An enhanced adaptive-LQR procedure for under-actuated systems using relative-rate feedback to dynamically reconfigure the state-weighting-factors

Abstract

This paper synthesizes an innovative nonlinear-type self-adaptive Linear Quadratic Regulator (LQR) to enhance the robustness of under-actuated systems against bounded exogenous disturbances by using the relative-rate and state-error feedback. The control procedure is realized by augmenting the generic LQR with an online reconfiguration block that acts as a superior regulator to dynamically adjust the state-weighting-factors associated with the quadratic-performance index. The Riccati Equation uses the modified state-weighting-factors to re-compute the LQR problem and delivers the time-varying state-feedback gains. The said weighting-factors are adaptively modulated via a conventional state-error-magnitude-driven adaptation law that is retrofitted with auxiliary relative-rate-driven reconfiguration blocks. These blocks utilize error acceleration to deduce the response speed and thus re-adjust the variation rate of the weights in real time. This arrangement reinforces the controller’s adaptability to flexibly manipulate the tightness of the applied control effort. The proposed scheme is analyzed by conducting real-time hardware experiments on the QNET Rotary Pendulum. The experimental outcomes validate the superior position-regulation and disturbance-rejection behavior of the proposed scheme.