On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On...
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![Page 1: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/1.jpg)
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
![Page 2: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/2.jpg)
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.
![Page 3: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/3.jpg)
Application Main view
Comparative Nyquist Plot Step Response
Continuous Time pole-zero map S-Plane
Discrete Time pole-zero map Z-Plane
![Page 4: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/4.jpg)
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
![Page 5: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/5.jpg)
Continuous-Time pole-zero map
You can change the values of the poles and zero by dragging over them !!!
![Page 6: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/6.jpg)
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 …
![Page 7: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/7.jpg)
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
![Page 8: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/8.jpg)
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)
![Page 9: On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon.](https://reader036.fdocuments.us/reader036/viewer/2022082422/5697c0281a28abf838cd6dce/html5/thumbnails/9.jpg)
Enjoy it !!!