Mapping of S-Plane to Z-Plane Analytically and Verification using Simulation 
Procedure
Steps to perform the simulation
- At first enter the desired value of sampling time. Here default value is 1 sec for sampling time.
- Click on 'Select Entry Method' dropdown button and select the available options to enter the values.
- For Pole - Zero entry: click on 'Add Poles' button to enter the pole values and click on 'Add Zeros' button to enter the zero values. Click 'Add Pole' or/and 'Add Zero' buttons multiple times to enter multiple pole/zero values.
- Click on 'Plot' button to get the Pole-Zero map of S plane and Z plane. Plot can be downloaded by clicking on 'Download' button.
- Click on 'Enter ζ , ωn Values' dropdown button. Enter the values of damping ratio (ζ)and natural frequency (ωn). Click on 'Run' button in the dropdown-menu to get the Pole Map of S plane and Z plane. Plot can be downloaded by clicking on 'Download' button.
- Click on 'Clear' button before every new simulation to clear the previous map.
- Note: Do not click on 'Clear' button if you want to enter values of multiple poles and zeros.

Fig.1. Select Entry Method dropdown button

Fig.2. Add Poles and Add Zeros buttons

Fig.3. Entry of poles and zeros values

Fig.4. Enter ζ , ωn values