Linear Quadratic Regulator: A Simple Thrust Vector Control System for Rockets

Abstract

The paper focuses on developing, tuning, and testing a controller for a two-stage finless rocket during its boost phase that is based on the Linear Quadratic Regulator (LQR) optimal control method. This is accomplished by deriving and adopting a simplified rigid body rocket model that represents accurately its physical properties and the corresponding aerodynamic forces acting on the rocket system during the flight phase. The launcher is commanded through the control input thrust gimbal angle δ to the desired altitude using the implemented LQR-based controller. Emphasis is given to the Thrust Vector Control (TVC) system, and to the minimization of the drift caused by wind gust disturbance phenomena, which may result in a sideway motion of the rocket, and, consequently, in deviating from its desired trajectory; this is addressed, and it is overcome by considering the output parameters expressed in terms of the pitch angle, pitch rate (or angular body rate) and drift. The linearized state-space model is validated for analysis and design compensation of the pitch control logic of the ascent flight control system. The derived algorithm is, then, implemented in a Matlab/Simulink setting to demonstrate that the LQR controller provides closed-loop dynamic tracking, while the tuning of the LQR controller through the weighting matrices Q and R allows for simulating and testing how the variation of the gain directly impacts the performance of the closed-loop system and, in turn, the controller.