Identification Of Linear Paraemter Varying Systems

Many advanced model-based control and optimization strategies have been devel-oped to meet the performance requirements of the process and process modeling servesas the prerequisite for the design and implementation of these strategies. The continu-ously increasing scale and complexity of the process have made it very di?cult or evennot possible to build a first-principle model for the process. Since the process data con-tains the information of the process dynamic behaviors, the data-based identification hasbecome a main approach for complex industrial process modeling.Most of the practical industrial processes are inherently nonlinear/time-varying andthe well-established linear time-invariant modeling theories are not able to produce amodel that is valid in the global operating range. Great efforts have been made to finda feasible model structure to facilitate the modeling and controller design for modern pro-cesses. Among the results obtained in the literature, the linear parameter varying(LPV)system model has attracted great attentions of many researchers due to its linear modelstructure and capability to approximately describe the nonlinear/time-varying processes.Recently, the control theories and industrial applications of LPV system have enjoyedrapid development, however, the results about linear parameter varying system identifi-cation are very limited. Many practical problems in industry, such as parameter varyingdelay, uncertain measurement delay, irregularly sampled data or multirate data, measure-ment missing, robust parameter estimation and so on, have not been fully consideredin LPV system identification domain. Therefore, This thesis investigates the data-basedLPV identification method aiming at addressing these problems. The main contents ofthis thesis are:The identification problem of linear parameter varying time-delay systems is consid-ered. The local identification approach is used to handle the parameter varying propertyof the system and the global LPV model is constructed by weighted combination of sev-eral local linear models. The identification of LPV system with parameter varying time-delay is firstly considered and an iterative algorithm is proposed based on the maximumlikelihood principle and expectation-maximization(EM) algorithm to estimate the modelparameters and the parameter varying time-delay simultaneously. For the LPV systemwith constant time-delay, the prior information that all the local models have a commontime-delay parameter is utilized in the mathematical derivation and an iterative parameteridentification algorithm is proposed.The parameter estimation for LPV systems with missing output measurements isconsidered. The global LPV model is constructed by combining several local modelsbased on output interpolation strategy. In order to handle missing output measurements,the local model is firstly taken to have the finite impulse response(FIR) model struc-ture. The prior distributions of the global model parameters are constructed and an iter-ative parameter identification algorithm is proposed based on the maximum a posteriorprinciple and the generalized expectation-maximization(GEM) algorithm for the output-interpolated LPV FIR model. For general control purpose, the output-interpolated LPVoutput error(OE) model is then identified based on the estimated FIR models.The identification problem of LPV multirate system with uncertain measurementdelay is considered. Based on the local identification approach and EM algorithm and itsextensions, the parameter varying property of the process and uncertain measurement de-lay problem are handled simultaneously. Two separate iterative identification algorithmsare proposed to identify the fast-rate output-interpolated LPV FIR model and output-interpolated LPV OE model directly based on the multirate data.The parameter estimation for LPV time-delay systems with missing output measure-ments is considered. The parameter of the LPV model is expressed as a polynomial func-tion of the current value of the scheduling variable. Based on the maximum likelihoodprinciple and the GEM algorithm, an iterative identification algorithm is proposed to esti-mate the coe?cients of the polynomial function of the parameter and time-delay simulta-neously based on the incomplete-data set. One auxiliary variable is introduced to rewritethe LPV model into the linear regression form and the problems of non-commutativity ofthe multiplication with back shift operator over the scheduling variable dependent coe?-cients and nonlinear numerical optimization are avoided which simplify the identificationprocedure.The robust identification problem of LPV systems is considered. In order to handlethe outliers in data set, a robust model is constructed based on Student’s t-distribution.According to the maximum likelihood principle, a robust iterative algorithm is proposedto identify the coe?cients of the polynomial function of the parameter, scale parameter,and the degrees of freedom parameter simultaneously. In this algorithm, the estimatesof the model parameters are obtained by optimizing a weighted mean square error costfunction using one-step damped-Newton optimization and the negative influence of theoutliers imposed on parameter estimates is diminished su?ciently by assigning adaptivelya small weight in the cost function to the measurements which are outliers; The estimateof the degrees of freedom parameter is derived by solving an equation and it can be usedas an indicator of the data quality.