slowly decreasing oscillation for PID

[Blokk]

In my project now I face a very interesting problem, and I would like to ask others' opinion.

I control the temperature of a phyiscal object using LabView PID toolkit, with good results, I tuned my controller manually using the closed-loop Ziegler-Nichols tuning rule. The process value (PV) reaches the setpoint (SP) fast (about one and a half period time and oscillation is gone), and I reach the ultimate precision (deviation around SP) quite fast.

However, I realized that, actually in my experiment a slowly decreasing oscillation would be beneficial in the beginning of the control process due to some physical phenomena.

I guess I should use some kind of gain scheduling? For example, I would like my control system to have an oscillation only decreasing with 5% in amplitude in one period time.

Every advice is welcomed! 🙂

Regards,

[nathand · Accepted solution]

I suspect that with the right tuning values you could get the controller to do this for you. Try increasing the proportional gain - but remember that with the LabVIEW PID, that will also affect integral and derivative gain, so you may need to adjust those too. You know from the Ziegler-Nichols tuning approach that there is a proportional gain at which you get stable sustained oscillations, so you're looking for a proportional gain below that ultimate gain that gets you the the decay in oscillations that you want.

For more about the math, try a search for "PID decay ratio." Classical tuning methods aim for a quarter decay ratio - each successive oscillation has an amplitude 1/4 of the previous oscillation. It sounds like you want your controller tuned for a much larger decay ratio, where each successive oscillation has an amplitude only slightly less than the prior one.

Alternatively you could superimpose a decaying oscillation on the setpoint. This might be easier.

Gain scheduling is used when you want different PID gains depending on the setpoint. Based on your description, I do not think gain scheduling is a solution to your problem.

[AndyClegg]

If you have a transfer function model of your system and controller - you can find equations that relate the rate at which your oscillation decays (normally refered to as "damping ratio", a number between 0 and 1 indicates it will have decaying oscillations) to certain parameters in your control loop and hence controller gains. I've only seen equations for this where the closed loop system is either 2nd or 3rd order, so depending upon your system / controller it may not fit well.

Nathand's approach of changing gains until you get an acceptable response is probably best.

[Blokk]

thanks nathand and AndyClegg,

Actually what I did, I used a much smaller gain P and a bit larger I parameter, in this way I got a very slowly decreasing oscillation. This was a kind of "brute force" solution, since I did not do any calculation, but I get the desired behaviour: in the first 1-2 hours I use this non optimal PID control, and when the system reaches the state what I need, I change the PID parameters to the optimal tuned ones, so I reach the ultimate stability.

thanks for advices,

regards,