Mixed-objective optimization of track-following controllers using linear matrix inequalities

In this paper, we present a mixed-objective optimization method for the track-following controller design in hard disk drives using linear matrix inequalities. The objective of achieving minimal position error in the presence of operational vibration and model variations is formulated into a set of constrained l-norm minimization problems. The minimization of the position error in the root-mean-square sense is formulated as an H₂ norm minimization while the robustness to the dynamics variation is treated as an H_∞ norm constraint. The external vibration and bias rejection requirement is treated as either an H₂ or H_∞ norm constraint. The optimization problems are treated purely in the discrete-time domain to avoid any performance degradation involved with continuous-time to discrete-time conversion. The resulted LMIs are solved by convex optimization after being transformed into a set of synthesis LMIs. The proposed controller is implemented and tested on production disk drives with fixed-point DSP controllers. The test showed 7∼11% improvement in position error over the conventional track-following controllers while achieving the comparable robust stability and the vibration rejection capability.