用一种新的极点配置方程确定双输入多输出系统的控制律

 本文导出了双输入多输出系统的极点配置方程。它们的形式和通常所用的极点配置方程形式不同。证明了方程的一个性质,利用这个性质可以较好地控制各个特征值配置的精度。算例表明,用这种方法配置的极点的精度比用“秩一控制器”方法有较大改善。

APPLICATION OF A NEW TYPE OF POLE COLLOCATION EQUATIONS TO DESIGNING THE CONTROL LAW OF A BI-INPUT-MULTI-OUTPUT SYSTEM

A method for designing the control law of a bi-input-multi-output system using the pole collocation method is presented.The pole collocation equations（Eqs 10 and ll）of a bi-input-multi-output system are derived in a different form from the general. In their derivation the eigenvalues and eigenvectors of the dynamic matrix[F] （see Eqn 1 ） of the open-loop system are used. Corresponding to every pole （or a pair of poles）, a real（or a complex）equation is deduced. A nature of Eqn 11 is verified （see Eqn 13）. Then Equation 11 can be weighted to minimize the mean square of the relative errors of the real and imaginary parts of poles.So each equation can be weighted separately to improve the accuracy of poles which have predominant effect on stability. But it is Iimpossible to weight the pole collocation equations in general form to improve the accuracy of a specific pole.The numerical results show that the accuracy of poles obtained by the present method is better than that obtained by the "rank one controller" under the same unperfect conditions.