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 selecting a multirate system controller from multiple candidate controller designs, comprising the steps of:
 (a) determining a frequency response of the multirate system;   (b) modeling a frequency response of each candidate controller design;   (c) determining effectiveness of each candidate controller design using the frequency response of the multirate system determined in step (a) and the frequency response of the candidate controller design determined in step (b); and   (d) selecting a candidate controller design as the multirate system controller based on results from step (c).   
     
     
         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 step of determining a frequency response of the multirate system includes:
 (a1) selecting a frequency of interest;   (a2) injecting a first disturbance at the frequency of interest as an input into a multirate system;   (a3) measuring a response of the multirate system after the step (a2) of injecting;   (a4) injecting a second disturbance at an alias frequency of the frequency of interest as an input into a multirate system;   (a5) measuring a response of the multirate system after the step (a4) of injecting; and   (a6) repeating steps (a1) through (a5) for different frequencies of interest.   
     
     
         5 . The method according to  claim 4 , wherein steps (a1) through (a5) are repeated for hundreds of different frequencies of interest. 
     
     
         6 . The method according to  claim 5 , wherein the different frequencies of interest range from about 0 Hz to about the Nyquist frequency. 
     
     
         7 . The method according to  claim 4 , wherein the frequency of interest has more than one alias frequency and steps (a4) and (a5) are carried out separately for each of the alias frequencies.