Electrical Engineering (EE) 15 min read
Control Systems: Bode Plots, Nyquist Stability Criterion & State Space
Essential open-loop and closed-loop stability analysis methods for engineering services and research interviews.
#Control Systems#Bode Plot#Nyquist#Stability#State Space
In-Depth Interview Questions & Model Solutions
Q1State the Nyquist Stability Criterion and explain how encirclement of (-1 + j0) predicts closed-loop stability.
The Nyquist Stability Criterion is based on Cauchy’s Argument Principle: `N = P - Z`, where N is the number of clockwise encirclements of the critical point `(-1 + j0)` by the open-loop Nyquist contour G(s)H(s), P is the number of open-loop poles in the Right Half s-Plane (RHP), and Z is the number of closed-loop poles in the RHP. For a stable closed-loop system, we must have `Z = 0`, which requires `N = -P` (i.e. the Nyquist plot must encircle `(-1 + j0)` counter-clockwise exactly P times). If the open-loop system is already stable (P = 0), then N must be 0 (no encirclement of -1+j0 permitted).
Key Technical Takeaways:
- N = P - Z (en-route clockwise conventions).
- Gain Margin (GM) is inverse of magnitude at Phase Crossover Frequency (-180°).
- Phase Margin (PM) = 180° + Phase angle at Gain Crossover Frequency (|G(jω)| = 1).
Technical Panel Interview Strategy Tips
- Draw Bode magnitude and phase asymptotes accurately showing slope changes of -20 dB/decade for simple poles.
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