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Please help me to find related topics/books for this problem:

enter image description here For example, assume we have a water heater, and a tank of water. We can design a controller to heat the water in the tank and keep it in a certain temperature. This can be achieved by a bang-bang controller/PID controller.

If we want to add a new controller to add water or drain water from the tank, and the new controller's goal is maybe modify the tank water level, how to make sure the first controller can still perform well?

Alex
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  • what does "perform well" mean to you? – Rollen S. D'Souza Jan 04 '24 at 00:45
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    @RollenS.D'Souza For example, the first controller performs well if it can keep the tank temperature within [T-dt, T+dt], where T and dt are constants. And any state outside this range can be adjusted back to the [T-dt, T+dt] range within 5 minutes.

    One example of break the system is to add a lot of cold water into the tank, which causes the first controller cannot adjust the temperature in 5 minutes.

     – Alex Jan 04 '24 at 05:21
  • @RollenS.D'Souza I am wondering is there a well-studied model for this problem(adding a new controller to a system with a controller)? – Alex Jan 04 '24 at 05:22
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    The amount of water in the tank changes the total heat capacity of the tank, and thus time constant while heating. So if you limit how much the water level changes, then the heater controller should still perform well. If you want allow for larger changes in water level one could look at gain scheduling or non-linear control for the temperature controller. – Kwin van der Veen Jan 04 '24 at 08:08
  • The amount of energy needed to heat the water in the tank will depend on the amount of water (ie the volume). So changing this volume during the heating/cooling in order to adjust the water level will obviously have some coupling effect to the heating loop, so the two control loops are not independent. So, depending on the severeness of the coupling, "adding a new controller" might break the old controller in the sense that it works well with constant water level but doesn't work anymore with a time varying level. A MIMO design (taking the coupling into account) could solve this. – SampleTime Jan 04 '24 at 08:11

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