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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。
In this paper, the root locus method is used to determine the feedback matrix K according to the expected pole position, and the partial row vector of P is obtained by K, so that the nonlinear Riccati equation can be degenerated into a linear equation. Then, on the basis of not more than n (n + 1) / 2 linear equations, the negativity of the diagonal matrix Q is checked. If Q (?) 0 holds, then it is proved that the control law composed by K u (t) = - Kx (t) is the optimal control law that minimizes the quadratic performance index J and the corresponding closed- Under the quadratic optimization system, and has the desired pole configuration. In this paper, SCR-D speed governing system is taken as an example to show that the method is simple and the experimental results are consistent with the theory.