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 a robust-stable and quadratic optimal controller such that (a) the active suspension system with elemental parametric uncertainties can be robustly stabilized, and (b) a quadratic finite-horizon integral performance index for the nominal active suspension 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 involving only algebraic computation is derived in this paper for solving the nominal active suspension feedback dynamic equations. By using the OFA and the LMI-based robust stabilizability condition, the dynamic optimization problem for the robust-stable and quadratic optimal control design of the linear uncertain active suspension system is transformed into a static-constrained optimization problem represented by algebraic equations with the constraint of the LMI-based robust stabilizability condition; thus greatly simplifying the robust-stable and quadratic optimal control design problem of the linear uncertain active suspension system. Then, for the static-constrained optimization problem, the HTGA is employed to find the robust-stable and quadratic optimal controllers of the linear uncertain active suspension system. A design example is given to demonstrate the applicability of the proposed integrative approach.
Optimal Control Design of Active Suspension System Based on Quarter Car Model