Abstract
We have established the big advantage of introducing Pontryagin's Maximum Principle into an optimal gauge control system for cold rolling mill.
Automatic gauge control (AGC) for cold rolling mills is said to have been perfected for many years. But recently, we have a new possibility of improving the system with the aid of developing digital computers, high performance control devices and many highly acculate sensors.
In this paper, the optimal control theory is applied to the electro-hydraulic screw down device controller which contributes to the response time of the Sendzimir mill AGC system. The dynamics of the electro-hydraulic screw down system can be sufficiently approximated as the second order system which is constructed by the combination of the servo-valve and the hydraulic screwdown cylinder. By use of the Maximum Principle, a time minimum control of this system can be realized by the Bang-Bang control, which has one switching point at maximum.
We have made further attempts to eliminate logarithmic and other complicated caluculations and reduce the amount of steps in the program. A suboptimal control has been developed and adopted into the No. 3 ZM of Hikari Works Nippon Steel Corporation. This system extremely simplifies the control's algorithm while keeping the quick response time.
The improvement has been such that the response time is two to five times shorter when it is compared with that in a conventional feed back control systems. It is typical of an open loop system that an accuracy of system modelling directly infuluences the performance of control. So the parameter error must be kept within a few percent.
As result of practical operation, this suboptimal control system was proven to be very useful in improving the response and accuracy of the AGC system.
