Parameter And Time-delay Estimation For A Class Of Closed-Loop Systems Based On The Greedy Method

Identification of a plant in closed-loop operation is of great significance in system identification,which has received considerable attention in the literature.Identification of time-delays is unavoidable in most system identification,therefor it is important to identify the time-delays of a closed-loop system.Inspired by the recovery theory of compressed sensing,in this paper,a class of closed-loop identification methods based on the greedy algorithms are developed.We consider to use the greedy algorithms to modify the Least Squares algorithm,the instrumental variable method and the iterative method.These algorithms can effectively estimate the parameters and time-delays of frontal and feedback channel.The concrete contains are as follows.1.For a class of closed-loop systems with unknown time-delays in both the control plant and the feedback controller,and the frontal channel model is controlled autoregressive model,a threshold orthogonal matching pursuit algorithm is applied to estimate the closed-loop system,the algorithm can estimate orders,time-delays and the parameters of the control plant with a small number of observations;In order to improve the anti noise ability,a Compressed Sampling Matching Pursuit(Co Sa MP)algorithm is developed.2.For a class of closed-loop systems with unknown time-delays in both the control plant and the feedback controller,and the frontal channel model is the output error model,because the unmeasurable noise terms appear in the information vector of identification model,an instrumental variable based on the Co Sa MP method is developed.This algorithm can estimate the parameters and time-delays of the frontal and the feedback path.3.For a class of closed-loop systems with unknown time-delays in both the control plant and the feedback controller,and the frontal path model are the equation error moving average model model and the output error moving average model,a compressed sampling matching pursuit iterative algorithm is applied to estimate the closed-loop system.These algorithm can not only estimate the parameters and time-delays of the frontal and the feedback path,but also estimate the noise model.4.For a class of closed-loop systems with unknown time-delays in both the control plant and the feedback controller,and the model orders of frontal and feedback channel areunknown,a sparsity adaptive subspace pursuit algorithm is applied to estimate the closed-loop system.This algorithm can estimate the parameters and time-delays of the frontal and the feedback path in case of the parameters and orders of the frontal and the feedback path are unknown.In summary,for a class of closed-loop systems with unknown time-delays in both the control plant and the feedback controller,and the frontal path with different noise,a class of greedy algorithms are applied to estimate the closed-loop system.This algorithm can estimate the parameters and time-delays of the frontal and the feedback path.The numerical simulation results verify the effectiveness of the proposed algorithms.