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Cancellation Versus Approximation

To reduce the order of a model, you can either simplify your model, or compute a lower-order approximation. The following table summarizes the differences among several model-reduction approaches.

ApproachCommands
Simplification — Reduce model order exactly by canceling pole-zero pairs or eliminating states that have no effect on the overall model response
  • sminreal — Eliminate states that are structurally disconnected from the inputs or outputs. Eliminating structurally disconnected states is a good first step in model reduction because the process does not involve any numerical computation.

  • minreal — Eliminate canceling or near-canceling pole-zero pairs from transfer functions. Eliminate unobservable or uncontrollable states from state-space models.

Approximation — compute a lower-order approximationbalred — Compute a lower-order 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 pole-zero cancellations may be better reduced by approximation than simplification. Similarly, using balred to reduce state-space models can yield more accurate results than minreal.

When you use a reduced-order 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 open-loop responses for the original and reduced plant and controller models.

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