LQG controllers for unstable systems with transport delays: thickness control in rolling mills

The design of a LQG stochastic optimal regulating system is considered for a discrete-time system with a transport delay. The state equation based controller includes a Kalman predictor and state-estimate feedback. A form of the separation principle is invoked that applies to linear systems containing transport delays. The system is assumed to be represented in state equation form and may be unstable and nonminimum phase. The process and measurement system noise terms may be correlated and coloured or white. The control of the thickness of strip in rolling mills is then considered. The transport-delay occurs because the X-ray thickness gauge measurement is some distance from the roll gap which causes the reduction. Under some circumstances the mill can be an unstable system and it is demonstrated how the X-ray feedback controller can stabilise it