Design of an Adaptive Linear Quadratic Regulator for a Twin Rotor Aerodynamic System

Abstract

This paper deals with a twin rotor aerodynamic system (TRAS), which is a multi-input multi-output (MIMO) system with high crosscoupling between its two channels. It proposes an adaptive linear quadratic regulator (ALQR) to stabilize this system. The justification for using an adaptation technique is that the conventional LQR—designed by linearizing the TRAS about a certain equilibrium point—can no longer achieve the design specifications when the system operating point deviates significantly from the equilibrium point. To introduce an adaptation mechanism in the system, formulas for determining the operating points of the TRAS in terms of the reference inputs are deduced, and the linearized TRAS model is parameterized in terms of the reference inputs so that when the reference inputs change, a new LQR is designed with respect to these new reference inputs, resulting in an ALQR. To demonstrate the superiority of the ALQR over the LQR, transient response specifications (rise time, settling time, and percentage overshoot) as well as integral square error (ISE), integral absolute error (IAE), integral time squared error (ITSE), and integral time absolute error (ITAE) are calculated for both systems. The main contribution of this paper is that it identifies the operating range by its width and its position with respect to the equilibrium point (width, position), and it investigates the effect of these two attributes on the performance of the closed-loop system by considering five cases with different width and position. Simulation results (carried out by MATLAB) show that the ALQR outperforms the LQR and the PID controller in all cases, and its superiority becomes more significant for cases that are characterized by a large deviation from the equilibrium point.