This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# TransferFunctionCancel

 TransferFunctionCancel[tf] cancels common poles and zeros in the TransferFunctionModel object tf. TransferFunctionCancelcancels 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:
 Out[1]=

Cancel common pole-zero pairs that are stable:
 Out[1]=

Cancel stable pairs within a specified tolerance:
 Out[1]=
 Scope   (6)
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:
 Options   (2)
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:
 Applications   (1)
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:
TransferFunctionCancel is equivalent to MinimalStateSpaceModel for SISO systems:
A system with an unstable pole-zero cancellation may appear stable:
But it is internally unstable:
New in 8