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SingularValuesTransformationMatrix

8.6 Pole-Zero Cancellation

Canceling common pole-zero pairs.

For the model reduction purposes, PoleZeroCancel in its current implementation is most useful for SISO systems.

Here is a -plane transfer function for a SISO system.

In[28]:=

Out[28]=

This is the transfer function after the pole-zero pair at is canceled.

In[29]:=

Out[29]=

Note that if the common factors coincide within the precision of the elements, they can be canceled without calling PoleZeroCancel—for example, just by factoring the elements of the transfer matrix. Therefore, PoleZeroCancel is most useful when the match is not exact. In fact, the Tolerance option allows cancellation of the factors within any desired difference.

The common pair in the preceding transfer function cancel in the factored form, too.

In[30]:=

Out[30]=

Here is another transfer function.

In[31]:=

Out[31]=

Tolerance allows cancellation of pairs with a significant difference. The pole at and the zero at cancel so long as Tolerance is set to .

In[32]:=

Out[32]=

Option to PoleZeroCancel.

SingularValuesTransformationMatrix



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