Continuous Casting Tutorial
The problem is that of continuous casting (described more fully in Section 2.3), where molten steel flows into a mold (at a rate controlled by a valve) which is open from above and below. Through cooling, the steel in the mold is transformed into a semi-solid state and the steel comes out in continuous slab. This is illustrated in Figure 2.2. This photo shows the continuous caster at BHP in Newcastle, Australia.
It is desirable to be able to control the level of the molten steel in the mold to prevent it from overflowing or emptying. We can control this level by adjusting the control valve, based on measurements of the casting speed and the valve position. Figure 2.4 and Figure 2.5 illustrate the model of the system and the controller implemented. For more details, see Section 2.3.
Java Applet Simulation
The JAVA applet below is a simulation of this model which allows you to alter the various system parameters and see the results. Edit the value for the controller gain K and the level of noise (set this to zero to remove noise completely). The set-point type can also be altered between square and sinusoidal. Note: you must press the "Update" button to see the results of your changes. The simulation can be stopped and restarted by pressing the start and stop buttons.
Now there are several things you should notice. For small controller gains (e.g. K = 1), the system does not respond very quickly, and is not very susceptible to noise. For larger controller gains (e.g. K = 5), the system responds more quickly, but is much more susceptible to noise. (Obviously, susceptibility to noise is not desirable, since in this case, the controller is working with an incorrect measurement (due to measurement noise).)
This immediately hints at a trade-off between response speed and noise sensitivity. At this point, you might ask whether or not this can be solved with a better controller (so that we can have both good noise rejection and fast response speed), or whether this is a fundamental constraint. The rest of the book is dedicated to answering this (and many other questions).