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

Mahmoud N Ali,Josep M Guerrero,Matti Lehtonen,Karar Mahmoud,Mohamed M F Darwish,Mahmoud Soliman

doi:10.1109/access.2021.3100415

Mahmoud N Ali, Josep M Guerrero + Show 4 more

Open Access

https://doi.org/10.1109/access.2021.3100415

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Abstract

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.

Highlights

One of the principal control loops in electric power systems is the voltage control loop [1], [2]
For the controller resiliency, the maximum resilient robust PID controller is determined using the principle of the maximum-area circle that can be inscribed in the robust control basins (CBs)
The CB of a specific control objective is systematically traced in the space of PID gains using a pair of frequency polynomials, namely kp and ki for an arbitrary value of kd

Summary

INTRODUCTION

One of the principal control loops in electric power systems is the voltage control loop [1], [2]. Parametric uncertainties of a power system model and yet the perturbations of the gains of controllers represent a challenge to guarantee stability robustness and optimal performance. In [35], a robust non-fragile PID based AVR control system is designed, while RHC and KT were dedicated for guaranteeing robust stability with perturbation in controller gains. Techniques are widely used to compute optimized controller gains that provide fine performance in different engineering applications. Among these AI-based methods, PID gains are adjusted using the anarchic society optimization (ASO) method [38]. Three control concerns (performance optimality, stability robustness, and controller resiliency) are accounted in a simultaneous manner rather than the contributions of [36], [37]. The computation, validation as well as simulation results are presented in Section VI, while Section VII provides conclusions

DYNAMIC MODEL OF THE AVR SYSTEM

Findings

CONCLUSION