You are here : Control System Design - Index | Simulations | Tank Level | Part 1 ## Tank Level Tutorial - Part 1Before continuing, make sure you have read Chapter 7 and Chapter 19. ## System ModelBefore we continue with the observer design, we must make a model of the system. The height of tank 1 can be described by the equation
Similarly,
The flow between the two tanks can be approximated by the free fall velocity for the difference in height between the two tanks.
Now, if we measure the heights of the tanks in % (where 0% is empty
and 100% is full), we can convert the flow rates into equivalent values
in % per second (where
where
We can then choose to linearise this model for a nominal steady state height difference (or operating point). Let
then
since
then
This yields the following linear model
where
Since we are assuming that
to estimate the value of
so we can choose the observer poles which gives us values for The equation for the observed system is then
Where
is the measured value of .
Here we model
as follows: where represents measured noise. Alternatively, we could use the non-linear model in our observer to attempt to get better performance:
## Java Applet SimulationThe JAVA applet below is a simulation of the above tank system. The purpose of this simulation is to investigate the difference between the linear and non-linear observers. Thus, we will not concern ourselves with the controller at this stage. The graph has a vertical scale of 25% per division and a horizontal
scale of 10 sec per division. It shows the set-point (the orange trace),
the actual h
(the red trace) and the actual _{1}h (the green trace).
_{2}Pressing the "Change Parameters" button allows you to
change the set point type, the measurement noise level, the type of
observer (linear or non-linear) and the observer gain matrix
By pushing the observer poles out towards negative infinity, we get a faster response from the observer, but we also change the sensitivity to modelling errors (particularly relevant in the linear observer) and measurement noise. By now, this should be a familiar trade-off. |