LIST-I LIST-II A. Nyquist Criterion I. Polar Plots B. Bode Plot II. Rectangular Plots C. Phase Margin III. Amount of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability D. Gain Margin IV. It is the reciprocal of the magnitude $|G(j\omega)|$ at the frequency at which the phase angle is $-180^\circ$.
Matching Control System Concepts
The question requires matching key concepts from control system stability analysis (LIST-I) with their corresponding definitions or representations (LIST-II).
Analysis of Matches
- A. Nyquist Criterion is directly associated with analyzing system stability using frequency response plots. The Nyquist plot itself is a type of I. Polar Plot.
- B. Bode Plot consists of two graphs, magnitude and phase, plotted against frequency, typically using logarithmic scales on II. Rectangular Plots (semi-log axes).
- C. Phase Margin quantifies stability by measuring how much additional phase lag is needed at the gain crossover frequency to destabilize the system. This matches the definition: III. Amount of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability.
- D. Gain Margin quantifies stability concerning gain variations. It is defined based on the system's gain at the phase crossover frequency (where phase is $-180^\circ$). The definition provided is: IV. It is the reciprocal of the magnitude $|G(j\omega)|$ at the frequency at which the phase angle is $-180^\circ$.
Correct Matching
Based on the analysis:
- A matches with I
- B matches with II
- C matches with III
- D matches with IV
This corresponds to the pairing A-I, B-II, C-III, D-IV.
Important Questions from Basics of Control Systems
The term control system means:
Which of the following is the transfer function of:
\(\frac{{dc\left( t \right)}}{{dt}} + 2c\left( t \right) = r\left( t \right)\)
Where, r(t) is the unit impulse signal
- Which statement is correct for open loop system?
- In open loop control systems, the control action is independent of the desired_____.
- A system is said to be ______, if its output is under control
