Using PID code different from its mathematics equation

Question

I asked this question at stack overflow but i did not receive any replies, i think it was the wrong place to ask, so i am re-posting it here.

Short question: How wise is it to change the PID formula/equation based on the needs of your project?

Is it really a technique a proffesional would use?

Longer question: I am making my first PID in embedded MCU (Atmega328p).

I have a hotplate and i want it to reach a certain temperature, and i made it, easy.

As a reference for my PID i followed electronoob's tutorial. what i dont understand from his tutorial, is the line 171 of his code:

  pid_i = pid_i+(ki*error);  

His integral is using the error instead of the dt (time lapse). I see in the video (and i understand why he does that)

He actually does this:

/*The integral part should only act if we are close to the
desired position but we want to fine tune the error. That's
why I've made a if operation for an error between -2 and 2 degree.
*/
if(-3 <error <3)
{
  pid_i = pid_i+(ki*error);  
}

So the question is how wise is it to change the default PID equations to match your project?

What would you consult me to do to my present/future projects regarding changing the basic PID formula?

Answer 1

My answer to Understanding the flow of a PI controller may be useful (or not!). In it I give a simplistic example of PI control for a car's cruise control.

I don't like the sample code comment "The integral part should only act if we are close to the desired position but we want to fine tune the error." Here's why:

Figure 3. The classic PID control function. Source: Wikipedia - PID controller.

1. The classic PID control function has no if statement in it. The integrator, if implemented, is running continuously from power-up.
2. As explained in my linked answer, P-only control will never reach the target (unless there is overshoot) and will settle down with an offset. In your implementation, if the offset is greater than your ±3° then your integral control will never turn on and the offset will never be eliminated.

As pointed out in the linked answer, when the integral action zeros the error the contribution of the proportional action is zero and the output depends only on the integral action.

Answer 2

Ye, you can change.

He wanted a control of +/- 2 degrees, you might need a range of +/- 4 degrees for your project.

So it can be changed according to the circumstances. You just need to understand your own project to know what assumptions are valid.

Answer 3

Here is a (slightly simplified) code snippet of the integrator-suppression logic I have been using for several years. Posting it in case it may be helpful.

The first feature here, is that the positive and negative saturation cases have their own logic.

Secondly, is the external rise/fall suppress flag, but you don't need to worry about that for temperature control. But in general, if there is an inner loop, it is helpful for the outer loop to know when the inner loop is saturating or rate limited, so I'm leaving it in just to illustrate that point.

Thirdly, for temperature control, output-rate-limit is probably a non issue.

    if
        (
            (pid_config->Ti == 0)
            ||
            (
                (fxdpt_err < 0)
                &&
                (
                    external_integ_suppress_fall_flag
                    ||
                    output_saturated_low
                    ||
                    output_rate_at_limit_low
                )
            )
            ||
            (
                (fxdpt_err > 0)
                &&
                (
                    external_integ_suppress_rise_flag
                    ||
                    output_saturated_high
                    ||
                    output_rate_at_limit_high
                )
            )
        )
    {
        // for any of above conditions, integral accumulator remains unchanged
    } else {
        // otherwise, add onto integral accumulator as normal
    }

Besides this, you should enforce a limit the integral accumulator, which for configuration purposes can be non-dimensionalized vs the full-scale input, full-scale output, and various Kp Ki terms etc.

Final footnote:

Another thing that makes a pleasant PID controller is set-point-rate limits. It is not hard but not entirely trivial, needs logic to make it "do the right thing" when a change in set point results in a sudden direction change while ramping. If interested, ask.