Question

Match List - I with List - II.

List - I	List - II
A. Root Locus Plot B. Bode Plot C. Nyquist Plot D. Signal flow chart	I. Corner frequency II. Breakaway point III. Critical point IV. Transmittance

• A. A-II, B-I, C-IV, D-III
• B. A-I, B-II, C-III, D-IV
• C. A-IV, B-III, C-II, D-I
• D. A-II, B-I, C-III, D-IV

Hint:

Important control system associations:
• Root locus \(\rightarrow\) Breakaway point
• Bode plot \(\rightarrow\) Corner frequency
• Nyquist plot \(\rightarrow\) Critical point
• Signal flow graph \(\rightarrow\) Transmittance

Answer 1

The Correct Option is D

Concept: Different graphical techniques in control systems are associated with specific characteristic parameters.
• Root locus deals with breakaway and break-in points.
• Bode plot uses corner frequencies.
• Nyquist plot studies encirclement of the critical point.
• Signal flow graph represents transmittance relationships. Understanding these associations is extremely important in control system analysis.

Step 1: Matching Root Locus Plot. Root locus analysis studies movement of system poles as gain varies. An important feature in root locus is: \[ \text{Breakaway point} \] Thus: \[ A \rightarrow II \]

Step 2: Matching Bode Plot. Bode plots are frequency response plots. The frequencies where slope changes occur are called: \[ \text{Corner frequencies} \] Hence: \[ B \rightarrow I \]

Step 3: Matching Nyquist Plot. Nyquist stability criterion depends on encirclement of: \[ (-1+j0) \] which is called the: \[ \text{Critical point} \] Therefore: \[ C \rightarrow III \]

Step 4: Matching Signal Flow Chart. Signal flow graphs describe system variable relationships using: \[ \text{Transmittances} \] Hence: \[ D \rightarrow IV \]

Step 5: Writing the complete matching. Thus: \[ A-II,\quad B-I,\quad C-III,\quad D-IV \] Hence the correct option is: \[ \boxed{(4)} \]