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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.

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