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BSNL JE (TTA) 26 September 2016 Shift 1 Paper

Option 2 : ∞, 0

ST 1: Logical reasoning

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**Concept:**

Steady-state error is defined as the difference between the input and the output of a system in the limit as time goes to infinity (i.e. when the response has reached steady state).

The steady-state error will depend on the type of input (step, ramp, etc.) as well as the system type (0, I, or II).

The steady-state error of a unity feedback stable system

\({e_{ss}} = \mathop {\lim }\limits_{s \to 0} \frac{{s.R\left( s \right)}}{{1 + G\left( s \right)}}\)

KP = position error constant = \(\mathop {\lim }\limits_{s \to 0} G\left( s \right)H\left( s \right)\)

Kv = velocity error constant = \(\mathop {\lim }\limits_{s \to 0} sG\left( s \right)H\left( s \right)\)

Ka = acceleration error constant = \(\mathop {\lim }\limits_{s \to 0} {s^2}G\left( s \right)H\left( s \right)\)

Steady-state error for different inputs is given by

Input |
Type - 0 |
Type - 1 |
Type - 2 |

Unit step |
\(\frac{1}{{1 + {K_p}}}\) |
0 |
0 |

Unit ramp |
∞ |
\(\frac{1}{{{K_v}}}\) |
0 |

Unit parabolic |
∞ |
∞ |
\(\frac{1}{{{K_a}}}\) |

**Explanation:**

For type 2 system with input as unit ramp, velocity error constant and steady state error are respectively ∞, 0.