PI controller in VHDL

i would like to tell you the equation of PI controller that i used:

u(k)=u(k-1) + err(k)*(kp +(ki*ts/2)) + err(k-1) * ( (ki*ts/2) - kp)

where:

u : is the output of controller.

err: error signal that injected to the controller.

kp: proportional constant.

ki : integral constant.

ts : sampling time.

Thanks very much for your replies.

thanks Kaz i understand the proportional term but rely i didn't understand the integral term.

can you explain it again and with its equation?

note: for the proportional term there no value for sampling time.

I have done sort of PI that consisted of two branches only (proportional and integral parts). I used it for phase error control in a receiver carrier tracking.

It was very simple in vhdl (but have the code misplaced).

The proportional part is just a multiplier; you multiply the error(input) by a constant (I used .1 ~ 200).

The integral part is just an acuumulator; you add up the error nonstop and hopefully will not overflow. You will need to add a term here to decide how much to feedback = leakage (e.g. .001 ~ 1), again needs multiplier in the accumulator loop.

The two branches are just added up.

Testing is more difficult and best is in-system testing