sum_error in PID controller

Question

I'm trying to implement a PID controller by myself and I've a question about the sum_error in I control. Here is a short code based on the PID theory.

void pid()
{
  error = target - current;

  pTerm = Kp * error;

  sum_error = sum_error + error * deltaT ;
  iTerm = Ki * sum_error;

  dTerm = Kd * (error - last_error) / deltaT;
  last_error = error;

  Term = K*(pTerm + iTerm + dTerm);
}

Now, I start my commands:

Phase 1, If at t=0, I set target=1.0, and the controller begins to drive motor to go to the target=1.0, Phase 2, and then, at t=N, I set target=2.0, and the controller begins to drive motor to go to the target=2.0

My question is, in the beginning of phase 1, the error=1.0, the sum_error=0, and after the phase 1, the sum_error is not zero anymore, it's positive. And in the beginning of phase 2, the error=1.0 (it is also the same with above), but the sum_error is positive. So, the iTerm at t=N is much greater than iTerm at t=0.

It means, the curves between phase 2 and phase 1 are different!!!

But to end-user, the command 1, and the command 2 is almost the same, and it should drive the same effort.

Should I set the sum_error to zero or bound it? Can anyone tell me how to handle the sum_error in typical?

Any comment will be much appreciated!!

Kevin Kuei

Answer 1

I would recommend implementing

• anti-windup
• an averaging (or other) filter for the derivative term (spanning across 2-3-4 timesteps

Here is a referece implementation from Atmel in C with integrator reset.

EDIT: Please consider Chucks questions in the comments and his answer, since anti windup prevents unwanted error accumulation only in the case when the system is not able to execute the desired set-point.

Answer 2

First, please respond to the questions I ask in the comments on your question.

You mention that the device to be controlled is a motor. Bear in mind that rotating power is $P = \tau \omega$, or torque times speed, so you won't get the same response at high speed that you get at low speed because motor torque typically declines with increasing speed.

I'm not sure if this is the cause of your differing responses or not, but I believe it would have a large impact unless you're just using "1.0" and "2.0" as placeholders for some other value, or they are literally 1 and 2 and are very close together percentage-wise in terms of the entire speed band of the motor.

Regarding wind-up, mentioned in 50k4's answer, I wouldn't think it would be an issue unless your process is saturating, which is to say that it shouldn't be an issue unless your motor is hitting some physical limits that would prevent it from responding, like a current limit or something similar. Note however that if you are getting to the point where your response is saturating that you are also likely operating at a point where motor power is limited and thus you are unlikely to get the same response curves no matter what actions you take to tune a standard PID controller.

Ultimately, if I were you, I would evaluate the errors and determine if there is a problem with your error accounting or if you are realizing the physical limitations of a motor. Keep in mind that the entire point of the integral term is to accumulate error - this will speed control response if it is "taking too long". Accumulated error before settling is both normal and desirable as long as the controller output is still able to effect change in the system. Only when the system becomes unresponsive: linear actuators at an end stop; motors at top speed; motor drivers at a current limit; etc., will wind-up become an issue.

I would output integral error, set the motor setpoint to 1.0, then wait until integral error is (effectively) zero, then change the setpoint to 2.0. If the output response is still inconsistent, then you have a problem with the physical limitations of the system (increasing torque required at higher speeds). If you get consistent responses then you are entering "Phase 2" at time "t=N', which is still inside the response time for Phase 1. As the controller is still actively responding it will naturally generate a different response. At that point, consider waiting longer to enter Phase 2 or increasing the gains on your controller to achieve a settled response by time "t=N".

As a final comment, the last line of your code has "Term = k * (error terms)". If you are doing everything else correctly (generally, have your sampling time correct), then you should leave $k=1$, or just use the sum of the PID terms as the controller output.