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如何确定加权阵 Q 的问题,是控制系统二次型性能指标最优设计的一个关键。但至今尚未得到彻底解决,由于工程实际问题往往是以时域指标提出的,因此可以将 Q 阵与系统的时域指标结合起来,对 Q 阵进行寻优。从而使系统在满足二次型设计的特点前提下,使时域指标为最佳。本文着重介绍了将正交回归设计的思想用于以数字仿真为基础的对 Q 阵寻优的过程中,以解决对复杂的非线性函数寻优之不足。文中给出了此寻优算法的流程图以及与几种算法的比较实例。经大量实验证明,此算法具有对初值不敏感,收敛速度快等优点。尤其对维数较高、较复杂的非线性函数之应用特点更显著。
How to determine the weight matrix Q is the key to the optimal design of quadratic performance index of control system. However, it has not yet been completely solved. Since engineering practical problems are often based on time-domain indexes, the Q-array can be combined with the time domain index of the system to optimize the Q-array. So that the system to meet the characteristics of quadratic design under the premise of making the best time domain indicators. This article focuses on the use of the idea of orthogonal regression design to optimize Q array based on digital simulation to solve the problem of searching for complex nonlinear functions. The flow chart of this optimization algorithm and its comparison with several algorithms are given in this paper. After a large number of experiments show that this algorithm has the initial value is not sensitive to the advantages of fast convergence. Especially for the higher dimension, the application of more complex nonlinear function features more significant.