Spectral over-bounding of frequency data for modeling product variability in hard disk drive actuators

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.