Topic: Control Systems
Consider a unity feedback system whose open loop transfer function is
$G(s)=\frac{k}{s(s^{2}+2s+2)}$
The Nyquist plot for this system is
- A. [Plot starting from real axis]
- B. [Plot starting from negative imaginary axis and ending at origin]
- C. [Plot entirely in 2nd quadrant]
- D. [Plot entirely in 3rd quadrant]
Answer: B. [Plot starting from negative imaginary axis and ending at origin]
Explanation: $G(j\omega) = \frac{K}{j\omega(-\omega²+2j\omega+2)}$.
At $\omega=0$: $|GH(0)| = \infty, \angle GH(0) = -90^\circ$.
At $\omega=\infty$: $|GH(\infty)| = 0, \angle GH(\infty) = -270^\circ$.
The Nyquist plot starts at $-\infty$ on the imaginary axis ($-90^\circ$) and spirals into the origin at an angle of $-270^\circ$ (approaching along the positive imaginary axis). Option (b) matches this profile.