Controller Design using Routh-Padé Approximants with Stability Margin

A model reduction-based controller design approach is presented, addressing the challenge that a lower-dimensional model, though open-loop stable, may not guarantee closed-loop stability—an essential criterion in controller design. To overcome this, a novel error minimization approach is presented for finding reduced-dimensional models of stable linear time-invariant higher-order systems, ensuring both open-loop and closed-loop stability. Open-loop stability is preserved using Lyapunov's second method, while closed-loop stability is enforced by incorporating gain margin and phase crossover frequency constraints into the optimization process. An initial reduced-order model is obtained without relative stability (RS) constraints, and a PID controller (PIDC) is derived. For comparison, PIDC is applied to both the higher-dimensional system (HDS) and the modified reduced model derived, that includes stability margin constraints. The effectiveness of the approach is validated via an example.