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The PID-1 Controller consists of an integrator and differentiator with proportional gain. It resembles a PID Controller, but has different input parameters.


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).
Length Li: The length Li determines the frequency at which integration starts, that is fi / Li in Hz. A decrease of this frequency corresponds to a more pure integration behavior.
Length Ld: The length Ld determines the frequency at which differentiation stops, that is fd * Ld in Hz. An increase of this frequency corresponds to a more pure differentiation behavior, reducing the tameness of the controller.
Frequency fi: The integration behavior of the controller stops at frequency fi in Hz.
Frequency fd: The differentiation behavior of the controller starts at frequency fd in Hz.

Transfer function of the controller:

EquationPID-1.gif (2826 bytes)

that equals


EquationPID-11.gif (4060 bytes)