Multirate System Frequency Response Characterization
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Solution Overview
Problem
Conventional methods for characterizing the frequency response of hard disk drives (HDDs) are limited by aliasing issues at frequencies above the Nyquist frequency, making it impossible to accurately identify higher frequency dynamics and resonant modes, which are crucial for designing effective servo controllers.
Innovation Solution
A method is introduced to characterize the frequency response of multirate systems by injecting disturbances at frequencies of interest and their alias frequencies, solving a matrix equation to compute the frequency response, allowing for the synthesis of the transfer function and evaluation of controller designs without additional measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional frequency response characterization methods are used, then measurement simplicity is maintained, but accuracy deteriorates at frequencies above the Nyquist frequency due to aliasing
Solution Approach 1:
The frequency response characterization is divided into multiple measurement components: injecting disturbances at both the target frequency and its alias frequencies, then separating the results through matrix equation solving. This segmentation allows accurate measurement beyond Nyquist frequency by treating aliasing as a measurable phenomenon rather than an error to be avoided.
Solution Approach 2:
The patent introduces an intermediary mathematical model (matrix equation) that relates the measured responses at alias frequencies to the unknown frequency response at the target frequency. This intermediary model enables indirect measurement of high-frequency characteristics through low-frequency aliasing components.
2Measurement precision
If sampling frequency is increased to avoid aliasing, then measurement accuracy improves, but system complexity and cost increase due to fixed disk rotation speed and sector configuration
Solution Approach 1:
The patent converts the harmful aliasing effect into a useful measurement tool. By injecting disturbances at alias frequencies and measuring the responses, the system can actually extract accurate frequency response information beyond the Nyquist frequency. The aliasing that was previously considered a measurement error becomes the primary mechanism for accessing high-frequency system characteristics.
3Reliability
If closed-loop frequency response is measured, then system performance evaluation is enabled, but measurement accuracy deteriorates due to confounding alias components with real mechanical resonances
Solution Approach 1:
The measurement process is segmented into multiple frequency points including both the target frequency and its aliases. The matrix equation then segments the mixed measurements into separate components, allowing the real mechanical resonances to be isolated from the alias components even in closed-loop conditions.
Solution Approach 2:
The patent uses feedback from multiple frequency measurements (including alias frequencies) to solve for the frequency response at the target frequency. The measured responses at alias frequencies provide feedback information that, when processed through the matrix equation, reveals the true system characteristics without the confounding effects of aliasing.
Data Source
AI summary
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.