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Nyquist Stability Criterion
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Nyquist Plot
A graphical representation of the frequency response of a system used to predict stability. It plots the complex-valued transfer function as a function of frequency.
Nyquist Criterion
A graphical method for determining the stability of a closed-loop system by counting the number of clockwise encirclements of the critical point (-1,0j).
Gain Margin
A measure of how much gain can increase before a system becomes unstable, obtained from the Nyquist plot as the inverse of the gain at the phase crossover frequency.
Phase Margin
A measure from the Nyquist plot of how much additional phase lag at the gain crossover frequency would lead to instability.
Critical Point
The point in the Nyquist plot (-1,0j) around which the number of encirclements determines the stability of the closed-loop system.
Encirclement
The act of tracing the Nyquist plot around the critical point; can be clockwise or counterclockwise, indicating different implications for system stability.
Open-Loop Transfer Function
A function that characterizes the input-output relationship of a system without feedback, used in generating the Nyquist plot.
Closed-Loop Stability
A concept referring to whether a system with feedback tends to return to its equilibrium state after a disturbance, as analyzed by the Nyquist plot.
Nyquist Path
The contour in the complex plane used to trace the frequency response of the open-loop system and create the Nyquist plot.
Bode Plot
Though not part of the Nyquist plot, it's a precursor that shows the gain and phase of a system as functions of frequency which can inform the Nyquist plot.
Stability Margin
A quantitative measure of how close a system is to instability, such as gain margin or phase margin derived from the Nyquist plot.
Pole
A value of 's' for which the transfer function becomes infinite. Poles to the right of the imaginary axis in the complex plane imply system instability.
Zero
A value of 's' for which the transfer function becomes zero. Zeros affect the shape of the Nyquist plot but not directly the stability.
Gain Crossover Frequency
The frequency at which the magnitude of the transfer function equals one (0 dB). This frequency is critical for determining phase margin on the Nyquist plot.
Phase Crossover Frequency
The frequency at which the phase angle of the transfer function is -180 degrees. This frequency is useful for determining gain margin on the Nyquist plot.
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