Design of Stabilizing Flight Control Law by Applying Balanced Truncation for Linear Quadratic Regulator

Abstract

This paper proposes a method to design a multiple-input-multiple-output stabilizing flight control law via controller order reduction. In this procedure, first, Linear Quadratic Regulator (LQR) is designed for a full-order plant model. Then the order of the LQR closed-loop system is reduced by applying balanced truncation to obtain a static output feedback control law, i.e., proportional-control law. The closed-loop order reduction is performed by applying a model order reduction technique called fractional balanced reduction to the controlled system modified by the weighting matrices of the LQR. This design method is applied to linear aircraft models. The simulation results show that the proposed method can design stabilizing flight control laws that provide closed-loop properties close to the LQRs. In addition, the obtained control laws can achieve a control performance better than conventional single-input-single-output roll and yaw dampers and comparable to or better than that designed by a numerical search algorithm and an LMI (Linear Matrix Inequality) approach.