Question

A second order control system has the transfer function T(s) = C(s)/R(s)

The system specifications for a step input are given below as
(i) Percentage overshoot ≤5%.
(ii) Settling Time <4 seconds
(iii) Peak Time Tp<1sec
Show the permissible area for the poles of T(s) in order to achieve the desired response. Use a 2% tolerance band criterion to determine the settling time. 04

Answer 1

To determine the permissible area for the poles of T(s) in a second-order control system, we can use the 2% tolerance band criterion to calculate the settling time. The specifications require the percentage overshoot to be less than or equal to 5%, the settling time to be less than 4 seconds, and the peak time to be less than 1 second.

Step-by-step explanation:

A second-order control system with transfer function T(s) = C(s)/R(s) can be analyzed in terms of its poles. The system specifications require that the percentage overshoot is less than or equal to 5%, the settling time is less than 4 seconds, and the peak time is less than 1 second. To determine the permissible area for the poles of T(s) that satisfy these specifications, we can use the 2% tolerance band criterion to calculate the settling time.

The settling time is the time it takes for the response to reach and stay within a certain percentage (typically 2%) of the final value. In this case, the settling time should be less than 4 seconds. By using the 2% tolerance band criterion, we can determine the maximum allowable damping ratio for the system. From there, we can calculate the permissible range for the poles of T(s) using the damping ratio and the desired peak time constraint.

For more detailed calculations and derivations, it would be helpful to have the specific transfer function or additional information about the system.