Example of Basic Frequency-weighted Model Reduction

In the case of model order reduction, a note of caution should be made. In the time domain, the range of time constants which have to be considered, depends on the area of application of the model. For control applications, small time delay times and time constants are of interest. However, for dynamic optimization purposes, these small delays and lags can be ignored, since only the time constants which influence the course of the dynamics are important. 

For the frequency domain, similar criteria are applicable. In control applications, the higher frequency range is of interest, owing to the sensitivity of the PID controller settings to the phase shift. It makes a large difference, whether a response is described by a first-order, a second-order, a time delay plus first-order or a lead lag (Fade) approximation. The phase shift of a first-order and lead-lag approximation remains limited, whereas the phase shift of a delay approximation will go to negative infinity. 

For dynamic optimization purposes, only the lower frequency range has to be considered and a first-order approximation of process dynamics is often adequate. 

3 Example of Basic Frequency-weighted Model Reduction 

As pointed out in section 26.1, one way of performing frequency weighted model reduction is by ensuring that the real and imaginary parts of the original model and the reduced model are similar. 

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