A unity feedback system has open-loop transfer function such that it is a type-1 system and subjected to a unit step input, then1.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?

Correct Answer: A - 1, 2 and 3 only

Quick Concept 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.

Statement-wise Verification

• Statement 1 - Correct.
  The steady-state error for step input is zero.
  One integrator makes the position constant Kp infinite, so unit-step steady-state error is zero (for a stable closed loop).
• Statement 2 - Correct.
  The steady-state error for ramp input is finite.
  The velocity constant Kv is finite for a type-1 system, so unit-ramp error is finite.
• Statement 3 - Correct.
  Increasing system gain reduces steady-state error for ramp input.
  Increasing system gain typically increases Kv and therefore reduces ess,ramp=1/Kv.
• Statement 4 - Incorrect.
  The steady-state error for step input increases with increase in gain.
  Step error remains zero for a stable type-1 system; it does not increase with gain.

Core Concept

System type is the number of pure integrators in the open-loop transfer function GH(s). It determines the order of polynomial input that can be tracked with zero/finite/infinite steady-state error, provided the closed loop is stable.

Formula / Key Relationship

Type 1: Kp=lim_{s→0}GH=∞ → ess,step=1/(1+Kp)=0; Kv=lim_{s→0}sGH finite → ess,ramp=1/Kv.

Step-by-Step Check

Static-error constants directly produce the truth set {1,2,3}. Option A.

Why the Other Options Are Wrong

Option B is incorrect because it omits correct statement(s) 2. Option C is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.

Answer-Key Verification Note

The uploaded provisional key marks C . After independent technical verification, the defensible answer is A . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

Type-1 mnemonic: step → zero error; ramp → finite error; parabolic → infinite error.

Common Mistake

Ignoring the closed-loop stability condition when applying steady-state error formulas.

Quick Revision

Type-1 Error Constants is linked with System Type, Steady-State Analysis and Control Systems. Type-1 mnemonic: step → zero error; ramp → finite error; parabolic → infinite error.