Date of Defense
17-11-2025 12:00 PM
Location
F1-1164
Document Type
Thesis Defense
Degree Name
Master of Electrical Engineering (MEE)
College
COE
Department
Electrical and Communication Engineering
First Advisor
Dr. Rachid Errouissi
Abstract
This thesis presents the design, development, and practical implementation of various robust current control strategies for LCL-filtered gridtied inverters, with the aim of maintaining robust stability over a range of plant perturbations, while ensuring high-quality current delivery to the utility grid. Chapter One presents the literature review, while Chapter Two focuses on the modeling of the system under study. In the third Chapter, the system dynamics are augmented with an appropriate servo-compensator to ensure that, at steady-state, the grid current accurately tracks its sinusoidal reference with zero steady-state error, even in the presence of model uncertainties. This augmented system serves as the basis for designing a simple state-feedback controller using the linear quadratic regulator (LQR) approach. Notably, the LQR technique is formulated to achieve robust stability across a range of plant perturbations. The performance of the closed-loop system under the LQR approach depends primarily on the elements of the weighting matrices, whose dimensions are dictated by those of the controlled system. However, the inclusion of the servo-compensator increases the number of plant states from the original three (associated with the LCL filter) to five, thereby complicating the selection of appropriate weighting matrices for the augmented system. Thus, selecting appropriate weighting matrices remains the primary challenge for applying this LQR approach to robustly stabilize the system under study. To overcome this challenge, a disturbance observer-based control (DOBC) scheme is proposed in the second part of this chapter. This approach combines a disturbance observer (DO) with the LQR controller. Acting as a servo-compensator, the DO estimates and compensates for unknown disturbances using the measured states of the LCL filter system. Meanwhile, the LQR approach, serving as the stabilizing component, is designed to maintain closed-loop stability across a range of model uncertainties. Unlike the previous approach, the LQR design here is based only on the original plant dynamics, which have an order of three. This significantly reduces the complexity associated with selecting appropriate weighting matrices for LQR control design. The main limitation of the LQR approach lies in the difficulty of explicitly specifying the desired transient response of the closed-loop system. In the third part of Chapter three, the LQR-based state-feedback controller is replaced by a design approach using linear matrix inequalities (LMIs). This method ensures stability of the closed-loop system by constraining the eigenvalues to lie within predefined regions of the complex plane despite a range of model uncertainties. As a result, not only does this method ensure robust closed-loop stability, but it can also meet certain requirements regarding the transient response such as limits on overshoot and settling time. As in the second part of the chapter, DO observer is employed to achieve zero steady-state error, provided that the closed-loop system is stable under the LMI-based state-feedback controller.
Chapter four employs the H∞ loop-shaping procedure to design a robust current controller for LCL-filtered grid-tied inverters. Specifically, an H∞ controller is synthesized by solving an algebraic Riccati equation, with the objective of enhancing the stability margin of a composite control structure that combines a conventional proportional-resonant (PR) controller with an active damping component. The PR controller is designed based on nominal system parameters to ensure zero steady-state error in the presence of model uncertainties. Similarly, the active damping component, also based on nominal parameters, employs capacitor current feedback to attenuate the resonance effects inherent to LCL filters, thereby ensuring the overall stability of the closed-loop system. However, the inherent mismatch between the actual and nominal system parameters can negatively impact the closed-loop stability. To address this issue, an H∞ controller is designed in this chapter to maximize the stability margin of the overall control system. Towards this end, the coprime factorization approach is applied to the open-loop system, comprising the nominal plant and the composite controller, to derive a perturbed model that captures system uncertainties. Then, H∞ loop-shaping procedure is employed on this perturbed model to synthesize a controller capable of maximizing the closed-loop stability margin with respect to model uncertainties.
Finally, Chapter five explores H∞ approach to design a robust current controller for LCL-filtered grid-tied inverters. Two controllers are proposed in this chapter: the first uses both the grid current and the converter current, while the second relies only on the converter current to regulate the grid current. Specifically, the first control structure is the same as that used in Chapter four to implement the PR controller with active damping. However, compared with Chapter four, the context in this chapter is different in that the PR controller and the active damping component are replaced by H∞ controllers. In other words, H∞ design procedure is used to develop a servo-compensator that guarantees asymptotic tracking of the grid current, along with a stabilizing controller that effectively attenuates the resonance associated with the LCL filter. H∞ design procedure relies on minimizing an H∞ performance objective, which in turn requires selecting appropriate weighting functions to achieve specific control objectives. The first key contribution of this chapter is the incorporation of a weighting function that accounts for the effect of measurement noise during the control design process. The second contribution of this chapter lies in using the H∞ design procedure to synthesize a current controller for grid current regulation based only on the converter current, thereby reducing the number of required current sensors. All controllers developed in Chapter three are validated through simulation tests, while those presented in Chapters four and five are validated through both simulation and experimental tests considering balanced voltages, unbalanced voltages, and 50% modeling errors. The results demonstrate strong robustness to parameter variations, accurate tracking of the current reference, and high-quality grid currents.
Included in
ROBUST CONTROL OF LCL-FILTERED THREE-PHASE GRID-TIED INVERTERS USING H∞ SYNTHESIS: DESIGN, ANALYSIS, AND EXPERIMENTAL VALIDATION
F1-1164
This thesis presents the design, development, and practical implementation of various robust current control strategies for LCL-filtered gridtied inverters, with the aim of maintaining robust stability over a range of plant perturbations, while ensuring high-quality current delivery to the utility grid. Chapter One presents the literature review, while Chapter Two focuses on the modeling of the system under study. In the third Chapter, the system dynamics are augmented with an appropriate servo-compensator to ensure that, at steady-state, the grid current accurately tracks its sinusoidal reference with zero steady-state error, even in the presence of model uncertainties. This augmented system serves as the basis for designing a simple state-feedback controller using the linear quadratic regulator (LQR) approach. Notably, the LQR technique is formulated to achieve robust stability across a range of plant perturbations. The performance of the closed-loop system under the LQR approach depends primarily on the elements of the weighting matrices, whose dimensions are dictated by those of the controlled system. However, the inclusion of the servo-compensator increases the number of plant states from the original three (associated with the LCL filter) to five, thereby complicating the selection of appropriate weighting matrices for the augmented system. Thus, selecting appropriate weighting matrices remains the primary challenge for applying this LQR approach to robustly stabilize the system under study. To overcome this challenge, a disturbance observer-based control (DOBC) scheme is proposed in the second part of this chapter. This approach combines a disturbance observer (DO) with the LQR controller. Acting as a servo-compensator, the DO estimates and compensates for unknown disturbances using the measured states of the LCL filter system. Meanwhile, the LQR approach, serving as the stabilizing component, is designed to maintain closed-loop stability across a range of model uncertainties. Unlike the previous approach, the LQR design here is based only on the original plant dynamics, which have an order of three. This significantly reduces the complexity associated with selecting appropriate weighting matrices for LQR control design. The main limitation of the LQR approach lies in the difficulty of explicitly specifying the desired transient response of the closed-loop system. In the third part of Chapter three, the LQR-based state-feedback controller is replaced by a design approach using linear matrix inequalities (LMIs). This method ensures stability of the closed-loop system by constraining the eigenvalues to lie within predefined regions of the complex plane despite a range of model uncertainties. As a result, not only does this method ensure robust closed-loop stability, but it can also meet certain requirements regarding the transient response such as limits on overshoot and settling time. As in the second part of the chapter, DO observer is employed to achieve zero steady-state error, provided that the closed-loop system is stable under the LMI-based state-feedback controller.
Chapter four employs the H∞ loop-shaping procedure to design a robust current controller for LCL-filtered grid-tied inverters. Specifically, an H∞ controller is synthesized by solving an algebraic Riccati equation, with the objective of enhancing the stability margin of a composite control structure that combines a conventional proportional-resonant (PR) controller with an active damping component. The PR controller is designed based on nominal system parameters to ensure zero steady-state error in the presence of model uncertainties. Similarly, the active damping component, also based on nominal parameters, employs capacitor current feedback to attenuate the resonance effects inherent to LCL filters, thereby ensuring the overall stability of the closed-loop system. However, the inherent mismatch between the actual and nominal system parameters can negatively impact the closed-loop stability. To address this issue, an H∞ controller is designed in this chapter to maximize the stability margin of the overall control system. Towards this end, the coprime factorization approach is applied to the open-loop system, comprising the nominal plant and the composite controller, to derive a perturbed model that captures system uncertainties. Then, H∞ loop-shaping procedure is employed on this perturbed model to synthesize a controller capable of maximizing the closed-loop stability margin with respect to model uncertainties.
Finally, Chapter five explores H∞ approach to design a robust current controller for LCL-filtered grid-tied inverters. Two controllers are proposed in this chapter: the first uses both the grid current and the converter current, while the second relies only on the converter current to regulate the grid current. Specifically, the first control structure is the same as that used in Chapter four to implement the PR controller with active damping. However, compared with Chapter four, the context in this chapter is different in that the PR controller and the active damping component are replaced by H∞ controllers. In other words, H∞ design procedure is used to develop a servo-compensator that guarantees asymptotic tracking of the grid current, along with a stabilizing controller that effectively attenuates the resonance associated with the LCL filter. H∞ design procedure relies on minimizing an H∞ performance objective, which in turn requires selecting appropriate weighting functions to achieve specific control objectives. The first key contribution of this chapter is the incorporation of a weighting function that accounts for the effect of measurement noise during the control design process. The second contribution of this chapter lies in using the H∞ design procedure to synthesize a current controller for grid current regulation based only on the converter current, thereby reducing the number of required current sensors. All controllers developed in Chapter three are validated through simulation tests, while those presented in Chapters four and five are validated through both simulation and experimental tests considering balanced voltages, unbalanced voltages, and 50% modeling errors. The results demonstrate strong robustness to parameter variations, accurate tracking of the current reference, and high-quality grid currents.