Hello,

I have the following system to control:
electric shower that I have two inputs of water, one hot and one cold. I have two servo motors to control a flow valve for each entry. They then mix in a chamber with an electrical resistance that heats the water to the desired temperature. The goal is to control the flow and temperature output.

actuators:
- Servo-motors that control flow of each water intake;
- Electrical resistance that heats water;

sensors:
- Temperature and flow in the output of the system;

I need a mathematical model of the system and any idea how to control the plant. Can anyone help me?

thank you

 

Which class are you doing this homework for, is it a senior level class or a junior level?

 

Sounds like a homework problem I set my students when I was teaching ...

Model is very simple and you shouldn't need to ask.

Consider mass balance - flow out = cold flow + hot flow

And energy balance - energy out = cold energy in + hot energy in

Since the water has a thermal heat capacity that is more or less constant over the range of interest, this last one simplifies quite a bit.

That should be more than enough hinting .. and don't forget to reference this e-mail in your report!

Cheers,
Bruce.