Different Cases and Relationships of Unit Step Signal
Different signals can be derived from unit step signals some of them are discussed below.
Time Scaling
u(at) is a unit step function. Time scaling does not effect unshifted unit step function. The below equation represents the equation of the time scaling.
i.e., u(at) = u(t)
Proof :
u(at) = 0 ; for at<0 = 0 ; for t<0
u(at) = 1 ; for at>=0 = 1 ; for t>=0
Above equation proved that u(at) i.e., unshifted unit step signal does not effected by Time scaling and is equal to u(t).
Time Shifting
u(t-a)-u(t-b) represents a unit step function between a and b. The below representations are the equations of time shifting.
u(t-a)-u(t-b) =0 ; for t<a
u(t-a)-u(t-b) =1 ; for a<=t<b
u(t-a)-u(t-b) =0 ; for t>=b
Reflection
1-u(t) is a reflected unit step signal. The below-represented equations are the equations of the reflection of the unit step signal.
1-u(t)=1 ; for t<0
1-u(t)=0 ; for t>=0
Unit Step Signal in Control System
A Control System is a system which manages commands and regulates or directs the behaviour of other devices using control loops. A control system is a device which provides the desired response by controlling the output. A control system can also be defined as a system with a combination of mechanical or electronic devices that controls other devices or systems by way of a control loop is called as a control system. The below figure represents the simple block diagram of a control system.
Table of Content
- What is a Unit Step Signal?
- Types of Unit Step Signal
- Characteristics of Unit Step Signal
- Different Cases and Relationships of Unit Step Signal
- Applications of Unit Step Signal
- Advantages of Unit Step Signal
- Disadvantages of Unit Step Signal
A signal is a function of one or more independent variables that contain information. In a control system, signals play a crucial role in the analysis and design of the control system to achieve the desired performance and stability. Standard signals are impulse, step, ramp and parabolic. These standard signals are used to know the performance of the control system using the time response of the output. Now let us see the definitions and graphs of time response analysis and frequency response analysis of the control system.
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