Probabilistic robust approach for discrete multi-objective control of track-following servo systems in hard disk drives

This paper deals with the problem of different uncertainties in discrete time track following control of read/write head in hard disk drives (HDD). A multi-objective robust controller is designed which minimizes the worst case root mean square (RMS) value of the positioning error signal (PES) subject to the closed-loop stability in the presence of parametric and dynamic uncertainties. A sequential algorithm based on ellipsoid iteration is utilized to handle parametric uncertainty. Dynamic uncertainty is also represented as linear fractional transformation (LFT) and by the virtue of small gain theorem, the stability of closed-loop system is guaranteed. In this design, two sources of conservatism are avoided: embedding the original non-linear parametric uncertainty into affine structure (converting the original uncertain system into a polytopic uncertain system) and using a single Lyapunov matrix to test all the objectives. The resulting controller has much better track following performance compared to the classical robust approaches which tends to higher storage capacity of HDDs. Simulation as well as experimental results verify the effectiveness of the designed controller.