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...

This paper presents the development of an indirect adaptive state-feedback controller to improve the disturbance-rejection capability of under-actuated multivariable systems. The ubiquitous Linear-Quadratic-Regulator (LQR) is employed as the baseline state-feedback controller. Despite its optimality, the LQR lacks robustness against parametric uncertainties. Hence, the main contribution of this paper is to devise and retrofit the LQR with a stable online gain-adjustment mechanism that dynamically adjusts the state weighting-coefficients of LQR's quadratic cost-function via state-error dependent nonlinear-scaling functions. An original self-mutating phase-based adaptive modulation scheme is systematically formulated in this paper to self-adjust the state weighting-coefficients. The scheme employs pre-calibrated secanthyperbolic-functions whose waveforms are dynamically reconfigured online based on the variations in magnitude and polarity of state-error variables. This augmentation dynamically alters the solution of the Riccati-Equation which modifies the state-feedback gains online. The proposed adaptation flexibly manipulates the system's control effort as the response converges to or diverges from the reference. The efficacy of proposed adaptive controller is validated by conducting hardware-in-the-loop experiments to vertically stabilize the QNET 2.0 Rotary Pendulum system. As compared to the standard LQR, the proposed adaptive controller renders rapid transits in system's response with improved damping against oscillations, while maintaining its asymptotic-stability, under bounded exogenous disturbances. INDEX TERMS Hyperbolic functions, linear quadratic regulator, cost-function, rotary inverted pendulum, self-tuning control, state weighting-coefficients.

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