Maximum Likelihood Identification Of Dual Rate Sampled Hammerstein Output Error Systems

With the advancement of science and technology,control theory and control engineering have been widely developed and applied.At the same time,higher requirements have been placed on system identification theory.System identification has been widely used in the fields of scientific research and engineering practice.At present,the objects of most system identification are single-rate systems with the same sampling frequency of input and output data.However,in most practical systems,due to hardware and other conditions,it is often impossible to obtain sampling data of the same frequency.Thus the research on dual-rate systems has important theoretical significance and application value.Among the many identification methods,the maximum likelihood identification has been widely used because of its outstanding statistical properties,but its research in dual-rate systems is still relatively limited.This paper combines the multiinnovation identification theory,recursive and iterative identification methods to study the maximum likelihood identification of non-linear systems with dual rate Hammerstein output error type,which has important research significance.The main research contents and results of this paper are as follows:1.For the dual-rate Hammerstein output error moving average system,a polynomial transform technique is used to derive a maximum likelihood forgetting factor stochastic gradient identification algorithm.In order to obtain higher identification accuracy,combined with multi-innovation identification theory,a multi-innovation maximum likelihood forgetting factor stochastic gradient algorithm is derived,which can effectively improve the identification accuracy and convergence speed by extending the length of innovation.2.For the dual-rate Hammerstein output error auto regressive moving average system,in order to reduce the calculation load brought by the polynomial transformation technology,a maximum likelihood Levenberg-Marquardt iterative algorithm based on auxiliary model and a maximum likelihood recursive Levenberg-Marquardt algorithm based on auxiliary model are proposed.Compared with the identification method using polynomial transform technology,the parameters of the dual rate system can be directly estimated through the auxiliary model,and the calculation amount is smaller.3.Aiming at the dual-rate Hammerstein Box-Jenkins system,a maximum likelihood gradient iterative algorithm based on auxiliary model and a maximum recursive least squares based on auxiliary model are proposed.The simulation example shows that the proposed algorithms have better performance and higher convergence accuracy.Compared with the identification method using polynomial transform technology,the amount of calculation is reduced,and the parameter estimation error is smaller.4.The proposed system identification theory is applied to the actual system model,and the identification problem of the two tank liquid level system is studied.Firstly,the mechanism is modeled,and its transfer function model is transformed into a differential equation form by Z transform.Considering the influence of noise and the nonlinearity of the valve,a dual-rate Hammerstein model of the two tank liquid level system is established.The maximum likelihood forgetting factor stochastic gradient algorithm and the maximum likelihood multi-innovation forgetting factor stochastic gradient algorithm are used to estimate the parameters.The results show that the proposed algorithms have higher identification accuracy and can be applied to the parameters estimation of the two tank liquid level system.