Due to a lack of interest I am not going to pursue this topic any further unless there are questions.
I have a bunch of simulations done for one and two tanks.
http://deltamotion.com/peter/Mathcad/TwoTanks/
I concentrated on two tanks because that is more interesting ( difficult ). Also, I didn't bother with controlling tanks levels when the pump controls the out-flow because that is trivial.
If you are interested you will have to download the pdf files and look for the simple ones first and then look for the more difficult ones.
My general approach is to first write the differential equations. You don't understand the system until you can do that. I would give no student a passing grade without being able to write the differential equations.
At first I use the concept of time constants however, there are no real time constants in tank level control. Instead you must think of the instantaneous time 'constant' which is the something divided by the rate of change something. In this case it is the level divided by the rate of change in the level. The time 'constant' can and will vary in many applications and it will in tank level control because the flow through the valve or orifice on the output is not proportional to the level/pressure and the area of the tank may also change. These are all things that I don't see mentioned in the discussions here but they are real problems. Obviously the controller gains must change as the time constant or the gain changes yet no one considers that. Eventually I had to substitute flows and tank areas as a function of level for the time 'constants'.
In my more extreme examples I show how to change the controller gains on-the-fly as the level changes due to level set point changes, tank area changes and external water being poured into the tanks. Yes, this is extreme overkill for this application but the techniques are valid and should be mastered so can be applied to more difficult applications.
Sure you can get by without knowing all of this but if you are designing a system you need to be able to simulate the design and how it will be controlled. You need to know how tall to make the tanks so they don't overflow.
I made these for a student that had this problem as a class project. His teacher didn't even know if the level in the second tank can be controlled. His teacher wasn't qualified to teach the class in my opinion. Many suggested very simple solutions that would have worked but that isn't the point. You don't go to college just to tweak gains. A monkey can do that. You go to college to learn advanced techniques on simple systems so these techniques can be applied on more complicated systems in the future.
If you have questions ask but I will not try to make a series of lessons out of this topic.
