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基于二次型性能指标的最优控制问题,是首先给定权矩阵(Q),确定最优反馈增益矩阵(F),使性能指标为极小。而稳定控制一般首先给定特征值(λ),然后确定反馈增益矩阵(F),使闭环系统具有满意的稳定性。许多学者研究了最优控制和稳定控制的对应关系。他们提出的方法,有的虽然可以用于多输入系统,但计算过程是相当复杂的。本文提出了根据反馈增益矩阵(F)推算与此相应的最优控制的权矩阵(Q)的直接计算方法,对于单输入的控制系统其计算是非常简单的。
The optimal control problem based on the quadratic performance index is to give the weight matrix (Q) first and determine the optimal feedback gain matrix (F) so that the performance index is minimal. However, the stability control generally first gives the eigenvalue (λ) and then determines the feedback gain matrix (F) so that the closed-loop system has satisfactory stability. Many scholars have studied the correspondence between optimal control and stable control. The methods they propose, although some can be used for multi-input system, but the calculation process is quite complicated. In this paper, we propose a direct method to calculate the weight matrix (Q) of the optimal control based on the feedback gain matrix (F), which is very simple for the single-input control system.