2. On preserving passivity in sampled-data linear systems A Sysquake application to illustrate “On preserving passivity in sampled-data linear systems” Ramon Costa-Castelló Enric Fossas Colet

3. Theoretical Results To understand this application it is necessary to read : –On preserving passivity in sampled-data linear systems.Ramon Costa-Castelló and Enric Fossas. IOC-DT-P-2005-8.On preserving passivity in sampled-data linear systems.Ramon Costa-Castelló and Enric Fossas. IOC-DT-P-2005-8.

4. Application Main view Comparative Nyquist PlotStep Response Continuous Time pole-zero map S-Plane Discrete Time pole-zero map Z-Plane

5. Transfer functions Continuous Time transfer function It is assumed to be PR Z-transform Traditional Discretization Exact. Using zoh Proposed Discretization Exact. Preserve Passivity Passive Tustin Transform Inexact. Preserve Passivity

6. Continuous-Time pole-zero map You can change the values of the poles and zero by dragging over them !!!

7. 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 …

8. 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

9. 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)

10. Enjoy it !!!