Nonlinear Feedback Linearization and LQG/LTR Control: A Comparative Study for a Single-Machine Infinite-Bus System

TL;DR

The study tackles SMIB stability under nonlinear dynamics by comparing three control strategies: NFLC, INFLC, and LQG/LTR, using a $9^{th}$-order high-fidelity plant and a $5^{th}$-order CDM. NFLC/INFLC rely on exact feedback linearization to decouple and linearize the nonlinear system, with INFLC adding integral action for zero steady-state error, while LQG/LTR leverages an enhanced Kalman filter with loop-transfer-recovery to achieve robust, optimal control. Simulations across nominal, fault, and load-change scenarios show NFLC/INFLC deliver superior transient damping and fault resilience on the CDM, whereas LQG/LTR provides strong frequency control and robustness on the high-fidelity plant; INFLC often yields the best fault performance due to integral action. The results offer a practical framework for selecting control strategies in SMIB and scaling to multi-machine grids, highlighting trade-offs between performance, robustness, and complexity, and pointing to future work on IEEE benchmark systems.

Abstract

This paper presents a comparative study of three advanced control strategies for a single-machine infinite-bus (SMIB) system: the nonlinear feedback linearizing controller (NFLC), the integral-NFLC (INFLC), and the linear-quadratic-Gaussian/loop transfer recovery (LQG/LTR) control. The NFLC and INFLC techniques use exact feedback linearization to precisely cancel the SMIB system nonlinearities, enabling the use of decentralized, linear, and optimal controllers for the decoupled generator and turbine-governor systems while remaining unaffected by the SMIB system's internal dynamics and operating conditions. In contrast, the LQG/LTR approach employs an enhanced Kalman filter, designed using the LTR procedure and a detailed frequency-domain loop-shaping analysis, to achieve a reasonable trade-off between optimal performance, noise/disturbance rejection, robustness recovery, and stability margins for the SMIB system. We provide a control synthesis framework for constructing practical, verifiable, scalable, and resilient linear and nonlinear controllers for SMIB and multi-machine power systems by utilizing a high-fidelity plant model for validation, a reduced-order control-design model, and the correlations between the two models' control inputs. Rigorous simulations and comparative analysis of the proposed controllers and a full-state linear-quadratic regulator show the benefits, constraints, and trade-offs of each controller in terms of transient response, steady-state error, robustness, rotor angle stability, frequency control, and voltage regulation under different operating conditions. Ultimately, this study aims to guide the selection of appropriate control strategies for large-scale power systems, enhancing the overall resilience and reliability of the electric grid.

Figures (12)

• Figure 1: Structure of a single-generation unit.
• Figure 2: A synchronous generator schematic with the reference directions.
• Figure 3: Bode plots (magnitude and phase responses) of the transfer functions $H_{11}$(s) (top) and $H_{22}$(s) (bottom) for various $q$ parameter values.
• Figure 4: Nyquist diagrams of the transfer functions $H_{11}$(s) (top), $H_{22}$(s) (middle), and $H_{22}$(s) zoomed version (bottom) for various $q$ parameter values.
• Figure 5: System response plots ($V_t$, $\omega$, $\delta$, $T_m$, $E_{FD}$, $u_T$) for the NFLC, INFLC, and LQG/LTR controllers applied to the reduced-order SMIB CDM at Operating Point I.