Control Analysis with Modified LQR Method of Anti-Tank Missile with Vectorization of the Rocket Engine Thrust

Łukasz Nocoń,Zbigniew Koruba,Łukasz Nowakowski,Piotr Szmidt,Marta Grzyb

doi:10.3390/en15010356

Abstract

This article approaches the issue of the optimal control of a hypothetical anti-tank guided missile (ATGM) with an innovative rocket engine thrust vectorization system. This is a highly non-linear dynamic system; therefore, the linearization of such a mathematical model requires numerous simplifications. For this reason, the application of a classic linear-quadratic regulator (LQR) for controlling such a flying object introduces significant errors, and such a model would diverge significantly from the actual object. This research paper proposes a modified linear-quadratic regulator, which analyzes state and control matrices in flight. The state matrix is replaced by a Jacobian determinant. The ATGM autopilot, through the LQR method, determines the signals that control the control surface deflection angles and the thrust vector via calculated Jacobians. This article supplements and develops the topics addressed in the authors’ previous work. Its added value includes the introduction of control in the flight direction channel and the decimation of the integration step, aimed at speeding up the computational processes of the second control loop, which is the LQR based on a linearized model.

Highlights

The development of missile control methods has long been an area of interest to scientists
Some of the control methods are based on the Riccati equation [3] and are utilized for designing non-linear control systems
The simulation was conducted for a hypothetical missile described by equations of dynamics (5) and controlled using a modified linear-quadratic regulator (LQR)

Summary

Introduction

The development of missile control methods has long been an area of interest to scientists. Increasing missile accuracy is the major factor that necessitates the development of engineering methods based on integration of missile subsystems [2]. The operating effectiveness of the optimal LQR control method largely depends on the elements of the Q and R weight matrix. These matrices impact the minimization of offsets generated for state variables under the influence of control signals. Combining the PID regulator tuning method with the LQR concept enables the optimization of set value tracking, with the optimal selection of setpoints for the same control object. The optimal control theory has been extended in order to tune PID regulators [4]

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Results