Continuous to Discrete Time Conversion
A second order polynomial in continuous time is normally presented by a damping factor x and a natural frequency wn. A second order polynomial in z-1 corresponds to the continuous time specifications may be defined as follows:
P=1+a1z-1+a2z-2
where:
a1=-2e-xwncos(wn(1-x2)1/2)
a2=e-2xwn
This polynomial may be used for defining the fixed terms of the controller Hr and Hs, either for designing a pole placement digital controller or in the controller order reduction by identification .
See: Controller order reduction module .
(file ctod.htm)