REDUCED-ORDER COMPENSATION USING THE HYLAND-BERNSTEIN OPTIMAL PROJECTION EQUATIONS

Gradient-based homotopy algorithms have previously been developed for synthesizing H-2 optimal reduced-order dynamic compensators. These alg orithms are made efficient and avoid high-order singularities along th e homotopy path by constraining the controller realization to a minima l parameter basis. The resultant homotopy algorithms, however, sometim es experience numerical ill conditioning or failure due to the minimal parameterization constraint. A new homotopy algorithm is presented th at is based on solving the optimal projection equations, a set of coup led Riccati and Lyapunov equations that characterize the optimal reduc ed-order dynamic compensator. Path following in the proposed algorithm is accomplished using a predictor/corrector scheme that computes the prediction and correction steps hy efficiently solving a set of four L yapunov equations coupled by relatively low-rank linear operators. The algorithm does not suffer from ill conditioning because of constraini ng the controller basis and often exhibits better numerical properties than the gradient-based homotopy algorithms. The performance of the a lgorithm is illustrated by considering reduced-order control design fo r the benchmark four disk axial vibration problem and also reduced-ord er control of the Active Control Technique Evaluation for Spacecraft s tructure.