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Research in control design on the basis of identified models has lead to many iterative algorithms where performance weights in a control objective function are determined a-priori and remain fixed in order to evaluate performance improvement during iterations. This paper considers the case where performance weights are adjusted in iterative identification and control schemes where performance robustness is maintained during each iteration to yield a cautious control design. In order to adjust performance weights, a nominal model along with uncertainty description obtained from a system identification procedure are used to adjust the performance weighting function conjointly with robust control synthesis. A framework is developed for measuring performance comparison between iterations which allows adjustment of the performance weights during the iterative cautious control design.

This paper presents a method of finding a control relevant, low-order weighting filter that over bounds the uncertainty variations in measured frequency domain data. Frequency response measurements of hard disk drive actuators are used to model manufacturing and mounting variation. A polynomial positivity condition is use to guarantee that a minimal phase representation of the uncertainty that is found and linear constraints in the frequency domain are used to bound the magnitude of uncertainty model. The positivity condition can be formulated as a linear matrix inequality and linear constraints are used to shape the filter. Manufacturing and mounting variations in hard disk drives are modeled as a multiplicative uncertainty and a low-order over bound is found from data on a finite grid. This application compares a linear programming based methods for finding uncertainty models with the purpose of designing a robust controller.