Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

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 secant-hyperbolic-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.