The steady state error for a ramp input for a unity feedback system with open loop transfer function k/s(s + 1) is:

(Given k = 2)

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  1. 0
  2. 1
  3. Infinity
  4. 0.5

Answer (Detailed Solution Below)

Option 4 : 0.5

Detailed Solution

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Concept:

KP = position error constant = lims0G(s)H(s)

Kv = velocity error constant = lims0sG(s)H(s)

K= acceleration error constant = lims0s2G(s)H(s)

Steady state error for different inputs is given by

Input

Type - 0

Type - 1

Type - 2

Unit step

11+Kp

0

0

Unit ramp

1Kv

0

Unit parabolic

1Ka

 

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:

G(s)=ks(s+1)=2s(s+1)

Velocity error coefficient will be:

Kv=lims0s2s(s+1)=2

Steady-state error, ess = 1/2 = 0.5

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