System and Load Identification.

Graduate Course at Solid Mechanics at Chalmers, Autumn 2000.

 

Assignment 4. Validation

 

Two models, one ARX model and one discrete time state-space model, has been proposed as good models for the process under study. The process has been subjected to two sets of inputs, one for model estimation and one for model validation. Samplings have been performed with increments T=0.08s and the models are consistent herewith. Data can be downloaded from here. The ARX model is:

A0 = 1,  Ak = 0 k>0

B = 0.001*[0 5.4 12.7 16.0 16.7 15.6 13.4 10.7 7.7 4.8 2.0 -0.4 -2.5 -4.3 -5.7 -6.8 -7.5 -8.0 -8.2 -8.2 -8.0 -7.7 -7.3 -6.8 -6.2 -5.6 -5.0 -4.4 -3.8 -3.3 -2.7 -2.2]

and the state-space model is (using MATLAB syntax):

A = [0.9693 0.0027 0.0654 0.0054 ; 0.0014 0.9971 0.0054 0.0741 ; -0.7145 0.0601 0.6529 0.1228 ; 0.0150 -0.0688 0.1228 0.8596]

B = [0.0028 ; 0.0001 ; 0.0654 ; 0.0054]

C = [ 0 0 0 1]

 

Task: Use any of the validation criteria suggested by Ljung in chapter 16.6 (Residual Analysis) to select the model that is likely to be the best of the two. Motivate your choice of valitation criterion and model selection.

/TA 2001-01-09