Second Order System Response to Unit Step Input

When a second order system is subjected to a unit step input, it exhibits a response that can be characterized by various parameters such as rise time, settling time, peak time, and overshoot. The overshoot refers to the maximum percentage by which the response exceeds the final steady-state value.

Peak Undershoot and Overshoot

In the given question, it is mentioned that the first peak undershoot of the system response to a unit step input is 0.36. The peak undershoot refers to the maximum negative deviation from the final steady-state value before the response starts to rise towards the final value.

The overshoot, on the other hand, refers to the maximum positive deviation from the final steady-state value after the response rises above and then falls back towards the final value.

Determining the Second Overshoot

To determine the second overshoot, we need to find the maximum positive deviation from the final steady-state value after the first peak undershoot.

The magnitude of the peak undershoot is given as 0.36. Since the system response is a second order system, it follows a specific pattern for overshoot and undershoot. The magnitude of the second overshoot can be found using the formula:

Second Overshoot = First Peak Undershoot * Second Peak Overshoot Factor

The second peak overshoot factor for a second order system is given by the formula:

Second Peak Overshoot Factor = e^(-πζ/√(1-ζ^2))

Where ζ (zeta) represents the damping ratio of the system.

Calculating the Second Overshoot

In this question, the value of the first peak undershoot is given as 0.36. To calculate the second overshoot, we need to know the damping ratio of the system.

Unfortunately, the damping ratio is not provided in the question. Without the damping ratio, it is not possible to calculate the second overshoot accurately. Therefore, the answer cannot be determined based on the information given in the question.

However, if the damping ratio is known, we can substitute its value into the formula to calculate the second overshoot.

Conclusion

In conclusion, the answer to the question cannot be determined based on the information provided. The second overshoot of a second order system response to a unit step input depends on the damping ratio, which is not given in the question.