A Sysquake application to illustrate “On preserving passivity On preserving passivity in sampled-data linear systemsin sampled-data linear systems”

Ramon Costa-Castelló

Enric Fossas Colet

Theoretical Results

• To understand this application it is necessary to read :– On preserving passivity in sampled-data linea

r systems.Ramon Costa-Castelló and Enric Fossas. IOC-DT-P-2005-8.

Application Main view

Comparative Nyquist Plot Step Response

Continuous Time pole-zero map S-Plane

Discrete Time pole-zero map Z-Plane

Transfer functionsContinuous Time transfer function

It is assumed to be PR

Z-transform

Traditional DiscretizationExact. Using zoh

Proposed DiscretizationExact. Preserve Passivity

Passive

Tustin Transform

Inexact. Preserve Passivity

Continuous-Time pole-zero map

You can change the values of the poles and zero by dragging over them !!!

Discrete-Time pole-zero map

Poles in Z-transform and Passive are the same (exact discretizations)

Zeros in Z-transform and Passive are different (output is different)

Tustin transform is an inexact discretization so, poles and zeros are different …

Step Response

Z-transform step response equals continuous time output at sampling times

Proposed step response equals continuous time output mean value in sampling interval

Tustin step response approximate continuous time output at sampling times

You can change sampling time by dragging the samples

Nyquist Plot

Z-transform frequency response in similar to continuous time frequency response, but does not preserve PR

Passive frequency response in similar to continuous time frequency response and does preserve PR

Tustin frequency response equals continuous time frequency response so it preserve PR

Depending on the values of the continuous poles and zero continous time PR

may be lost (this will be indicated in this plot)

Enjoy it !!!