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Time Response of First Order System | Control Systems - Electrical Engineering (EE) PDF Download

Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)

In the above transfer function, the power of 's' is the one in the denominator. That is why the above transfer function is of the first order, and the system is said to be the first order system.

Response of 1st order system when the input is unit step -

Time Response of First Order System | Control Systems - Electrical Engineering (EE)

For Unit Step,
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Now, the partial fraction of above equation will be:
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Taking the inverse Laplace of above equation is:
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Where T is known as time constant of the system and it is defined as the time required for the signal to attain 63.2 % of final or steady state value. Time constant means how fast the system reaches the final value. As smaller the time constant, as faster is the system response. If time constant is larger, system goes to move slow.

Time response of first order system with unit ramp signal is -

Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Now, putting the value of R(S) in the equation
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Now taking the inverse Laplace of the above equation
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
The error signal e(t) will be
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
The steady state error is equal to 'T,' where 'T' is the time constant of the system. For a small time constant, the error is small, and the response of the system increases.

Response of 1st order system with unit impulse function is -

Value of impulse = 1
Time Response of First Order System | Control Systems - Electrical Engineering (EE)
Inverse Laplace
Time Response of First Order System | Control Systems - Electrical Engineering (EE)

The document Time Response of First Order System | Control Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Control Systems.
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