Question
Download Solution PDFThe D.C. gain and steady state error for step input for
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
DC gain:
The DC gain is the ratio of the magnitude of the steady-state step response to the magnitude of step input.
DC Gain of a system is the gain at the steady-state which is at t tending to infinity i.e., s tending to zero.
DC gain is nothing but the error coefficients.
For type 0 system:
For type 1 system:
For type 2 system:
Steady state error for different inputs is given by
|
Input |
Type -0 |
Type - 1 |
Type -2 |
|
Unit step |
|
0 |
0 |
|
Unit ramp |
∞ |
|
0 |
|
Unit parabolic |
∞ |
∞ |
|
Calculation:
Given:
It is a type 0 system, so:
Kp = 1 = DC Gain
Steady-state error for unit step input is given as:
ess = 0.5
Last updated on Jul 2, 2025
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