Rolling Mill Shape Control - Part 2
Before continuing, make sure you have read Chapter 14.
The previous simulations assumed that the spray valves could be opened infinitely, and also assumed that the sprays could somehow suck water back into the spray when required. Clearly, these are not realistic assumptions, since the valves have physical saturation levels.
The block diagram of the system with this actuator saturation in place is shown below:
The saturation can cause integrator windup in the PI controller, so we use the anti-windup controller from chapter 15. Note that C(s) is diagonal with the same entry on each diagonal. M-1 is non-dynamic and can be commuted with C(s). This gives the anti-windup arrangement shown below:
This controller form reduces the overshoot in the step response, but interferes with the decoupling, since the saturation occurs after the matrix inversion.
Java Applet Simulation
The JAVA applet below is a simulation of the saturated shape control system. It is almost identical to the previous simulation, except the decoupling mechanism is always enabled.
As before, pressing the "Change Parameters" button allows you to change the set point type, the PI controller parameters, and the amount of measurement noise in the shape meters. The anti-windup controller can be enabled or disabled through the check box. Also, the parameter can be altered to change the level of interactivity between the sprays. If you check the "Reset roll to default state" box, the roll shape will be reset to its (bumpy) initial shape. Try experimenting with these parameters.
The saturation of the spray valves interferes noticably with the decoupling. This suggests that a more sophisticated control strategy is needed to overcome these difficulties. The problem is that the saturation does not allow the decoupling matrix to work effectively. One method of overcoming this would be to scale the error for each PI controller, so that the controller output is never larger than the saturation limit. This ensures that the decoupling will work, since the valve saturation will have no effect on the control signal (since it is already within the saturation limits). However, such a control strategy is difficult to implement. This highlights the difficulties posed by non-linearities in MIMO systems.