The practical analysis for closed-loop system identification

Abstract

As the existed theories for closed-loop system identification are very mature, and in this short note, one common closed-loopclosed-loop system is considered, then the classical prediction error identification is reviewed for closed-loop system identification. Based on above-existed results on closed-loop system identification, here we continue to do some research on closed-loop system identification from the practical perspective. It means all mathematical derivations and results, proposed here are more general than those existed results from references, and all results are more suited for the practical application. More specifically, the cost function, used to minimize with respect to the unknown parameter, is derived again to its more simplified form. The identification for the unknown plant is obtained again from the point of its usual spectral analysis estimation. After choosing one suited coefficient matrix into the explicit expression about the cost function, one optimal feedback controller or optimal control input is derived to be global minimum. Our derived spectral analysis estimation, simplified cost function, and optimal feedback controller are beneficial for embodying the relations with all input– output signal and other variables, such as the true plant, parameter estimator, spectral analysis estimation etc. Finally, one simulation example has been performed to demonstrate the effectiveness of the theories proposed in this paper.