Design of state feedback control laws based on reduced order models

Abstract

Suboptimal linear quadratic control law of high dimensional systems based on reduced order models derived via balancing reduction method is derived. The proposed law is compared to suboptimal control laws based on aggregation and singular perturbation. Performance evaluation based on stability, suboptimality degree, quadratic cost degradation, closed loop step responses and controls, and closed loop pole positions has shown the superiority of the proposed suboptimal control law. The comparison is done through the application of the suboptimal control laws to several physical plants. The base of the comparison is the optimal control law. Also, a new reduction method, which combines features of balancing and aggregation, called Balagg, is introduced and evaluated. The use of reduced order models based on balancing, aggregation, balagg, and singular perturbation in pole placement is also considered. In pole placement, two design purposes are considered: 1. placing only some of the open loop eigenvalues and 2. shaping the open loop responses to nominal ones. Aggregation and balagg perform the best for the first design purpose while none of reduction methods meet the second design purpose.