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The PI Controller consists of an integrator with a proportional gain.

Gain Kp: The controller gain Kp determines the high frequency gain of the controller.
Gain Ki: The controller gain Ki determines the frequency gain of the controller at frequency w = 1 [rad/s].
Frequency fi: The integration behavior of the controller stops after frequency fi in Hz. A decrease of this frequency corresponds to a more pure integration behavior.

Transfer function of the controller:

EquationPI.gif (1247 bytes)

that equals

EquationPI1.gif (1913 bytes)