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.

1 . A method for determining performance of a controller for a disk drive, comprising the steps of:
 (a) determining a frequency response of the disk drive;   (b) modeling a frequency response of the controller; and   (c) determining effectiveness of the controller using the frequency response of the disk drive determined in step (a) and the frequency response of the controller determined in step (b),   wherein the frequency response of the disk drive is determined using frequency responses of the disk drive to multiple frequencies of interests and to one or more alias frequencies to each of the frequencies of interest.   
     
     
         2 . The method according to  claim 1 , wherein the effectiveness is determined based on factors including gain margin, phase margin, and vector margin. 
     
     
         3 . The method according to  claim 2 , wherein the effectiveness is determined at different operating conditions. 
     
     
         4 . The method according to  claim 1 , wherein the multiple frequencies of interest comprise hundreds of distinct frequencies. 
     
     
         5 . The method according to  claim 4 , wherein the multiple frequencies of interest range from about 0 Hz to about the Nyquist frequency. 
     
     
         6 . The method according to  claim 1 , wherein the controller includes a notch filter.