Order Identification For Single-Input Single-Output Systems

The system identification includes order identification and parameter estimation ln thepractical application,these two issues are closely related,that is needed for known order inparameter estimation,while the value of parameter estimation in order identification Toidentify the system parameter,people have done further research,and surilriled up a set ofmature method The order identification papers is not SO many,while journal published eachyear at home and abroad of identification papers is quit a few And order identification inequation error type models is in the majority,rarely involve output error type models So thispaper has very important theoretical and practical value in the research of the system orderThis paper with the national natural science fund projects for the background,put forwardthe order identification for single-input single-output systems On the basis of referring to therelated literatlUres and the fu rther sttUdjes the research resUlts Obtajned as follOWSl It firstly for state space model of single-input single-output constant linear discrete time system,is deduced by the rank of Hankel matrix made of impulse response in system order identification It derives the Hankel matrix with the singular value decomposition(SVD)rank method and uses Hankel matrix determinant the absolute value of average ratiomethod to judge the system order The simulation results demonstrate the effectivenessof the presented algorithm At the same time,single-input single-output constant lineardiscrete time system not only can be described in state space model,but also has thecorresponding difference equations describe,that is deterministic autoregressive movingaverage model The simulation results show the proposed method also equally to thesystem represented of the deterministic autoregressive moving average model2 For the output error model,first put forward by using the determinant ratio estimation model order．similar to the Hankel matrix rank method The determinant ratio method use input and output data,while Hankel matrix made of the impulse response with system So it is put forward the order identification algorithm based on the auxiliary model identification recursive least square algorithm Another basic thought method is put forward by using residual variance estimation model order In fact,it is a criterion function of judging the end of order operation Then,auxiliary model by the recursive least square algorithm is putforward order identification algorithm Finally,through the simulation example to verifythe effectiveness of the proposed algorithm 3 For output error moving average model,not only solve the problem of identify output error model,but also consider the model identification including both system model and noise model order identificaon The solution iS to fixed noise model order constant to identify system model,then fixed system model order constant to identify noise model The determinant ratio estimation order and residual the variance estimation model order of the previous chapteris is improved Finally,through the simulation example to verify the effectiveness of the proposed algorithm4 Paper presented summary and outlook at last．and made a simple introduction of sorfle difficulties faced and the direction of further research in this project For example,the order identification algorithm given needs further theory proved,and the proposed method is to be further extended to the multivariable system order identification,and SO on...