Design of Linear Quadratic Regulator (LQR) Based on Solving Algebraic Riccati Equation (ARE) for Minimize the Performance Index

Abstract

This paper deals with the theoretical and computational analysis of linear quadratic regulator (LQR) problems, with the aim of providing solutions to them with MATLAB simulation and implementation. Linear quadratic regulator is a special type of optimal control problem that deals with linear system and minimization of cost or objective functions that are quadratic in state and in control (subject to some constraints) with performance index J determination. This work involves solving the associated algebraic Riccati equation (ARE) of the control systems and obtaining the optimal control gain. The work is mainly applicable in satellite and spacecraft launching technology to determine minimum time for spacecraft to meet its target, minimum fuel consumption for the operation of a rocket or spacecrafts and the minimum cost in the design of the spacecraft, through finding solution to the Algebraic Riccati Equation (ARE), whose solutions give the minimization parameters for the design and operation of the spacecraft. It is interesting to observe that minimizing the quadratic performance index J will always yields a stable closed loop system. Structure of Q and R parameters are needed in the determination of optimal control gain of the systems, as they vary minimization of the quadratic performance index J. These structures are explicated extensively in this work. If the main goal of the design procedure is solution to linear quadratic regulator problems is achieved through the use of the MATLAB, as it gives the positive definite matrix P, poles of the control system which shows that the system is always stable and the optimal control gain which shows that the cost or objective function is minimized. In summary this paper has introduced a method of a control design that has the ability to minimize the performance index based J on (LQR).