Characterizing Frequency Response of a Multirate System

Abstract

Frequency response is characterized for mechanical components of a multirate system operating in a closed-loop environment. A disturbance is injected at the frequency of interest and at each of the alias frequencies thereof as an input into the multirate system, and a matrix equation composed of resulting measurements of the response of the multirate system is solved to compute the frequency response at the frequency of interest and at each of the alias frequencies. The resulting frequency response can be used to synthesize the transfer function of the entire system, which allows simulation and evaluation of the relative performance of multiple controller designs without the need for further frequency response measurements.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS[0001]This application is a divisional of co-pending U.S. patent application Ser. No. 12 / 201,915, filed Aug. 29, 2008, entitled: CHARACTERIZING FREQUENCY RESPONSE OF A MULTIRATE SYSTEM, the contents of which is herein incorporated by reference.BACKGROUND OF THE INVENTION[0002]1. Field of the Invention[0003]Embodiments of the present invention relate generally to magnetic disk drives and, more particularly, to characterizing the frequency response of multirate systems, such as magnetic disk drives.[0004]2. Description of the Related Art[0005]In the vernacular of feedback control systems, a conventional hard disk drive (HDD) has a closed-loop servo control system comprising a “plant” with one or more moveable elements, e.g., a spindle motor, magnetic disk, and actuator assembly, and a servo controller for driving the moveable elements. Multirate controllers, which generate two or more corrections for each position measurement, are one type of ser...

AI Technical Summary

Benefits of technology

[0011]In one or more embodiments of the invention, frequency response is characterized for mechanical components of a multirate system operating in a closed-loop environment. A disturbance is injected at the frequency of interest and at each of the alias frequencies thereof, and a matrix equation composed of the resulting measurements is solved to compute the frequency response at the frequency of interest and at each of the alias frequencies. The resulting frequency response is then used to synthesize the transfer function of the entire system, which allows simulation and evaluation of the relative performance of multiple controller designs without the need for further frequency response measurements.

[0013]A method for selecting a multirate system controller from multiple candidate controller designs, according to an embodiment of the invention, includes the steps of determining a frequency response of the multirate system, modeling a frequency response of each candidate controller design, determining effectiveness of each candidate controller design using the frequency response of the multirate system and the frequency response of the candidate controller design, and selecting a candidate controller design as the multirate system controller based on the effectiveness of the candidate controller designs.

Problems solved by technology

Due to the nature of digital control systems, however, aliasing of the actual mechanical response of the plant occurs.

According to Shannon's sampling theorem, aliasing makes it impossible to recover the information lost during digital conversion if the sampling frequency is less than half the maximum frequency present in the signal.

Because the frequency response measurements of an HDD plant take place in a closed-loop environment, both the mechanical resonances and the alias components are fed back through the closed-loop control system being measured, thereby confounding the alias components with the real mechanical resonances of the system and rendering the resultant characterization of the frequency response of the system inaccurate at best.

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