最小方差控制中的最优输入信号设计

Optimal Input Signal Design for Minimum Variance Control

为研究最小方差控制中的最优输入信号设计问题,推导了最小方差控制器与闭环反馈结构中对象模型、噪声模型之间的关系。基于闭环反馈系统中频响函数估计的渐近分析,考虑系统对象模型、噪声模型和控制器三者之间的摄动性。分别采用输出端误差平方的均值、输入端误差平方的均值和输出端估计值平方的均值作为评价性能指标函数,推导三种情况下最优输入信号设计问题对应的约束优化问题。通过求解对应的约束优化问题,得到三种情况下最优输入信号的功率谱密度表达式。最后用仿真算例验证本文方法的有效性和可行性。

To study the problem of designing the optimal input signal in minimum variance control, the paper deduces the relationship between the system model and disturb model in the structure of the minimum variance controller and closed-loop feedback. Based on asymptotic analysis of frequency ring function estimation in the close-loop feedback system, perturbation of the relationship among system object model, noise model and the controller is considered. The average value of output error square, input error square and the output estimating value square as evaluating performance index function are adopted to deduce constraint optimization problems of the design of the optimal input signal in the three situations. By solving the corresponding constraint optimization problem, the power spectral density expression of the optimal input signal in the three situations is obtained. Finally, simulation results show the feasibility and effectiveness of the method in this paper.