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Nyquist Stability Criterion

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Phase Crossover Frequency

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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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Closed-Loop Stability

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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.

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Open-Loop Transfer Function

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A function that characterizes the input-output relationship of a system without feedback, used in generating the Nyquist plot.

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Zero

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A value of 's' for which the transfer function becomes zero. Zeros affect the shape of the Nyquist plot but not directly the stability.

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Nyquist Criterion

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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).

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Gain Margin

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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.

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Bode Plot

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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.

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Pole

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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.

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Gain Crossover Frequency

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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.

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Critical Point

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The point in the Nyquist plot (-1,0j) around which the number of encirclements determines the stability of the closed-loop system.

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Nyquist Path

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The contour in the complex plane used to trace the frequency response of the open-loop system and create the Nyquist plot.

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Encirclement

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The act of tracing the Nyquist plot around the critical point; can be clockwise or counterclockwise, indicating different implications for system stability.

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Stability Margin

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A quantitative measure of how close a system is to instability, such as gain margin or phase margin derived from the Nyquist plot.

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Nyquist Plot

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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.

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Phase Margin

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A measure from the Nyquist plot of how much additional phase lag at the gain crossover frequency would lead to instability.

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