LQG controllers for state-space systems with pure transport delays: Application to hot strip mills

The design of LQG stochastic optimal tracking and regulating systems is considered for continuous-time systems with different time-delays in different paths. The state equation based controllers for both tracking and regulating systems include a Kalman predictor and state-estimate feedback. A form of the separation principle holds for linear systems containing transport delays on inputs and outputs. The system is assumed to be represented in state equation form and may be unstable, non-minimum phase and nonsquare. The process and measuring system noise terms may be correlated and be coloured or white. The linear quadratic performance criterion to be minimised includes a cross-product weighting term. It is shown that for certain classes of system the optimal controller can be implemented using a combination of finite dimensional and pure delay elements. The structure of the optimal controller is similar to that of a Smith predictor. The control of the thickness of strip in rolling mills is then considered. This was the physical problem which motivated the design study. The transport-delay occurs because the X-ray thickness gauge measurement system is some distance from the roll gap which causes the reduction. The engineering design issues are explored and it is shown that the controller structure proposed is effective in thickness profile regulation. (C) 1998 Elsevier Science Ltd. All rights reserved.