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BSNL JE (TTA) 26 September 2016 Shift 1 Paper

Option 4 : parabolic function

BSNL JE (TTA) 25 September 2016 Shift 1 Paper

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__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, \({K_p} = \mathop {\lim }\limits_{s \to 0} G\left( s \right)\)

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.