You are here : Control System Design - Index | Simulations | Rolling Mill | Part 5 ## Rolling Mill Tutorial - Part 5Before continuing, make sure you have read Section 21.11: Linear Optimal Filters. ## ObserversTo estimate roll eccentricity, we view the output of the BISRA gauge
(which is
The output of this "system" is simply
for this system to estimate the state variables of the system:
The closed loop characteristic polynomial of this observer is
and using this equation with the desired characteristic polynomial, we
can place the observer poles at the desired locations. Alternatively, we
can use the Kalman filter equation to find the optimal Once we have this estimate of eccentricity (i.e. the estimated
To improve performance further, we then emulate disturbance feedforward
by subtracting the estimated eccentricity from the controller output This leads us to the following model for the closed loop system:
## Java Applet SimulationThe JAVA applet below is a simulation of the above system. The control
parameters have been chosen as k
= 200. The graph has a vertical scale of 0.1mm per division and as in the
previous simulation, the horizontal scale of the graph can be altered by
the user. It shows the set-point (the blue trace), the actual exit
thickness _{i}h (the green trace) and the estimated eccentricity signal
centred around 0.6mm (the red trace). Normally, the eccentricity is
centred around 0, but the plot of it was shifted because the vertical axis
of the graph is from 0 to 0.8.Pressing the "Change Parameters" button allows you to change
the same parameters as in the previous simulation, plus the amplitude of
the eccentricity signal and the observer gain matrix
This simulation shows that with the observer, the effect of roll
ecentricity is vastly reduced. In fact, for an eccentricity of 0.03, the
effect on the output is 0.0024, which represents a 92% reduction, which is
quite respectable considering the uncontrolled system performs a 66%
reduction. The effect of the eccentricity signal could only be zero if (1)
we had an always perfect estimate of eccentricity and (2) we could
subtract the estimated eccentricity directly from You may have observed the oscillation in both the set-point response and the disturbance response. This is due to the inaccuracies of the eccentricity estimation at these points (a fact easily observed from the graph of estimated eccentricity). The observer will see a change in its input signal, and will take some small amount of time to correct for this. As we have seen with the progression of these simulations, as we delve deeper into the control problem, we can achieve better performance using more sophisticated methods from control science. However, with each solution comes a new limit on performance (which is better than the previous limit), and hence a new problem to be solved. As you may have guessed, the Kalman filter solution (allowing increased system bandwidth) is by no means the final solution - there exists a phenomenon known as the "hold-up effect" which prevents the system from achieving the promised 10ms response time. This is addressed (particularly in relation to reversing mills - photo) in Section 9.8 (page 242) of the book. Even after this problem is solved, there are further, more complex ones awaiting. This concludes the interactive demonstration of rolling mill control. |