A lag compensator decreases the bandwidth/speed of response:.The phase-lag characteristic is of no consequence in lag compensation.The primary function of a lag compensator is to provide attenuation in the high-frequency range to give a system sufficient phase margin.The pole/zero plot of the example lead compensator: The Bode plots of the example lead compensator: The lead controller helps us in two ways: it can increase the gain of the open loop transfer function, and also the phase margin in a certain frequency range. Increases the phase margin: the phase of the lead compensator is positive for every frequency, hence the phase will only increase.Increases response speed and bandwidth.Pushes the poles of the closed loop system to the left.The pole-zero map of the example notch filter: The Bode plots of the example notch filter: Since the both pole/zero pair are equal-distance to the origin, the gain at zero frequency is exactly one.
To obtain a good notch filter, put two poles close the two zeros on the semicircle as possible. However, such a filter would not have unity gain at zero frequency, and the notch will not be sharp. Notch filter could in theory be realized with two zeros placed at +/-(j omega_0). The Bode plots of the example three high-pass filters: Higher order results in more aggressive filtering (-20 dB per decade per pole) and phase lag. Three examples are provided : single-pole, complex-pole, and three-pole. The Bode plots of the example three low pass filters:Ī high-pass filter decreases the magnitude of low frequency components.
The corner frequency of all three filters is 100 rad/s. See the First-Order Low-Pass Filter Discretization article for more details on low-pass filters.
% MatLab(©) Script to generate Bode plots of custom zero/pole location.
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