This is really pathetic. I know I should know this but for the life of me I cannot remember how to do this.
Here's my (simplified) problem:
I have an stirred tank filled with water. In the tank I have a heating coil. When I switch on the coil the water in the tank heats up. The heating of the water can be characterised by a transfer function (I'm ignoring lag-times for simplicity's sake). When I switch off the coil the water will start to cool down. However, due to the insulation of the tank, the cooling process is remarkably slower. So, the cooling can be characterised by another transfer function.
Let's say that the heating process is characterised by 1/(15s+1) and the cooling is characterised by 1/(230s+1).
Now, I want to make a model of this tank and ultimately put it in a control loop using a PID controller. To model this I use MatLab/Simulink). How can I model this system? I can't figure out how to connect the two transfer functions. When I put the blocks in serial order then the slower block will also slowdown the heating up and not just the cooling down.
How should I place these blocks in order to get a good representation of the physical system?