Topic practiceQ1Moderate
A unity feedback system has open-loop transfer function such that it is a type-1 system and subjected to a unit step input, then
1. The steady-state error for step input is zero.
2. The steady-state error for ramp input is finite.
3. Increasing system gain reduces steady-state error for ramp input.
4. The steady-state error for step input increases with increase in gain.
Which of the above statements is/are correct?
1. The steady-state error for step input is zero.
2. The steady-state error for ramp input is finite.
3. Increasing system gain reduces steady-state error for ramp input.
4. The steady-state error for step input increases with increase in gain.
Which of the above statements is/are correct?
View answer & solution
Correct answer: A. 1, 2 and 3 only
Quick explanation
It determines the order of polynomial input that can be tracked with zero/finite/infinite steady-state error, provided the closed loop is stable. Static-error constants directly produce the truth set {1,2,3}. Key relation: Type 1: Kp=lim_{s→0}GH=∞ → ess,step=1/(1+Kp)=0; Kv=lim_{s→0}sGH finite → ess,ramp=1/Kv.
Exam focus: Type-1 mnemonic: step → zero error; ramp → finite error; parabolic → infinite error. Common trap: Ignoring the closed-loop stability condition when applying steady-state error formulas.
Type 1: Kp=lim_{s→0}GH=∞ → ess,step=1/(1+Kp)=0; Kv=lim_{s→0}sGH finite → ess,ramp=1/Kv.