Mixed-objective optimization of a track-following controller using linear matrix inequalities

This work describes a design method for track-following controllers in data storage drives using mixed-objective optimization. Stability and performance requirements on the track following controller are established using norm conditions, which are converted to linear matrix inequalities (LMIs). The minimization of the position error in the root-mean-square sense is shown to be an H₂ norm minimization problem, whereas the vibration rejection requirements are expressed as H₂ or H_∞ norm constraints. The robust stability requirement is enforced by an H_∞ norm constraint. The mixed-norm problem is converted into a constrained minimization problem in LMIs, which is solved by convex optimization algorithms. The controller is designed directly in the discrete time domain to avoid typical degradation caused by continuous-time to discrete-time conversion. The proposed controller is implemented and tested on production hard disk drives. Experiments show that the proposed controller reduces the position error by 7%-11% while maintaining comparable stability margins and vibration rejection capability compared with the conventional controllers.