Question:
The control system with single pole at origin is
The control system with single pole at origin is
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A single pole at origin always indicates a Type-1 system and such a pole contributes marginal stability.
Updated On: Jun 25, 2026
- Unstable
- Stable
- Marginally stable
- Absolutely stable
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The Correct Option is C
Solution and Explanation
Concept:
The stability of a system depends upon the location of its poles in the \(s\)-plane.
• All poles in left half plane \(\Rightarrow\) Stable
• At least one pole in right half plane \(\Rightarrow\) Unstable
• Simple pole on imaginary axis and remaining poles in left half plane \(\Rightarrow\) Marginally stable
Step 1: Identify the pole location.
A single pole at origin means \[ s=0. \] This pole lies on the imaginary axis.
Step 2: Determine stability.
A simple pole at the origin produces a response of constant amplitude. The output neither grows nor decays with time. Hence the system is neither asymptotically stable nor unstable.
Step 3: State the conclusion.
Therefore, \[ \boxed{\text{System is Marginally Stable}} \] Hence, \[ \boxed{\text{Correct Option (C)}} \]
• All poles in left half plane \(\Rightarrow\) Stable
• At least one pole in right half plane \(\Rightarrow\) Unstable
• Simple pole on imaginary axis and remaining poles in left half plane \(\Rightarrow\) Marginally stable
Step 1: Identify the pole location.
A single pole at origin means \[ s=0. \] This pole lies on the imaginary axis.
Step 2: Determine stability.
A simple pole at the origin produces a response of constant amplitude. The output neither grows nor decays with time. Hence the system is neither asymptotically stable nor unstable.
Step 3: State the conclusion.
Therefore, \[ \boxed{\text{System is Marginally Stable}} \] Hence, \[ \boxed{\text{Correct Option (C)}} \]
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