用逆推法建立二次型最优调节系统

A Recusive Algorithm for Synthesizing an Optimal Quadratic Control System

摘要: 本文用根轨迹法根据预期极点位置确定反馈阵K，由K求出P的部分行向量，从而使非线性Riccati方程蜕化为线性方程式．然后，根据不大于n（n+1）/2个线性方程式，验算对角阵Q的非负定性．如果Q≥0成立，则表明由K构成的控制律u（t）=-Kx（t）是使二次型性能指标J为最小的最优控制律，相应的闭环系统是上述Q条件下的二次型最优系统，并且具有预期的极点配置．文中以SCR-D调速系统为例，说明本法计算简单，实验结果与理论相符．

Abstract: In this paper the feed back matrix K is determined according to the desired polelocation by means of the root-locus method.From K we obtain a row of the matrix P,which makes the nonlinear Riccati equation a linear one.Then the property of the matrix Q is examined with no difficulty.If Q≥0,it means that the control law u(t)=-Kx(t) is an optimal one,which minimizes the value of the quadratic performance index J and so the related closed-loop system is an optimal quadraticone considering Q given above.And it gives a desired pole configuration.A SCR-Dsystem is given as an example,which shows that the calculation of this method is simple.

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