Question

The error signal produced in a control system is constant. The output of derivative action will be

• A. zero
• B. linear
• C. constant
• D. Infinity

Hint:

Derivative action = Rate-of-change controller.
Derivative of a constant is always zero.
This is why derivative action cannot eliminate steady-state offsets on its own.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to determine the output signal of a derivative control action when the incoming error signal remains completely constant over time.

Step 2: Key Formula or Approach:
The output of a derivative control action ($u_d(t)$) is directly proportional to the rate of change of the error signal ($e(t)$) with respect to time:
\[ u_d(t) = K_d \frac{de(t)}{dt} \] where $K_d$ is the derivative gain.

Step 3: Detailed Explanation:

• Let the error signal be a constant value, $e(t) = C$ (where $C$ is a constant).

• The derivative of a constant value with respect to time is mathematically zero:
\[ \frac{de(t)}{dt} = \frac{d}{dt}(C) = 0 \]
• Substituting this derivative back into the control output equation:
\[ u_d(t) = K_d \cdot 0 = 0 \]
• This occurs because derivative action is purely rate-sensitive. It only produces an output when the error is actively changing. If the error is steady, the derivative term produces no control response.

Step 4: Final Answer:
The output of the derivative action will be zero.