Standard Test Signals Used
These are some signals that are used to know the characteristics and performance of a system. These signals are unit impulse, unit step, ramp, parabolic signals. Any arbitrary input signal can be made using these standard signals.
Unit Impulse Signal
The unit impulse signal is one of the signal used in control systems. It is denoted by δ(t). This signal exists only at t=0 and it has very short duration pulse with an area under the curve equal to 1 or unity.
It is defined as follows,
δ(t)= ∞,t=0 and δ(t)= 0, t ≠0
Unit Impulse Signal
Unit Step Signal
This signal is denoted by u(t). This signal only exists for positive side of the plot. In simple words, the signal is zero for all values less than zero and unity for all values equal and greater than zero. There is sudden change in the system from 0 to 1 at time t=0.
It is defined as follows,
u(t)= 0, t<0 and u(t) =1, t ≥0
Unit Step Signal
Unit Ramp Signal
This signal is defined as r(t). This signal represents a linear increase or decrease in magnitude with time. Ramp function is zero for all values less than zero and for values greater than or equal to zero it increases linearly. The rate of increase of the function is linear, which means for each unit increase in time the function also increases by same amount.
It is defined as follows,
r(t)= 0, t<0 and r(t) =t, t ≥0
Unit ramp signal can be written in terms of step signal as r(t)=tu(t).
Unit Ramp Signal
Unit Parabolic Signal
It is denoted as p(t). Unit parabolic signal is zero for all values less than zero and follows a quadratic increase with time for values greater than or equal to zero. The rate of increase is non-linear.
It is defined as follows,
p(t)= t2/2; t ≥0 and p(t)=0; t<0
Unit parabolic signal can be written in terms of step signal as p(t)=(t2/2)u(t).
Parabolic Signal
Steady State Response
In this article, we are going to discuss the steady-state response. We will see what is steady state response in Time domain analysis. We will then discuss some of the standard test signals used in finding the response of a response. We also discuss the first-order response for different signals. We will discuss the second-order system and its cases. Along with these, we will also discuss some specifications and errors. Later in the article, we will discuss some applications, advantages, and disadvantages of steady-state response.
Table of Content
- What is steady state response?
- Standard Test Signals Used
- Type and Order of a System
- Steady State Specification
- Advantages of Steady State Response
- Disadvantages of Steady State Response
- Applications of Steady State Response