Performance optimization of LQR‐based PID controller for DC‐DC buck converter via iterative‐learning‐tuning of state‐weighting matrix

Abstract

This paper presents a numerically optimized linear-quadratic-regulator-based tuning mechanism for a ubiquitous proportional-integral-derivative controller to improve the output-voltage regulation capability of a direct-current (DC)-DC buck converter. The linear-quadratic-regulator minimizes the quadratic cost of variations in the control signal and error-dynamics of output-voltage to provide a trivial set of optimized proportional-integral-derivative controller gains in the form of the state-feedback gain vector. In order to further improve the controller's time-domain performance and its disturbance-rejection capability against load-transients and input-fluctuations, an iterative-learningtuning mechanism is adopted to optimize the state-weighting matrix of the linear-quadratic cost function. The proposed optimization mechanism iteratively converges in the direction of the steepest gradient-descent of another performance index that directly captures the transient response characteristics, and thus, optimally selects the weighting matrix to achieve the desired natural frequency and damping ratio of the closed-loop system. Credible hardware-inthe-loop experiments are conducted on a low-power DC-DC buck converter circuit to validate the aforementioned propositions.A lot of research has been done to devise robust and optimal voltage controllers for effectively regulating the v o of the buck converter, despite the exogenous disturbances in load impedance and input voltage. A detailed comparative performance analysis of the conventional and contemporary control techniques has been presented in previous tudies. 4-6 These controllers are divided in two categories, namely, model-free controllers and model-based controllers. The model-free controllers do not depend on the mathematical model of the converter. Hence, they are relatively simpler to construct. 7 Although they can significantly improve the transient and steady-state response of the system, they lack optimality in minimizing the deviations in state-trajectories or energy consumption. The proportional-integralderivative (PID) controllers, and their variants, are the most widely used model-free controllers in the industry. 8,9 However, evaluating a trivial set of controller gains to obtain optimal control effort is a cumbersome process. Several autotuning techniques for PID gains have been proposed in the literature to enhance the robustness of the controller design. [10][11][12][13][14] The fuzzy-logic controllers infer the control decision based on a heuristically synthesized set of logical rules. 15,16 However, these rules are empirically defined and hence cannot completely compensate all the nonlinearities associated with the system's dynamics. Other widely used control schemes include the sliding-mode controller, 17,18 fractional-order PID controller, 19 and adaptive controller. [20][21][22] The model-based controllers depend on the mathematical model of the system and thus use the complete knowledge of system dynamics to provide optimal control effort. 23 Se...

Self‐adaptive fractional‐order LQ‐PID voltage controller for robust disturbance compensation in DC‐DC buck converters

“…An ill‐postulated PID controller renders detrimental influence on the system's time‐domain response. Hence, this research employs an LQR‐based tuning strategy for the selection of PID gains . The LQR minimizes a quadratic cost function of the state variables and the control input associated with the linear dynamical system to deliver optimal control decisions.…”

“…where, P ∈ ℝ 3 × 3 is a positive definite and symmetric matrix. It is also computed offline by solving the algebraic Riccati equation shown in Equation (22) …”

“…The details of the optimized controller‐parameters are provided in Table . It is well‐known that selecting large magnitudes of state weighting factors of J lqr minimizes the state variations while inducing large peaks in the control response, which may saturate the controlling switch in the circuit . Hence, in this research, the state weightages are limited within the interval [0, 10] in order to minimize the control energy expenditure, whereas, the augmented adaptive system serves to manipulate the system's time optimality.…”

Time‐optimal control of DC‐DC buck converter using single‐input fuzzy augmented fractional‐order PI controller

“…A plethora of feedback control schemes have been proposed by research engineers to optimally control the output voltage of buck converters, even in the presence of load transients and input‐voltage fluctuations . The proportional‐integral‐derivative (PID) controllers have been widely used to effectively regulate the output voltage of DC‐DC converters due to their simple structure . It is a linear model‐free controller that provides a robust control effort based on the weighted sum of the error dynamics.…”

“…[3][4][5] The proportional-integral-derivative (PID) controllers have been widely used to effectively regulate the output voltage of DC-DC converters due to their simple structure. 6,7 It is a linear model-free controller that provides a robust control effort based on the weighted sum of the error dynamics.…”