Examples of Model State Reduction Techniques

In this section, MATLAB will be used to illustrate the differences between the different model reduction techniques that have been discussed in the previous section. Data is obtained for a process with two inputs and two outputs and was taken from Zhu (2001). The file is called glassdata2.mat and can be downloaded from Zhu (2001). In this exercise only output 7i will be modeled. 

First an ARX model will be developed. Using file F2604.m, Fig. 26.4 was created showing the percentage fit against the model order. 

As can be seen, the higher the model order, the higher the percentage fit. From an order of twenty-five onward, there seems to be little improvement. Therefore a 25th order ARX model is selected as a stating point for die model reduction exercise. 

It can be seen that the first 10 states are really significant, states 11 25 are less relevant. Therefore a 10th order state space model could be developed as a simplification of the 25th order ARX model. One should note that a 10th order state space model still contains a considerable number of model parameters. 

When the model is going to be used for control purposes, a steady-state model offset is usually not so important because most control strategies can cope with limited errors in dynamics and process gain. 

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