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

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-learning-tuning 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-in-the-loop experiments are conducted on a low-power DC-DC buck converter circuit to validate the aforementioned propositions.