# Transient Response and Steady State Error Problem 1 - Time Response Analysis - Control Systems | Summary and Q&A

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April 11, 2022
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Ekeeda
Transient Response and Steady State Error Problem 1 - Time Response Analysis - Control Systems

## TL;DR

This video explains how to analyze the time response of a second order control system with a given transfer function, including finding transient response specifications and the steady state error.

## Questions & Answers

### Q: What is the purpose of time response analysis in control systems?

Time response analysis helps to understand how a control system will behave over time and provides information about its performance and stability.

### Q: How do you derive the characteristic equation for a control system?

The characteristic equation is derived by considering the sum of the open loop transfer function and the feedback transfer function to be equal to zero.

### Q: How can transient response specifications be determined from the characteristic equation?

By comparing the characteristic equation with the standard form of a second order control system, the values of damping ratio and natural frequency can be determined, which are used to calculate specifications like peak time, rise time, and maximum overshoot.

### Q: What is the steady state error and how is it calculated?

Steady state error refers to the difference between the desired output and the actual output of a control system after it has stabilized. It is calculated by finding the limit of the error as the input tends to zero.

## Summary & Key Takeaways

• The video discusses the problem of analyzing the time response of a second order control system with a given transfer function.

• It explains how to draw the block diagram for the system and derive the characteristic equation.

• The video then demonstrates how to calculate the transient response specifications, such as peak time, rise time, maximum overshoot, and settling time, and also how to determine the steady state error for a ramp input.