Feedback Systems: Stability, Gain, and Compensation Quiz Quiz

Assess your knowledge of feedback control systems focusing on system stability, gain adjustments, and compensation techniques. This quiz covers key concepts and practical scenarios relevant to feedback loop analysis and design in engineering and electronics applications.

1. Identifying Stable Feedback Systems

   Which of the following systems described by its open-loop transfer function is considered stable when unity feedback is applied?

   1. A system with a pole at +3 and -4
   2. A system with poles at 0 and -1
   3. A system with poles at -2 and -5
   4. A system with poles at +2 and +5

   Explanation: A system with poles at -2 and -5 will have negative real parts, indicating all poles are in the left half of the s-plane, which means the closed-loop system is stable with unity feedback. If a system has a pole at 0 (option B), it's marginally stable but not strictly stable. Poles with positive real parts, as in options C and D, indicate instability regardless of feedback. Hence, only negative real poles assure stability under these conditions.

2. Effect of Gain on Closed-Loop Stability

   If you increase the gain in a negative feedback system described by a second-order transfer function, what is a likely effect on stability?

   1. The system's stability is unaffected by gain
   2. The system output will stop responding to input
   3. The system may become unstable if the gain is too high
   4. The system will always become more stable

   Explanation: Increasing gain in a negative feedback system can move closed-loop poles closer to the imaginary axis or even to the right-half plane, potentially causing instability. Option B is incorrect as higher gain does not always enhance stability; in fact, it often reduces the margin. Option C is also incorrect since gain directly impacts pole locations. Option D is implausible; higher gain changes response but does not stop output altogether.

3. Purpose of Lead Compensation

   In a feedback system, why is lead compensation often introduced?

   1. To reduce the steady-state error for a ramp input
   2. To decrease the bandwidth for noise reduction
   3. To intentionally add a time delay
   4. To increase system phase margin and improve transient response

   Explanation: Lead compensation adds phase lead, which helps increase phase margin and thus improves the system's transient response and resistance to oscillations. Reducing steady-state error for ramp inputs (option B) is handled by other compensators such as lag or PI compensation. Decreasing bandwidth (option C) is not the purpose of a lead compensator. Adding time delay (option D) would typically degrade phase margin, not improve it.

4. Distinguishing Open- and Closed-Loop Gain

   Which statement best describes the difference between open-loop gain and closed-loop gain in a feedback amplifier?

   1. Open-loop gain is always equal to closed-loop gain
   2. Open-loop gain is determined by feedback network components only
   3. Closed-loop gain is always higher than open-loop gain
   4. Closed-loop gain is typically lower and more stable than open-loop gain

   Explanation: Closed-loop gain is set by including feedback and is generally lower but more stable and predictable compared to the open-loop gain, which can vary widely. They are not always equal (option B), nor is closed-loop gain always higher (option C); actually, it's usually less. The open-loop gain is intrinsic to the amplifier, not determined by external feedback network components as stated in option D.

5. Interpreting Nyquist Plots for Stability Assessment

   When analyzing a feedback system with a Nyquist plot, what indicates the possibility of closed-loop instability?

   1. The plot encircles the point -1 in the complex plane
   2. The plot never crosses the real axis
   3. The plot passes through the origin
   4. The plot is entirely in the right-half of the complex plane

   Explanation: Encirclement of the -1 point in the complex plane by the Nyquist plot can indicate closed-loop instability due to the Nyquist criterion. Passing through the origin (option B) has no direct implication for stability. A plot entirely in the right half (option C) might suggest instability, but it's not the Nyquist criterion regarding -1. Never crossing the real axis (option D) also does not directly indicate stability or instability.