Question

Derivative error compensation:

• A. Improvement in transient response
• B. Reduction in steady state error
• C. Reduction in settling time
• D. Increase in damping constant

Hint:

PID Controller Terms. P (Proportional): Reduces error, faster response, may cause offset. I (Integral): Eliminates steady-state error, can worsen transient response. D (Derivative): Improves transient response/stability, adds damping, reduces overshoot/oscillations, sensitive to noise.

Answer 1

The Correct Option is D

Derivative error compensation, commonly implemented as the 'D' term in a PID controller (Proportional-Integral-Derivative), introduces a control action proportional to the rate of change of the error signal (\(d(error)/dt\))
Effects of Derivative Control: - Anticipatory Action: It anticipates future error based on its current rate of change
- Damping: It adds damping to the system, which reduces oscillations and overshoot during the transient response
This relates to increasing the damping ratio (\(\zeta\))
- Transient Response Improvement: By adding damping and reducing overshoot, it generally improves the stability and quality of the transient response (Option 1)
- Settling Time: Increased damping usually leads to a reduction in settling time (Option 3), although excessive derivative action can sometimes slow response
- Steady-State Error: Derivative control primarily affects transient response and has little or no effect on steady-state error (Option 2)
Integral control is used to reduce/eliminate steady-state error
While improvement in transient response and reduction in settling time are consequences, the fundamental effect causing these is the addition of damping
Option (4), "Increase in damping constant" (more accurately, damping ratio \(\zeta\)), represents this primary effect