Question

Match List - I with List - II.

List - I	List - II
A. Derivative control B. Integral control C. Rate feedback control D. Proportional control	I. Improved over shoot response II. Less steady state errors III. Less stable IV. More Damping

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

Hint:

Effects of controller actions:
• Derivative control \(\rightarrow\) Better transient response
• Integral control \(\rightarrow\) Reduced steady-state error
• Rate feedback \(\rightarrow\) Increased damping
• High proportional gain \(\rightarrow\) Reduced stability

Answer 1

The Correct Option is D

Concept: Different control actions affect system behavior differently.
• Derivative control improves transient response and overshoot.
• Integral control reduces steady-state error.
• Rate feedback improves damping.
• Proportional control alone may reduce stability at high gain. These are fundamental effects in classical control systems.

Step 1: Matching Derivative Control. Derivative control predicts future error trends and improves transient response. It reduces overshoot. Hence: \[ \text{Derivative control} \rightarrow \text{Improved overshoot response} \] Thus: \[ A \rightarrow I \]

Step 2: Matching Integral Control. Integral control accumulates error over time. This helps eliminate steady-state error. Hence: \[ B \rightarrow II \]

Step 3: Matching Rate Feedback Control. Rate feedback introduces damping into the system. Thus: \[ C \rightarrow IV \] because it increases damping and improves transient behavior.

Step 4: Matching Proportional Control. High proportional gain can reduce stability margins. Thus proportional control may make the system: \[ \text{Less stable} \] Hence: \[ D \rightarrow III \]

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