基于MATLAB的线性二次型最优控制算法及应用研究

The Algorithm and Application Research of LinearQuadratic Optimal Control based on MATLABAbstractIn early 1950,there appeared for the research of the linear quadratic optimalcontrol LQ (Linear Quadratic),with the deepening study of LQ,LQ has nowbecome one of the most classical optimal control of the modern control theory.Inmany of research on LQ,one of them which based on state feedback controller is themost systematic and complete.And the linear inverted pendulum system as anexperimental platform which research the control theory,it not only has theadvantages of simple structure,low price,but also can reflect many typical controlproblem,so it has been applied in many fields.MATLAB,as the representative of thesystem software used in the field of digital simulation,and has a powerful functionlibrary,so it can make the researchers easily achieve the goals of modern controltheory.In this paper,for the first-order linear system,the quadratic function formed bythe state variable x and the control input variable U is the objective function,andstudies three major issues in the linear quadratic optimal control algorithm,which arethe state regulator problem,the output regulator problem and tracker problem,andgives the specific numerical examples and simulates these problems by MATLAB.Then this paper studies the application of linear quadratic optimal control in theinverted pendulum controller design,gives system model and the MATLABsimulation waveform.Key Words:Linear quadratic optimal control state regulatoroutput regulatortracker MATLAB inverted pendulum system