Mixed Sensitivity Problem in Sampled-Data Positioning Control System

Abstract

We have developed an analysis and synthesis method for mixed-sensitivity problems in sampled-data positioning control systems. The method uses frequency responses of the controlled object and the digital controller for calculating the characteristics of the control system without complicated calculations involving matrices. Our proposed method indicates relationships between the sensitivity function and complementary sensitivity function for the mixed sensitivity problem in a sampled-data positioning control system. We also address the mixed sensitivity problem for multi-rate control systems that include an interpolator, a multi-rate filter, and a multi-rate hold. To show the validity of the proposed method, we conducted simulations and experiments on the sampled-data positioning control system of a head-positioning control system in a hard disk drive. These results show that control engineers should know the difference between the discrete-time control system and the sampled-data control system even for frequencies below the Nyquist frequency.

Robust track following in Hard Disk Drives with time delays: An infinite dimensional approach

“…Various robust control algorithms has been widely discussed for HDD servo design (see [4][5][6][17][18][19], to cite just a few contributions). Note that in track following mode, the HDD servo system needs to reject various disturbances such that the head can operate close enough to the track center.…”

“…Therefore, the main control objective is to optimize the servo control loop to compromise the rejection capability and model uncertainties. An applicable H ∞ control method in servo loop shaping is mixed sensitivity optimization [19,34], where the nominal performance (determined by performance weighting W 1 (s)) and robust stability (determined by uncertainty weighting W 2 (s)) can be optimized simultaneously: inf…”

“…Among the abundant research results on HDD servo algorithms, one of the central topics is the optimal robust loop shaping problem for HDD track following, which determines the servo bandwidth, attenuations of disturbance, and transient behaviors of head motions. Robust control theory has been widely investigated for HDD servo loop shaping [17,18], as well as other nano-positioning applications [19][20][21], where standard H ∞ control [17] and µ-synthesis [18] algorithms have been successfully developed. The problem is further explored in more recent publications.…”