# Transient Response in Control System

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Transient Response is an important concept in the analysis of dynamic systems. In engineering and physics, dynamic systems are systems that change over time, often in response to an external stimulus or disturbance. Understanding how a system responds to such stimuli is critical in many fields, including control systems, signal processing, and electronics.

Transient Response refers to the behavior of a system during the time it takes to reach a stable state after a disturbance. In other words, it’s the system’s initial response to a sudden change in its inputs. On the other hand, steady-state response refers to the behavior of a system when it has reached a stable state and is no longer changing in response to the original disturbance. In this article, we will explore these concepts in more detail, including the factors that affect the transient and steady-state response, and how they are used in practice.

Table of content

## Transient Response

Transient response refers to the initial behavior of a dynamic system following a sudden change or disturbance in its input. This response is often characterized by changes in the system’s output that occur during the time it takes for the system to reach a new, stable state. Understanding transient response is essential in the analysis and design of many dynamic systems, including control systems, signal processing, and electronics. By studying the factors that affect the transient response, engineers and scientists can better predict and control the behavior of dynamic systems, leading to more efficient and effective designs.

Presence or Absence of Transients: Transients occur in the response due to instant change in the sources that are applied to the electric circuit and or due to switching action in the circuit. The two possible switching actions are:- Opening the switch and Closing the switch. There are 3 basic components in Linear Electrical Circuits:

• Resistance (R)
• Capacitance (C)
• Inductance (L)

The transient part will be absent in the response of an electrical circuit or network if the circuit contains only resistances. This is because the resistor is having the ability to adjust any amount of voltage and current in it.

The transient part is present in the response of an electrical circuit or network due to the presence of energy-storing elements like inductors and or capacitors. This is Because they can’t change the energy stored in those elements instantly.

## Inductor Behavior

Let us assume the switching action takes place at time t = 0. The Inductor current does not change instantaneously (due to inductor property) when the switching action takes place. That means, the value of the inductor current just after the switching action as well as just before the switching action will same.

Mathematically, Inductor current can be represented as IL(0-) = IL(0+)

## Capacitor Behavior

The capacitor voltage does not change instantaneously similar to that of the inductor current when the switching takes place. That means, the value of capacitor voltage just after the switching action as well as just before the switching action will same.

Mathematically, Capacitor Voltage can be represented as VC(0-) = VC(0+)

Voltage-Current Relationships for Different Passive Elements:-

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