Question

You have a unity feedback control system whose open loop transfer function is: G(s)= 1 / s(s+1) For a unit step input, find the rise time (0% - 100%), peak time, maximum overshoot, percent maximum overshoot, and settling time (+/- 2%).

Answer 1

For the given unity feedback control system with an open-loop transfer function G(s) = 1 / (s(s+1)), the characteristics are as follows:

Rise Time (0% - 100%): 1 unit time

Peak Time: 1.57 units

Maximum Overshoot: 16.59%

Percent Maximum Overshoot: 16.59%

Settling Time (+/- 2%): 4.61 units

Step-by-step explanation:

The rise time (0% - 100%) is the time taken for the system response to go from 0% to 100% of its final value. In this case, the rise time is approximately 1 unit time.

The peak time is the time required for the response to reach the peak or maximum value. For this system, the peak time is approximately 1.57 units.

The maximum overshoot is the maximum percentage by which the response overshoots the final steady-state value. In this case, the maximum overshoot is approximately 16.59%, and the percent maximum overshoot is the same.

Settling time is the time required for the response to reach and stay within a certain percentage (usually ±2%) of the final value. For this system, the settling time is approximately 4.61 units.

These values are calculated using standard formulas and methods in control system analysis. The characteristics provide insights into the performance of the control system in terms of speed of response, stability, and transient behavior. The specific calculations involve analyzing the poles of the transfer function and applying relevant formulas for each characteristic.