PID-Controller

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PID-Controller

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The PID Controller consists of an integrator and differentiator with proportional gain.

Gain Kp: The controller gain Kp determines the frequency gain of the controller in the pass band (where integration and differentiation are of no interest).
Gain Ki: The controller gain Ki determines the shape of the frequency response at low frequencies.
Gain Kd: The controller gain Kp determines the shape of the frequency response at high frequencies.
Frequency fi: The integration behavior of the controller starts at frequency fi in Hz. A decrease of this frequency corresponds to a more pure integration behavior.
Frequency fd: The differentiation behavior of the controller stops at frequency fd in Hz. An increase of this frequency corresponds to a more pure differentiation behavior, reducing the tameness of the controller.

Transfer function of the controller:

EquationPID

that equals

EquationPID1