虚拟参考反馈校正控制的统计渐近性分析

Asymptotic statistical accuracy analysis of virtual reference feedback tuning control

虚拟参考反馈校正控制(VRFT)是一种数据驱动的控制策略,其避免了系统对象的建模过程,广泛应用于比例—积分—微分(PID)控制器的调整中。因未知参数估计值的统计渐近方差矩阵是整个系统辨识领域中的一个重要的衡量指标,利用泰勒级数展开得到未知参数估计的误差,对此参数估计误差建立其对应的方差矩阵式,利用矩阵运算推导出该方差矩阵式中的两对角元素。此两对角元素则对应为闭环控制系统中关于两未知参数估计矢量的渐近方差矩阵子式。以此渐近方差矩阵为基础,通过建立其迹运算的最优化问题来求解最优的滤波器。最后用仿真算例验证该方法的有效性和可行性。

Virtual reference feedback tuning control is a data-driven control strategy. No model identification of the plant is needed in this control method. Now virtual reference feedback tuning control is a widely used procedure for controller tuning process. Because the asymptotic covariance matrix expression is an important factor in the whole system identification theory.This paper derived the error about the unknown parameter estimation through Taylor series expression. Then it established the corresponding covariance matrix of the parameter estimation error. It obtained the two diagonal sub-matrices in the covariance matrix using some matrix operations. These two diagonal sub- matrices were the asymptotic covariance matrix expression of the two unknown parameter estimation vectors in the closed-loop system. Based on this asymptotic covariance matrix,it obtained an optimal filter by solving an optimization problem which included some trace operation. Finally,the efficiency and possibility of the proposed strategy can be confirmed by the simulation example results.