Resilient Design of Robust Multi-Objectives PID Controllers for Automatic Voltage Regulators: D-Decomposition Approach

Resilient design of robust multi-objectives PID controllers via the D-decomposition method is presented in this paper for automatic voltage regulators (AVRs). The stabilizing interval of derivative gain ( k_{d} ) is analytically calculated by the Routh-Hurwitz criterion. The k_{p}-k_{i} domain, for a fixed value of k_{d} , is decomposed in root invariant regions by mapping the stability boundary from the complex plane. Two regions, described by fixed damping isoclines, are assigned for pole-clustering in the open-left half plane (LHP). Other than regional pole clustering, gain and phase margins, as frequency domain specifications, are considered. Both robust stability and robust performance are considered by stabilizing a set of principle segment plants simultaneously. Optimal pole-placer PID controllers are computed analytically. If a robust control basin does exist for a specific compromise of control objective, the criterion of the maximum inscribed circle is considered to compute the maximum radius of controller resiliency. The merit of the proposed design is the simultaneous consideration of three control concerns, namely performance optimality, stability robustness and controller resiliency. Computation, validation, and simulation results are presented to show the simplicity and efficacy of the suggested method in tracing control basins (CBs) of all admissible PID controllers.