Algebraic approach for selecting the weighting matrices of linear quadratic regulator

This paper proposes an algebraic approach for selecting the weighting matrices of linear quadratic regulator (LQR) for trajectory tracking application. One of the important problems in designing the state feedback controller via LQR is the choice of Q and R matrices. Normally, the weights of LQR controller are chosen based on trial and error approach to obtain the optimum state feedback controller gains, but it is often cumbersome and tedious to tune the controller gains via trial and error method. Hence to address the weight selection problem of LQR, a novel algebraic approach, which relates the time domain specifications of the system to be controlled to the weighting matrices of LQR, is proposed in this paper. The key idea of the proposed approach is the synthesis of time domain design specifications for the formulation of cost function of LQR, which directly translates the system requirement into cost function, so that an optimal performance can be obtained via a systematic approach. A nonlinear magnetic levitation system is used to validate the efficacy and robustness of the proposed methodology, and a detailed simulation results are presented.