# Acceleration error constant is a measure of the steady state error of the system when the input is _______

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Acceleration error constant is a measure of the steady state error of the system when the input is _______
1. unit step function
2. ramp function
3. impulse function
4. parabolic function

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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 Type-0 Type-1 Type-2 Unit step 1/(1+Kp) 0 0 Unit ramp Infinite 1/Kv 0 Unit parabolic Infinite Infinite 1/Ka

Kp is the positional error coefficient, ${K_p} = \mathop {\lim }\limits_{s \to 0} G\left( s \right)$

K 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.