Stability Analysis MCQs Aeronautical Engineering)

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What does the term ‘stability’ refer to in control systems? A) The system’s ability to return to equilibrium after a disturbance B) The system’s response time C) The system’s output accuracy D) The system’s ability to process inputs Answer: A) The system’s ability to return to equilibrium after a disturbance 2. Which method is used to analyze the stability of a linear time-invariant system? A) Root locus B) Frequency response C) Nyquist criterion D) Bode plot Answer: C) Nyquist criterion 3. In the Nyquist criterion, what does the encirclement of the point (-1, 0) in the complex plane indicate? A) Potential instability in the system B) System stability C) The system’s steady-state response D) The gain margin of the system Answer: A) Potential instability in the system 4. What is the significance of the ‘Routh-Hurwitz criterion’? A) It determines the stability of a system based on its characteristic polynomial B) It provides a method for designing controllers C) It measures the system’s transient response D) It calculates the system’s frequency response Answer: A) It determines the stability of a system based on its characteristic polynomial 5. Which of the following conditions must be satisfied for a system to be considered stable in the time domain? A) All poles of the system must lie in the left half of the s-plane B) All zeros of the system must lie in the left half of the s-plane C) The system’s gain margin must be zero D) The system must have zero phase shift Answer: A) All poles of the system must lie in the left half of the s-plane 6. What is ‘Gain Margin’? A) The amount by which the system gain can be increased before the system becomes unstable B) The maximum allowable phase shift before instability occurs C) The distance of the system’s poles from the origin D) The difference between the system’s maximum and minimum gains Answer: A) The amount by which the system gain can be increased before the system becomes unstable 7. What is ‘Phase Margin’? A) The additional phase lag required to make the system unstable B) The maximum phase shift before the system’s gain becomes zero C) The distance of the system’s poles from the critical point D) The system’s steady-state phase shift Answer: A) The additional phase lag required to make the system unstable 8. What does the ‘Root Locus’ method help determine? A) The locations of the system poles as a parameter changes B) The frequency response of the system C) The time-domain response of the system D) The system’s state-space representation Answer: A) The locations of the system poles as a parameter changes 9. Which criterion involves plotting the system’s open-loop transfer function on the complex plane? A) Nyquist criterion B) Routh-Hurwitz criterion C) Bode plot D) Root locus Answer: A) Nyquist criterion 10. What is the primary use of a ‘Bode plot’ in stability analysis? A) To analyze the system’s frequency response B) To determine the system’s poles and zeros C) To compute the time-domain response D) To measure the system’s transient response Answer: A) To analyze the system’s frequency response 11. What does a ‘pole-zero plot’ show? A) The locations of poles and zeros of the system’s transfer function B) The system’s time-domain response C) The frequency response of the system D) The system’s state-space representation Answer: A) The locations of poles and zeros of the system’s transfer function 12. What does the ‘Stability Margins’ analysis provide information about? A) The system’s tolerance to gain and phase variations before becoming unstable B) The system’s steady-state accuracy C) The time constant of the system’s response D) The amount of overshoot in the system’s response Answer: A) The system’s tolerance to gain and phase variations before becoming unstable 13. What is the purpose of ‘Lyapunov’s Direct Method’ in stability analysis? A) To determine the stability of a system using a Lyapunov function B) To design controllers for the system C) To analyze the system’s frequency response D) To measure the system’s gain and phase margins Answer: A) To determine the stability of a system using a Lyapunov function 14. In the context of control systems, what does ‘Asymptotic Stability’ mean? A) The system returns to its equilibrium point as time approaches infinity B) The system’s response oscillates indefinitely C) The system reaches a steady-state response quickly D) The system is always stable for any initial condition Answer: A) The system returns to its equilibrium point as time approaches infinity 15. What is ‘Marginal Stability’? A) The system oscillates indefinitely with constant amplitude but does not diverge B) The system’s output exponentially increases without bound C) The system’s poles are located in the right half of the s-plane D) The system quickly reaches a steady-state response Answer: A) The system oscillates indefinitely with constant amplitude but does not diverge 16. Which of the following methods is used to assess the stability of a nonlinear system? A) Lyapunov’s Direct Method B) Routh-Hurwitz criterion C) Bode plot D) Nyquist criterion Answer: A) Lyapunov’s Direct Method 17. What is the ‘Nyquist plot’ used for in stability analysis? A) To determine the stability of a system by analyzing the encirclements of critical points B) To plot the system’s poles and zeros C) To measure the system’s transient response D) To design controllers based on time-domain specifications Answer: A) To determine the stability of a system by analyzing the encirclements of critical points 18. In stability analysis, what is the ‘critical point’ referred to? A) The point (-1, 0) in the Nyquist plot B) The point where the system’s poles cross the imaginary axis C) The point where the system’s gain is maximum D) The point where the phase shift is zero Answer: A) The point (-1, 0) in the Nyquist plot 19. What does the term ‘Instability’ imply in control systems? A) The system’s output grows without bound or oscillates indefinitely B) The system’s response reaches steady-state quickly C) The system’s gain margin is zero D) The system’s phase margin is infinite Answer: A) The system’s output grows without bound or oscillates indefinitely 20. Which technique is used to analyze stability by observing how the poles of the system move with varying feedback gains? A) Root locus B) Bode plot C) Nyquist criterion D) State-space analysis Answer: A) Root locus 21. What is the role of ‘Feedback’ in improving system stability? A) To correct errors and improve the system’s robustness B) To increase the system’s response time C) To reduce the system’s gain margin D) To measure the system’s steady-state error Answer: A) To correct errors and improve the system’s robustness 22. What is ‘Static Stability’? A) The system’s ability to return to its original position after a small disturbance B) The system’s response to large disturbances C) The system’s phase shift at high frequencies D) The system’s steady-state accuracy Answer: A) The system’s ability to return to its original position after a small disturbance 23. In control systems, what is ‘Dynamic Stability’? A) The system’s ability to return to equilibrium over time after a disturbance B) The system’s response to sinusoidal inputs C) The system’s steady-state response D) The system’s performance under constant conditions Answer: A) The system’s ability to return to equilibrium over time after a disturbance 24. Which criterion is used to determine the stability of systems with higher-order polynomials? A) Routh-Hurwitz criterion B) Nyquist criterion C) Bode plot D) Root locus Answer: A) Routh-Hurwitz criterion 25. What is the effect of ‘Increasing Gain’ on system stability? A) It can lead to instability if the gain is too high B) It always improves system stability C) It has no effect on stability D) It decreases the system’s response time Answer: A) It can lead to instability if the gain is too high 26. What does the ‘Bode Stability Criterion’ involve? A) Plotting gain and phase margins to assess stability B) Analyzing the root locus of the system C) Measuring the system’s transient response D) Calculating the system’s poles and zeros Answer: A) Plotting gain and phase margins to assess stability 27. What is ‘Time Domain Stability’? A) The system’s ability to return to a steady-state after a disturbance over time B) The system’s frequency response characteristics C) The system’s ability to process inputs D) The system’s transient response time Answer: A) The system’s ability to return to a steady-state after a disturbance over time 28. What does a ‘Phase Lead Compensation’ do to system stability? A) It increases the phase margin and improves transient response B) It decreases the gain margin and worsens stability C) It has no effect on stability D) It increases the system’s steady-state error Answer: A) It increases the phase margin and improves transient response 29. What does ‘Stability Analysis of Nonlinear Systems’ usually involve? A) Using Lyapunov’s methods or describing functions B) Applying the Routh-Hurwitz criterion C) Plotting the Bode diagram D) Using the Nyquist criterion Answer: A) Using Lyapunov’s methods or describing functions 30. What is the significance of ‘Pole-Zero Placement’ in control system design? A) It helps in designing controllers to achieve desired system stability and performance B) It measures the system’s transient response C) It plots the system’s frequency response D) It evaluates the system’s gain margin Answer: A) It helps in designing controllers to achieve desired system stability and performance 31. What is ‘Stability in the Presence of Disturbances’? A) The system’s ability to maintain stable performance despite external disturbances B) The system’s steady-state error in the presence of disturbances C) The system’s transient response to disturbances D) The system’s phase shift in the presence of disturbances Answer: A) The system’s ability to maintain stable performance despite external disturbances 32. In the context of stability, what is a ‘Lyapunov Function’? A) A scalar function used to prove the stability of nonlinear systems B) A function that measures the system’s frequency response C) A function that determines the system’s gain and phase margins D) A function that calculates the system’s transient response Answer: A) A scalar function used to prove the stability of nonlinear systems 33. What is ‘Unconditional Stability’? A) The system remains stable regardless of any changes in system parameters B) The system’s stability under specific conditions only C) The system’s stability with guaranteed zero steady-state error D) The system’s stability with maximum allowable gain Answer: A) The system remains stable regardless of any changes in system parameters 34. What does the term ‘Closed-Loop Stability’ refer to? A) The stability of a system when feedback is applied B) The stability of a system in open-loop conditions C) The stability of the system’s poles in the s-plane D) The stability of the system’s transient response Answer: A) The stability of a system when feedback is applied 35. What does ‘Pole Location’ analysis involve? A) Determining the system’s stability based on the location of its poles in the s-plane B) Measuring the system’s steady-state performance C) Plotting the system’s frequency response D) Designing controllers based on time-domain specifications Answer: A) Determining the system’s stability based on the location of its poles in the s-plane 36. What is the ‘Character of Stability’ for a system with all poles in the left half of the s-plane? A) The system is asymptotically stable B) The system is marginally stable C) The system is unstable D) The system is stable only for a certain range of inputs Answer: A) The system is asymptotically stable 37. Which criterion assesses stability by examining the poles of a system’s transfer function? A) Routh-Hurwitz criterion B) Nyquist criterion C) Bode plot D) Root locus Answer: A) Routh-Hurwitz criterion 38. In stability analysis, what does ‘Stability Margin’ indicate? A) The system’s ability to withstand changes in system parameters before becoming unstable B) The maximum phase shift allowed before instability occurs C) The distance between the system’s poles and the origin D) The system’s steady-state response to various inputs Answer: A) The system’s ability to withstand changes in system parameters before becoming unstable 39. What is the role of ‘State Feedback’ in improving system stability? A) To place the system poles at desired locations to enhance stability B) To measure the system’s steady-state error C) To improve the system’s transient response without affecting stability D) To adjust the system’s gain margin Answer: A) To place the system poles at desired locations to enhance stability 40. What does ‘Frequency Domain Stability Analysis’ involve? A) Analyzing the system’s stability based on its frequency response characteristics B) Measuring the system’s time-domain response C) Designing controllers based on time-domain specifications D) Determining the system’s poles and zeros Answer: A) Analyzing the system’s stability based on its frequency response characteristics 41. What is ‘Stability Criterion’ in the context of control systems? A) A set of conditions or rules used to determine the stability of a system B) A measurement of the system’s steady-state response C) A method for designing system controllers D) A plot showing the system’s transient response Answer: A) A set of conditions or rules used to determine the stability of a system 42. What does a ‘Stability Plot’ typically show? A) The system’s response to changes in gain and phase B) The system’s poles and zeros in the s-plane C) The system’s response to sinusoidal inputs D) The system’s time-domain performance Answer: A) The system’s response to changes in gain and phase 43. What is the role of ‘Time Delay’ in stability analysis? A) Time delay can reduce the stability margin and make a system less stable B) Time delay improves the system’s stability C) Time delay has no effect on system stability D) Time delay decreases the system’s steady-state error Answer: A) Time delay can reduce the stability margin and make a system less stable 44. What is meant by ‘Poles on the Imaginary Axis’? A) The system is marginally stable and oscillates indefinitely with constant amplitude B) The system is asymptotically stable C) The system is unstable D) The system reaches steady-state quickly Answer: A) The system is marginally stable and oscillates indefinitely with constant amplitude 45. What does the ‘Routh-Hurwitz Stability Criterion’ involve? A) Constructing the Routh array from the characteristic polynomial to determine stability B) Plotting the system’s frequency response C) Measuring the system’s gain and phase margins D) Analyzing the root locus of the system Answer: A) Constructing the Routh array from the characteristic polynomial to determine stability 46. What is the effect of ‘Adding a Pole’ to the open-loop transfer function on system stability? A) It can affect the stability of the closed-loop system depending on the pole location B) It always improves system stability C) It has no effect on stability D) It decreases the system’s transient response time Answer: A) It can affect the stability of the closed-loop system depending on the pole location 47. What is a ‘Marginally Stable System’? A) A system that neither converges nor diverges but exhibits sustained oscillations B) A system that returns to equilibrium after a disturbance C) A system that is unstable and diverges over time D) A system that remains stable under all conditions Answer: A) A system that neither converges nor diverges but exhibits sustained oscillations 48. What does ‘Gain Margin’ indicate in the Bode plot analysis? A) The amount by which the gain can be increased before the system becomes unstable B) The system’s phase shift at a given frequency C) The system’s steady-state response to sinusoidal inputs D) The frequency at which the phase crosses -180 degrees Answer: A) The amount by which the gain can be increased before the system becomes unstable 49. What is a ‘Characteristic Polynomial’? A) A polynomial derived from the system’s differential equation that determines the system’s poles B) A polynomial used to design system controllers C) A polynomial representing the system’s frequency response D) A polynomial that defines the system’s time-domain response Answer: A) A polynomial derived from the system’s differential equation that determines the system’s poles 50. What is the purpose of ‘Nyquist Criterion’ in stability analysis? A) To assess the stability of a closed-loop system based on its open-loop frequency response B) To design controllers based on time-domain specifications C) To measure the system’s transient response D) To determine the system’s gain margin and phase margin Answer: A) To assess the stability of a closed-loop system based on its open-loop frequency response

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