Time Domain Specifications

Discuss the time specifications of the underdamped systems.

1. Control Systems Lecture - 8 E. Ramkumar Assistant Professor / EEE 27-03-2021 UEEC004 - Control Systems 1

2. Time response of Second Order System =       27-03-2021 UEEC004 - Control Systems 2

3. Time response of Second Order System =       27-03-2021 UEEC004 - Control Systems 3

4. Time response of Second Order System =       27-03-2021 UEEC004 - Control Systems 4

5. Time response of Second Order System =       27-03-2021 UEEC004 - Control Systems 5

6. Time Response Specifications 27-03-2021 UEEC004 - Control Systems 6 Delay time, t d : Time required for the response to reach 50% of the final value at first instance.   Rise time, t r : Time required for the response to rise from 10% to 90% of the final value for ODS and 0 to 100% of the final value for UDS, at first instance. . Peak time, t p : Time required for the response to reach peak value of time response. Peak Overshoot, M p : It is the normalized difference between the peak value of time response and the steady state value.   Settling time, t s : Time required for the response to reach and stay within a specified tolerance band of its final or steady state value of time response. Usually, tolerance band is 2 or 5%. t d t r t p M p t s Allowable tolerance

7. Rise Time, t r For above eqn to be ZERO,   27-03-2021 UEEC004 - Control Systems 7 t r  

8. Peak Time, t p 27-03-2021 UEEC004 - Control Systems 8 t p To find the first peak    

9. Peak Overshoot, M p 29-03-2021 UEEC004 - Control Systems 9 M p