Stability Analysis Basics - Essential Problem Set for Exams

Stability Analysis Basics - Problem Set

Q. What does a transfer function with poles in the right half of the s-plane indicate?

A. The system is stable.
B. The system is marginally stable.
C. The system is unstable.
D. The system is critically damped.

Solution

Poles located in the right half of the s-plane indicate that the system is unstable, as they correspond to exponential growth in the time response.

Correct Answer: C — The system is unstable.

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Q. What does the root locus technique help to visualize?

A. The frequency response of a system.
B. The locations of the poles of a system as a parameter varies.
C. The step response of a system.
D. The transfer function of a system.

Solution

Root locus is a graphical method used to analyze how the roots of a system's characteristic equation change with varying system parameters, typically gain.

Correct Answer: B — The locations of the poles of a system as a parameter varies.

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Q. What is the Routh-Hurwitz criterion used for?

A. To determine the frequency response of a system.
B. To analyze the stability of a linear time-invariant system.
C. To design PID controllers.
D. To plot Bode diagrams.

Solution

The Routh-Hurwitz criterion is a mathematical test used to determine the stability of a linear time-invariant system by analyzing the characteristic polynomial.

Correct Answer: B — To analyze the stability of a linear time-invariant system.

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Q. What is the significance of the Nyquist plot in control systems?

A. It shows the time response of a system.
B. It helps in determining the stability of a system in the frequency domain.
C. It is used for root locus analysis.
D. It provides the transfer function of a system.

Solution

The Nyquist plot is a graphical representation used to assess the stability of a control system in the frequency domain by analyzing the encirclements of the critical point.

Correct Answer: B — It helps in determining the stability of a system in the frequency domain.

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Q. Which controller is known for its ability to eliminate steady-state error?

A. Proportional controller
B. Integral controller
C. Derivative controller
D. PID controller

Solution

The integral controller is specifically designed to eliminate steady-state error by integrating the error over time.

Correct Answer: B — Integral controller

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Q. Which of the following is NOT a characteristic of a first-order system?

A. It has one energy storage element.
B. It has a single pole.
C. It exhibits exponential response.
D. It can oscillate indefinitely.

Solution

First-order systems do not oscillate indefinitely; they have a single pole and exhibit an exponential response without oscillations.

Correct Answer: D — It can oscillate indefinitely.

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Q. Which of the following represents a transfer function?

A. G(s) = Y(s)/U(s)
B. G(s) = U(s)/Y(s)
C. G(s) = Y(s) + U(s)
D. G(s) = U(s) - Y(s)

Solution

The transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input, G(s) = Y(s)/U(s).

Correct Answer: A — G(s) = Y(s)/U(s)

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Stability Analysis Basics - Problem Set

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