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TransferFunctionCancel

TransferFunctionCancel[tf]
cancels common poles and zeros in the TransferFunctionModel object tf.
TransferFunctionCancel
cancels only common pole-zero pairs for which is True.
Cancel common pole-zero pairs:
Cancel common pole-zero pairs that are stable:
Cancel stable pairs within a specified tolerance:
Cancel common pole-zero pairs:
In[1]:=
Click for copyable input
Out[1]=
 
Cancel common pole-zero pairs that are stable:
In[1]:=
Click for copyable input
Out[1]=
 
Cancel stable pairs within a specified tolerance:
In[1]:=
Click for copyable input
Out[1]=
Cancel the common pole-zero pair at the origin:
Cancel common pole-zero pairs of a fourth-order system:
The common pole-zero pair is evident by factoring the transfer function:
Cancel pole-zero pairs for a discrete-time system:
Cancel common pole-zero pairs that are stable:
Cancel pole-zero pairs with tolerance not greater than 0.01:
With zero tolerance nothing is canceled:
This system has two pole-zero pairs whose tolerance is less than or equal to 0.6:
Cancel the pair with frequency greater than 9 radians per time unit:
Visualize the responses of the three systems to a unit step input:
The tolerance is zero by default:
Cancel pole-zero pairs whose absolute difference is not greater than 0.15:
Pole-zero cancellation with a larger tolerance:
Use TransferFunctionCancel to obtain a simpler representation of a highly oscillatory system in a series with a notch filter:
A system of higher order is obtained without the cancellation:
In most cases the pole-zero cancellation has a negligible effect on the overall dynamics:
A system with an unstable pole-zero cancellation may appear stable:
But it is internally unstable:
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