative computational method

By integrating the robust stabilizability condition, the orthogonal-functions approach (OFA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented in this paper to design the robust-stable and quadratic finite-horizon optimal active vibration controller with low trajectory sensitivity such that (i) the flexible mechanical system with elemental parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-horizon integral performance index including a quadratic trajectory sensitivity term for the nominal flexible mechanical system can be minimized. In this paper, 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-stable and quadratic 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 robust-stable and quadratic finite-horizon optimal 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. A design example is given to demonstrate the applicability of the proposed integrative approach.