Topic: Control Systems
The bode plot of the delay transfer function $e^{-3s}$ has the following shape
- A. Straight line with negative slope
- B. Straight line with positive slope
- C. A curved line with resonance
- D. A curve with two straight parts
Answer: A. Straight line with negative slope
Explanation: For a pure transport delay transfer function $G(s) = e^{-Td s}$, substituting $s = j\omega$ yields $G(j\omega) = e^{-j\omega Td}$.
The magnitude is $|e^{-j\omega Td}| = 1$ (or 0 dB), which is a flat horizontal line.
The phase angle is $\angle G(j\omega) = -Td \cdot \omega$. In the context of a phase plot against a linear frequency axis, this equation $y = -mx$ represents a straight line with a negative slope.