Parameterization of robust multi-objective PID-based automatic voltage regulators: Generalized Hurwitz approach

Abstract

This paper presents robust design of multi-objective PID controllers for automatic voltage regulators (AVRs). The set of stabilizing PID controllers is computed analytically using Routh-Hurwitz criterion (RHC). Minimal damping factors and coefficients are guaranteed by pole-placement in convex regions located in the open left half plane (LHP) and bounded by the damping isoclines. Optimal α-pole placement PID is derived where all gains are computed explicitly. Further, frequency domain specifications specifically gain and phase margins (GM, PM) are considered. Enforcing pole-clustering, GM and PM requirements are reduced to solve Hurwitz stability of either a real or complex characteristic polynomial which are tackled by generalizing RHC. Control basins (CBs) realizing any design objective other than stability are traced in kp-ki parameter plane, and hence different design objectives can be met simultaneously if their corresponding basins intersect. Model parametric uncertainties are captured by a set of principle polynomials derived by Polyak’s corollary to guarantee robust stability and performance simultaneously. Computation and comparative simulation results are given to confirm the effectiveness and simplicity of the proposed design approach.