# Second Order Transfer Function Question regarding Overshoot

• Tom Hardy
In summary, the question asks if the formula for overshoot can still be used for a closed loop second order transfer function. It is uncertain if this formula can be applied and a confirmation is requested. A suggested online tool for plotting step responses is also provided. The response mentions splitting the transfer function into two parts and adding their time responses, with the answer depending on the value of KC.

## Homework Statement

If I have a closed loop second order transfer function such as:

$$\frac{10-s}{0.3s^2+3.1s+(1+24K_{C})}$$

Can I still use this formula for overshoot (when a step input is applied) ?:
$$\frac{A}{B}=e^{\frac{-\pi \zeta}{\sqrt{1-\zeta^2}}}$$
Where B is the step input size

I don't think you can but I'm not sure, can someone confirm?

Tom Hardy said:

## Homework Statement

If I have a closed loop second order transfer function such as:

$$\frac{10-s}{0.3s^2+3.1s+(1+24K_{C})}$$

Can I still use this formula for overshoot (when a step input is applied) ?:
$$\frac{A}{B}=e^{\frac{-\pi \zeta}{\sqrt{1-\zeta^2}}}$$
Where B is the step input size

I don't think you can but I'm not sure, can someone confirm?
https://en.wikipedia.org/wiki/Overshoot_(signal)

Split your xfr function into two parts: one is a low-pass 2nd order, the other a bandpass 2nd order. For both, there are expressions for overshoot in textbooks etc. Your answer depends on the numerical value of KC.

You then just add the time responses of the two separated xfr functions.
@nascent, thanks for the link! wow, even does nyquist plot!

## 1. What is a second-order transfer function?

A second-order transfer function is a mathematical model that describes the relationship between the input and output of a physical system, such as an electronic circuit or mechanical system. It is a second-order differential equation that can be used to analyze the behavior of the system over time.

## 2. What is overshoot in a second-order transfer function?

Overshoot is the maximum amount that the output of a second-order system exceeds its steady-state value before settling back to its final value. It is a measure of how much the output "overshoots" the desired response.

## 3. How is overshoot calculated in a second-order transfer function?

Overshoot can be calculated by measuring the peak value of the output and comparing it to the steady-state value. The percentage overshoot is then calculated as (peak value - steady-state value) / steady-state value * 100%.

## 4. How does overshoot affect the performance of a second-order system?

Overshoot can have both positive and negative effects on the performance of a second-order system. In some cases, it can improve the speed of the system's response, but in others, it can lead to instability or oscillations. It is important to carefully design a second-order system to minimize overshoot and achieve the desired performance.

## 5. How can overshoot be reduced in a second-order transfer function?

Overshoot can be reduced by adjusting the parameters of the system, such as the gain or damping ratio. The use of feedback control, such as a PID controller, can also help to reduce overshoot and improve the overall performance of the system.