自校正调节器逼近于最小方差控制器的主要条件

The Main Conditions for Approximation of Self-tuning Regulator to Minimum Variance Controller

摘要: 本文探讨了闭环条件下自校正调节器（STR）参数的最小二乘估计结果随β₀设定值变化的一般规律,简捷地证明了STR最终收斂于最小方差控制器（MVC）的条件是二者阶次相当,而在实际有限时间历程内,使STR最好地逼近于MVC的一个重要附加条件则是β₀等于真值β₀。
本文还证明了,STR相对于MVC的任何偏离都将导致控制效果恶化,即输出误差方差增大。此外,还分析了β₀存在下限的原因,并提出加速估计收斂过程的办法。文中还给出了数字仿真示例。

Abstract: The paper examines the general law of the least squares estimates for the self-tuning regulator（STR） parameters varying with the presetvalue, and,furthermore,verifies succinctly that the condition for the eventual convergence of a STR to minimum variance controller （MVC） is that they have the corresponding degrees,while the important additional condition for optimal approximation of a STR to MVC within a finite time duration is just β₀=β₀（true value）.
It is also proved that any deviation of a STR from MYC may lead to the deterioration in performance,i.e.the increase of the variance of output error.The reasons fort he existence of the lower limit of β₀ are analysed,and the measures for accelerating the convergence process of STR parameters are proposed. Numerical simulation examples are presented.