【摘要】 本文建立了权矩阵Q、反馈阵K和特征值λ三者之间的对应关系。经比较几种建立二次型最优系统的方法后,提出了λ→K→Q逆推法。文中以调速系统为例,说明此法保证λ满足动态要求,K在物理上可以实现,Q为非负定阵。而且在整个运算过程中不必求解非线性Riccati方程,计算十分简捷,便于在现场边调试边修改参数。更多还原

【Abstract】 This paper presents an inverse deduction method (i.e.a retrogradation method) for establishing an optimal control System with quadratic performance indices. The sufficient and necessary conditions for the existence of a solution of an inverse problem are testified. The corresponding relations among the weighting matrix Q, the feedback matrix K and the eigenvalue λ are established. On the basis of a comparison of different ways of establishing a quadratic optimal control system, the λ→K→Q inverse deduction method is recommended. Accordingly, a speed regulating system is taken as an example to illustrate that this method can assure λ satisfying the dynamic conditions as dictated and the physical realization of K, and Q being a non-negative definite matrix. Moreover, the use of this method makes it unnecessary to solee Riccati equation in the course of computation. The computation procedure is simple and easy to carry out to modify the parameters at the worksite for readjustments.更多还原