Tuning controller parameters for mass-produced hard disk drives is an iterative process. The controller needs to achieve desired performance and to provide sufficient robustness against disturbance and plant variation (we are designing a controller for millions of drives!). However, controller is conventionally designed in frequency-domain. Its time-domain performance index, Position Error Signal (PES), is then evaluated on hundreds of prototype drives and/or time-domain simulation tools. In the next cycle, controller is re-optimized based on the frequency-domain criteria that are adjusted according to the previous assessment of PES.

Apparently, it is much more efficient to directly include the PES prediction for a large population of drives in the optimization loop. The difficulty of doing this is that we do lack a good model that not only describes the characteristics of a family of drives but also requires little calculation efforts in PES projection.

We propose a new way to model the contributors of Position Error Signals (PESs) measured from multiple drives. Once the contributing components of PES are identified for each drive, a set of random variables are used to describe the power spectral of the contributors. Statistical analyses are applied to these random variables. This statistical model is used in a controller design tool to synthesize two time-domain performance indexes, average performance mean(var(PES)) and performance robustness var(var(PES)) in less than 0.1s (Matlab, PIII500). This model makes it possible to directly optimize the controller towards PES minimization for a family of drives.