Correct Answer - Option 4 : parabolic function
Concept:
The deviation of the output of the control system from the desired response during steady-state is known as steady-state error.
Steady-state error, \({e_{ss}} = \mathop {\lim }\limits_{s \to 0} \frac{{sR\left( s \right)}}{{1 + G\left( s \right)}}\)
Input
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Type-0
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Type-1
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Type-2
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Unit step
|
1/(1+Kp)
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0
|
0
|
Unit ramp
|
Infinite
|
1/Kv
|
0
|
Unit parabolic
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Infinite
|
Infinite
|
1/Ka
|
Kp is the positional error coefficient, \({K_p} = \mathop {\lim }\limits_{s \to 0} G\left( s \right)\)
Kv is the velocity error coefficient, \({K_v} = \mathop {\lim }\limits_{s \to 0} sG\left( s \right)\)
Ka is the acceleration error coefficient, \({K_a} = \mathop {\lim }\limits_{s \to 0} {s^2}G\left( s \right)\)
The steady-state error of a control system can be minimized by increasing the gain K.
Explanation:
Acceleration error constant is a measure of the steady-state error of the system when the input is parabolic function.
Positional error constant is a measure of the steady-state error of the system when the input is unit step function.
Velocity error constant is a measure of the steady-state error of the system when the input is ramp function.