You are here : Control System Design - Index | Simulations | Rolling Mill | Part 1 ## Rolling Mill Tutorial - Part 1Before continuing, make sure you have read Chapter 5. ## System ModelThe exit thickness
Another equation for force is
Combining these two gives
Usually, we find that and The problem is that the exit thickness This leads us to the following model for the closed loop system:
The controller is
## Java Applet SimulationThe JAVA applet below is a simulation of the above system. The control
parameters have been chosen as k
= 2.5 to provide a reasonable response. The graph has a vertical scale of
0.1mm per division and a horizontal scale of 2 seconds per division. It
shows the set-point (the blue trace), the actual exit thickness _{i}h
(the green trace) and the measured (delayed) exit thickness h
(the red trace)._{m}There is also a 10 ms time constant associated with changing the screw
position Pressing the "Change Parameters" button allows you to change
the set point, the input thickness k and the amount of measurement noise in the
system. It is not possible to have a set point larger than the input
thickness, neither of which may be negative. When you change the input
thickness, the animation shows the "disturbance" approaching,
and it only takes effect when it reaches the rolls. Try experimenting with
these parameters.
_{i}
You will notice that it is not possible to produce a good stable response due to the presence of the time delay. If you are wondering about the sinusoidal component in the output, then have patience - we'll come to that shortly. Next, we try some more advanced control ideas on this system to try and work around this time delay. |