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I'm struggling to code PI control using the frequency domain formula specified by Autosar (AUTomotive Open System ARchitecture).

Taken from Specification of Floating Point Math Routines AUTOSAR CP R21-11 (pg. 48/100)

8.5.4.7.2 ‘PI’ Controller – Type1 with limitation (Implicit type)" [SWS_Mfl_00326].

Yn = Yn-1 + (K * Xn) - (K * (1 - dT/Tn) * Xn-1)

I'm lost with the equation's dT/Tn term. Y is the output, X is the input, K is gain.

Digging as best I can "Structure definitions for controller routines" between many docs gives:

----------------------------

Tn : Follow-up time. Physical unit [sec] describes the Follow-up time.

Tn is expressed in us and have a resolution of 1/10ˆ6

Tn is given by a reciprocal value (Tnrec) to avoid a division in the implementation

The time and time equivalent parameters in the equation / implementation are given

by:

dT : Time step = sampling interval. dT is expressed in us (micro seconds) and shall

have a resolution of 1/10ˆ6.

Tnrec _<size>, Tnrec_C : Reciprocal follow-up time = 1/ Tn. The result shall be Rounded towards Zero.

dT_<size> : Time step = sampling interval [10-6 seconds per increment of 1 data representation unit]

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If my (PI) sample rate is 3Hz or 333msec, then dT is 333,333 [usec].

Tn = "Follow up time" or  I've seen it called "follow up time state variable". I don't know what this means.

I keep getting the (1-dT/Tn) term as massive negative value which does not work. Or dT=Tn gives a zero value.

Can anyone offer insight.