Why do the hydraulics function controller parameters on technology CPUs possess physical units which differ from the standard?
The controller parameters for the hydraulics function possess the following physical units:
|Controller parameter||Unit in
Gain is normally dimensionless.
|Ki||1/s2||The reset time Tn is generally indicated here in seconds.|
|Kd||dimensionless||The parameter corresponds to the rate time Tv which is indicated in seconds.|
The following applies, in general, for a PID controller with the controller input variable e(t) and output variable y(t):
The variable e(t) is the difference between the target value and the actual value. Signal y(t) represents the controller output. The reset time Tn = 1/Ki is frequently stated in place of the integration constant Ki. The derivative-action time constant Kd is identical to the rate time Tv, which is frequently used.
The input signal e(t) from the hydraulics function controller is an indication of positional difference measured in mm. The controller's output signal y(t) is velocity measured in mm/s. The requisite adaptation from mm → mm/s affects the physical units of the controller parameters. This is divided into P, I and D portions:
Gain (P portion):
Integration (I portion):
Differentiation (D portion):
Since the controller parameters of the hydraulics function are related to time, any changes can be made to the sampling time for the controller without any need to adapt the parameters.