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To reduce the order of a model, you can either simplify your model, or compute a lowerorder approximation. The following table summarizes the differences among several modelreduction approaches.
Approach  Commands 

Simplification — Reduce model order exactly by canceling polezero pairs or eliminating states that have no effect on the overall model response 

Approximation — compute a lowerorder approximation  balred — Compute a lowerorder approximation of your model by neglecting states that have relatively low effect on the overall model response 
In some cases, approximation can yield better results, even if the model looks like a good candidate for simplification. For example, models with near polezero cancellations may be better reduced by approximation than simplification. Similarly, using balred to reduce statespace models can yield more accurate results than minreal.
When you use a reducedorder model, always verify that the simplification or approximation preserves model characteristics that are important for your application. For example, compare the frequency responses of the original and reduced models using bode or sigma. Or, compare the openloop responses for the original and reduced plant and controller models.