Question

When a control signal is generated proportional to rate of change of position error, the controller is:

• A. Proportional Controller
• B. Derivative Controller
• C. Integral Controller
• D. Two-step Controller

Hint:

Derivative control reacts to how fast error is changing—not just its magnitude.

Answer 1

The Correct Option is B

Concept: Controllers in control systems are classified based on how the control signal depends on the error signal \(e(t)\). \[ e(t) = \text{desired output} - \text{actual output} \] Types:
• Proportional: \(u(t) \propto e(t)\)
• Integral: \(u(t) \propto \int e(t) dt\)
• Derivative: \(u(t) \propto \frac{de(t)}{dt}\)

Step 1: Understand the given condition.
The question states: \[ \text{Control signal} \propto \text{rate of change of error} \] Mathematically: \[ u(t) \propto \frac{de(t)}{dt} \]

Step 2: Identify the controller type.
This exactly matches the definition of a derivative controller.

Step 3: Physical interpretation.
A derivative controller:
• Predicts future error
• Improves system stability
• Reduces overshoot Final Answer: \[ \boxed{\text{Derivative Controller}} \]