The characteristic equation of a system is obtained from

 

1. The main purpose of a feedback in a control system is to:

a) Reduce the error
b) Increase the gain
c) Make the system unstable
d) Increase the bandwidth
Answer: a) Reduce the error
Explanation: Feedback continuously compares the actual output with the desired output and minimizes the difference, thereby reducing steady-state error.

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2. A closed-loop control system is one which:

a) Does not have feedback
b) Has feedback
c) Is very complex
d) Has open-loop gain zero
Answer: b) Has feedback
Explanation: Closed-loop systems use feedback to automatically correct the system output.

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3. The transfer function is defined as:

a) Output/Input for non-linear systems
b) Output/Input for linear time-variant systems
c) Output/Input for linear time-invariant systems with zero initial conditions
d) Input/Output for non-linear systems
Answer: c) Output/Input for linear time-invariant systems with zero initial conditions
Explanation: The transfer function applies only to LTI systems and assumes zero initial conditions.

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4. In control systems, the term “stability” refers to:

a) Output increases with time
b) Output decreases to zero
c) Output remains bounded for bounded input
d) System is oscillatory
Answer: c) Output remains bounded for bounded input
Explanation: A system is stable if a bounded input gives a bounded output (BIBO stability).

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5. Which of the following is an example of an open-loop control system?

a) Electric iron
b) Automatic toaster
c) Traffic light control system
d) Missile guidance system
Answer: c) Traffic light control system
Explanation: Traffic lights operate on preset timing without feedback; hence it’s open-loop.

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6. The time constant of a first-order system determines:

a) Stability
b) Damping ratio
c) Speed of response
d) Overshoot
Answer: c) Speed of response
Explanation: The smaller the time constant, the faster the system responds.

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7. The characteristic equation of a system is obtained from:

a) Denominator of the transfer function
b) Numerator of the transfer function
c) Both numerator and denominator
d) None of these
Answer: a) Denominator of the transfer function
Explanation: The characteristic equation is found by setting the denominator of the closed-loop transfer function equal to zero.

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8. The steady-state error is zero for a step input in:

a) Type 0 system
b) Type 1 system
c) Type 2 system
d) Type -1 system
Answer: b) Type 1 system
Explanation: Type 1 systems have one integrator, which eliminates steady-state error for step inputs.

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9. Root locus technique gives information about:

a) Time response
b) Frequency response
c) Stability and location of poles
d) System sensitivity
Answer: c) Stability and location of poles
Explanation: Root locus shows how the poles of the system move with variation of gain.

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10. The phase margin of a stable system is always:

a) Negative
b) Zero
c) Positive
d) Infinite
Answer: c) Positive
Explanation: A positive phase margin indicates stability; zero means marginal stability.