gives a matrix of roots of the denominators in the TransferFunctionModel tfm.
only gives the roots inside the region reg on the complex plane.
Examplesopen allclose all
Basic Examples (3)
The poles for specific values of damping ratio and natural frequency:
The poles of a MIMO system are the poles of the elements of the transfer function:
Time-delay systems may have an infinite number of poles:
But they always have a finite number of poles in a bounded region:
The poles of a fourth-order Butterworth filter:
The poles of a tenth-order Bessel filter:
The poles of a discrete-time second-order system:
The system is stable because the poles lie within the unit circle:
The poles of a time-delay system in a square around the origin:
The poles trace out paths on the complex plane:
Use TransferFunctionPoles to determine if a system is asymptotically stable:
Asymptotic stability of various systems:
Find the poles of the time-delay system near the origin:
Create a delay-free approximation using the poles:
Compare step responses of the time-delay system and the delay-free approximation:
Properties & Relations (4)
For a SISO system, the poles of the transfer function are the eigenvalues of its state matrix:
The poles determine the natural response of a system:
The exponentials in the response are the real parts of the poles:
The root locus plot gives the closed-loop poles as any parameter is varied:
The root locus plot as k is varied:
A stable third-order system with one symbolic pole:
It can be better approximated by a second-order system if the third pole is further to the left:
Possible Issues (1)
TransferFunctionPoles may not find solutions for time-delay systems:
Wolfram Research (2010), TransferFunctionPoles, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionPoles.html (updated 2012).
Wolfram Language. 2010. "TransferFunctionPoles." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/TransferFunctionPoles.html.
Wolfram Language. (2010). TransferFunctionPoles. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransferFunctionPoles.html