Re: [CAD_CAM_EDM_DRO] PID in a PIC

At 02:37 PM 8/10/00 -0700, you wrote:

>I came up with this 'C' code from an "Embedded Systems Programming"
>magazine pseudo code example, am I on the right track?
>
>dt = .001; // 1000 loops/sec?
>
>while(1)
> {
> Sum = OldSum + Error;
> Output = (Kp * Error) + (Ki * Sum * dt) + (Kd * (Error -
>OldError)/dt);
> OldError = Error;
> OldSum = Sum;
> }

This is an ok start. This is called the "ideal" or non-interactive
PID algorithm.

Error should be (SP - PV), so you get negative feedback.

A more usual algorithm you will see more frequently is

Output = K (1 + (dt/Ti) * sum + Td*(Error-OldError)/dt)

Where K is dimensionless (gain) and Ti, Td have units of time.

These algorithms are seldom used in practice as-is because they
don't work very well without modifications.

Normally the derivative equation has to be modified because of noise
considerations. You also have to think about the resolution of the
input and the effect that will have on the "D" operation. In fact, you
may only need a PI controller. I usually program a single pole
digital filter for this purpose. You also should make the sample
time reasonably large in comparision with the response time of the
system if you want to get a sensible derivative signal.
Imagine a situation where the sample rate was very high, the system
response rate slow and the resolution poor. You would get zero derivative
signal until the bit transitions when you would get a huge signal that
could saturate the output, then the signal would disappear with the next
sample.

You also need to initialize Sum to zero (!) or some other number in some
cases, and you should inhibit further integration when the output is
saturated, otherwise you will get what is called "reset windup" happening.
This can cause the controller to oscillate.

Best regards,


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