I am trying to find the transfer function of a plant that contains numerous equipment including a heater, several tanks, pumps, membranes etc.

I need to design 2 PID controllers: the first one to control the temperature of the stream entering one of the membranes, and the second PID controller needs to maintain the solution concentration in one of the tanks.

I have seen that there is a system identification tool in Matlab that I can use to find the plant transfer function. The problem is, I am not clear on exactly what the plant transfer function should describe. Should it represent the whole plant (e.g. all the tanks, pumps etc.) or only the part of the plant that I am interested in to be able to design the controllers (e.g. resulting in two different plant transfer function equations for each controller).

Thanks in advance.


When you're working on systems design, the plant is the thing you're controlling, and it's up to you to figure out what that thing is.

Keep in mind that your plant may not be my plant -- in fact, if you're buying a sub-system from me, that sub-system may be your plant, while to me it is my closed-loop system.

For the purposes of your control loops, for each controller the plant transfer function you're interested in is the one that describes the relationship between whatever plant input that your controller affects, and whatever plant output that is affected by your controller.

So, for example, one of your "plants" has a heater command as an input, and a temperature as an output. The other one (I presume) has a flow rate as an input, and a solution concentrate of the desired reactant as an output.

Keep in mind that if these two processes (temperature and concentration) are linked, so that each one affects the other, then you may not be able to design each PID controller independently. In such a case you'd first need to worry about whether the coupling is strong enough to be an issue, and then what to do about it (which would be an answer to a different question).

  • $\begingroup$ Thanks for replying. In my case, changing the temperature will change the concentration in the tank (indirectly). However, changing the concentration will not affect the temperature. Would it be reasonable to design the controllers independently of each other? (For the specific case I am modelling, I know how much the temperature changes over time and have therefore calculated the resulting change in the concentration. Therefore, the concentration controller will account for the effects caused by the temperature and will adjust the flow rate accordingly to give the desired concentration). $\endgroup$
    – Lin.1
    Jul 13 '19 at 18:22
  • $\begingroup$ Once you asked I realized that if the coupling is one way then you can do your controllers independently -- it's just if the coupling goes both ways that you run the risk of not stabilizing things. As it stands, changes in temperature will act as a disturbance on the concentration, and the concentration controller would eventually take care of that even if you weren't using a temperature feed-forward term. $\endgroup$
    – TimWescott
    Jul 14 '19 at 1:01

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