Estimation Method of Unobservable Oscillations in Sampled-Data Positioning Systems

Abstract

Unobservable oscillations of the controlled variable of sampled-data positioning control systems may degrade the performance and reliability of mechatronic products. For example, a control input in the sampled-data control system can easily excite transient vibrations of mechanical resonances around the sampling frequency. However, these vibrations are difficult to measure in the sampled-data control system. The degree to which these oscillations are unobservable or observable depends on the sampling frequency, oscillation frequency, and the initial phase of the oscillations. This paper shows the relationship between the sampling frequency, oscillation frequency, and the initial phase of the oscillations. As a result, two indexes of an unobservable position are proposed with maximum and root-mean-square amplitudes to estimate the effects of the unobservable oscillations of mechanical resonances in positioning control systems. These indexes show that the sampling frequency and number of samples of measurement data for estimating the unobservable magnitude of oscillations are important parameters that designers must choose carefully. To demonstrate the use of the proposed indexes, unobservable magnitudes of oscillations are analyzed for a head-positioning control system in a hard disk drive.