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For a unity feedback control system, the forward path transfer function is given by 

The steady-state error of the system for the input  is

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  1. 0
  2. ∞
  3. 20t2
  4. 30t2

Answer (Detailed Solution Below)

Option 2 : ∞
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Detailed Solution

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Concept:

KP = position error constant = 

Kv = velocity error constant = 

Ka = acceleration error constant = 

Steady state error for different inputs is given by

Input

Type -0

Type - 1

Type -2

Unit step

0

0

Unit ramp

∞

0

Unit parabolic

∞

∞

 

From the above table, it is clear that for type – 1 system, a system shows zero steady-state error for step-input, finite steady-state error for Ramp-input and  steady-state error for parabolic-input.

Calculation:

Input = 

It is a parabolic input.

The error coefficient for parabolic input is acceleration error constant.

Steady state error,

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