Parameter Estimation Of Linear Paraemter Varying Finite Impulse Response Model

System identification is an important branch of modern control theory.Most of the control technologies applied in the modern industrial processes are based on model and the accuracy of identified model directly affects the design of controller.Therefore,the model selection and estimation accuracy of model parameters play a crucial role in control system design.System identification has become an important tool to obtain the model of industrial processes and thus has outstanding significance both in academic research and engineering practice.Most of the practical industrial processes are not linear but complex nonlinear or parameter varying and the conventional linear model is not capable of describing these industrial processes.The linear parameter varying model has a simple linear structure and the nonlinear time-varying system can be accurately described by this model with time varying model parameters.The finite impulse response model is a simple model structure that the output data is only related to the historical input data and can be used to fit actual data effectively by selecting a high order.In practical industrial process,the problems,such as outliers,steady time delay,and uncertain time delay,occur due to hardware limitations and interference.These problems can lead to a decline in data quality and traditional identification methods cannot accurately estimate model parameters based on these corrupted data.This paper focuses on identification of linear parameter varying finite impulse response model and takes the problems of outliers,the steady time delay,and uncertain measurement delay into consideration.Three global identification algorithms are derived by using the expectation maximization algorithm.The main contexts of this paper are:1.The global identification of linear parameters varying finite impulse response model with constant time delay in output is studied.The Gaussian distribution is used to describe the interference noise.The global identification algorithm to estimate the model parameters,noise variance,and time delay is derived by using expectation maximization algorithm.2.The global identification of linear parameter varying finite impulse response multirate sampling model with uncertain measurement delays is studied.The multirate sampling data and uncertain measurement delays are common problems in industry andimpose great difficulty on parameter estimation.The identification problem is formulated in expectation maximization algorithm scheme and the global identification algorithm is derived to estimate the model's unknown parameter value,noise variance and uncertain time delays simultaneously.In this algorithm,the time delay estimation is achieved by calculating the time delay probability of each sampling time and taking the time delay with the maximum probability as the time delay value.3.The robust global identification of linear parameter varying finite impulse response model is studied.The Laplace distribution is a heavy-tailed distribution and can be decomposed into an accumulation of infinite Gaussian distributions,which make it capable of describing data with different qualities.In order to treat the outliers in output data,the Laplacian distribution is used to describe the interference noise.By applying the expectation maximization algorithm,a robust global identification algorithm is derived to estimate all the unknown parameters.In this algorithm,different weight coefficients are added to output data.When the data is an outlier,the weight is very small,thereby the influence of the outliers on the identification parameter is weakened.4.Numerical examples and continuous stirred tank reactor system example are used to verify the feasibility of the proposed algorithms.In the simulation process,the identification algorithm is implemented based on MATLAB programming,including data generation,system identification,and model verification.The performance of the identification algorithm can be evaluated by calculating whether the estimation value of the unknown parameters approaches the true value,or the error percentage of the self-verification and the cross-validation between the real output and estimated output data is within the allowable range.