Modelling And Model Mismatch Detection Method Based On Subspace Identification

Based on the design and operation of the model-based control system,the quality of the model is crucial.On the one hand,with the development of the process industry,the requirements for the accuracy of the process model are getting higher and higher.It is more difficult to construct a complex process model through the mechanism method;on the other hand,due to the actual production process,the valve is like a valve.The equipment has the characteristics of stickiness,easy changing of operating conditions,and being susceptible to disturbance changes.The model parameters of the actual object will change with time,and the model mismatch phenomenon will occur,thus causing the model to be inaccurate.The subspace identification method(SIM)can directly establish the state-space equation of a multi-input multi-output(MIMO)system,which has attracted much attention from researchers.In this paper,closed-loop subspace identification(CSMI)and recursive subspace model identification(RSMI)modeling and model mismatch detection methods are studied to improve the accuracy of the process model.Effectiveness is of practical significance.The details are summarized as follows:1?Aiming at the problem that open-loop model is difficult to apply in industrial process,a closed-loop subspace identification method based on orthogonal decomposition theory is proposed.By using orthogonal decomposition to obtain the deterministic components of the joint input and output signals,the closed-loop problem is transformed into an open-loop problem.Using the triangular structure form of the Toeplitz matrix,the subspace matrix composed of the coefficients of the impulse response model is decomposed into blocks,and the estimated impulse response model parameters are obtained by averaging the elements of the subspace matrix.2?In view of the time-varying nature of industrial processes and the large computational complexity of MIMO systems,a process modeling approach based on Recursive closed-loop subspace model identification(RCSMI)was proposed.The method converts the closed-loop identification problem into an open-loop identification problem by using a VARX model(Vector Auto Regressive with eXogenous input model)and adopts a natural power iteration method(Natural Power Method,NP)with a fast convergence rate to generate singular values.The decomposition is simplified as the subspace tracking problem,and the extended observation matrix is estimated to obtain the parameters of the system model.3?Aiming at the problem of model parameter mismatch during the operation of control system,this paper proposes a model mismatch detection method based on subspace identification and probability distribution distance metrics.The method obtains the Markov parameters of the reference model and the model to be detected through the subspace identification and combines the moving window method to extract the statistic of the Markov parameters,so as to obtain the probability density function of the Markov parameters PDFs.The Kullback-Leibler(KL)divergence using the divergence measure theory are used as statistical indicators to detect the dissimilarity between the reference and the Markov parameters of the model to be tested.Compared to conventional statistics such as T2 and Q statistics,KL divergence is more sensitive and describe the model mismatch directly.Numerical simulation and simulation of Wood-Berry distillation column prove that the paper proves the sensitivity and effectiveness of the proposed method.