This paper describes an optimization method for designing feedback systems subject to large parameter uncertainty. Following the design philosophy of the Quantitative Feedback Theory (Horowitz andSidi 1972, 1978) the objective is to minimize the magnitude of the open loop LOW) at high frequencies subject to: (a) low and intermediate-frequency bounds capturing the closed-loop robust-performance objectives; (b) a universal-frequency bound on LCjw) which limits the effects of disturbances; and (c) realization constraints on L(s) in the form of Bode's integral. This last relation is discretized at a number of frequencies and defines, together with ( a ) and (b), the overall set of linear constraints in a resulting linear programming optimization problem.

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SUMMARYA long established approximation, normally invoked in the development of classical rolling theory, is that the work roll-strip interface assumes a circular profile. Although valid for a wide range of practical rolling conditions, the approximation is definitely suspect for instance in the last and penultimate stand of a thin sheet tandem mill, and algorithms based on classical theory may fail to converge. This paper formulates the analysis of non-circular arc rolling conditions, and describes a new iterative procedure for computing solutions. In deriving the algorithm it is convenient to employ the formalism of functional analysis. The algorithm is of the 'hill climbing' variety, involving the calculation of suitable gradients.One notable feature is that the gradients have to be carefully defined with respect to the correct 'space', in order that physically inadmissible discontinuities are not introduced during the hill-climbing.Computed roll gap solutions sometimes display elastic deformation regions embedded within the normal plastic deformation zone. It is thought that this is the first time this possibility has been allowed for in the formulation, or solutions obtained exhibiting this feature.

The problem of tuning individual loops in a multivariable controller is investigated. It is shown how the performance of a specific loop relates to a row in the controller matrix. Several interpretations of this relation are given. An algorithm is also presented that estimates the model required for the tuning via a relay feedback experiment. The algorithm does not need any prior information about the system or the controller. The results are illustrated by an example.Qc 2012022

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