Frequency Response Function Analysis for Damped Natural Frequency Identification
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Solution Overview
Problem
Existing methods for determining damped natural frequencies of dynamic systems, especially with limited measurement locations, are inefficient and prone to misidentification due to noise and non-linear effects, which is critical for automating control loop tuning in motion control systems.
Innovation Solution
A method that smooths the frequency response function, identifies candidate frequencies by analyzing the derivative's sign changes, and applies stricter criteria to eliminate less significant candidates, using a combination of amplitude and phase analysis to differentiate between poles and zeros, while reducing noise effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing least squares methods are used to fit FRF measurements, then a complete model can be obtained, but the method fails when the number of measurement locations is limited
Solution Approach 1:
The patent segments the frequency identification process into two distinct phases: first identifying candidate frequencies using derivative sign changes (amplitude extrema), then filtering these candidates using phase analysis and optimization. This segmentation allows accurate frequency identification even with limited measurements by separating the frequency detection task from the parameter estimation task.
Solution Approach 2:
The patent performs preliminary identification of candidate frequencies by detecting where the derivative of the amplitude function changes sign, before applying the full least squares optimization. This preliminary action narrows down the search space to only relevant frequency candidates, making the subsequent optimization more robust and effective even with limited measurement data.
2Extent of automation
If heuristic methods like Moser's approach are used for servo tuning, then the process can be automated, but the method occasionally fails to identify poles or zeros that affect controller tuning
Solution Approach 1:
The patent incorporates feedback through an iterative optimization process that minimizes the least squared error between the original FRF and the synthesized FRF from identified poles and zeros. This feedback mechanism continuously refines the identification, ensuring that all significant poles and zeros affecting controller tuning are captured, thereby improving reliability while maintaining automation.
Solution Approach 2:
The patent employs dynamic, adaptive criteria for accepting or rejecting frequency candidates based on phase analysis and optimization results. Rather than using fixed heuristic rules, the method dynamically adjusts its acceptance criteria based on the actual FRF characteristics, ensuring reliable identification of all poles and zeros that impact controller performance.
3Productivity
If standard FRF analysis methods are used, then frequency identification can be performed, but noise and non-linear effects cause false pole identification
Solution Approach 1:
The patent introduces phase analysis as an intermediary verification step between frequency candidate identification and final acceptance. By using phase change direction as a mediator to validate amplitude-based candidates, the method effectively filters out false positives caused by noise and non-linear effects while maintaining rapid identification throughput.
Solution Approach 2:
The patent changes the analysis parameter from purely amplitude-based to a combined amplitude-phase approach. By monitoring both the magnitude and phase characteristics of FRF at candidate frequencies, the method distinguishes true system poles from noise-induced artifacts, significantly improving noise immunity without sacrificing identification speed.
Data Source
AI summary
The present invention is a novel device, system, and method for determining the damped natural frequencies of a dynamic system whose characteristics are available in the form of a “frequency response function” FRF. According to an exemplary embodiment of the present invention, the method identifies the dampened natural frequencies associated with the poles and zeros of a transfer function. The method is especially useful for analysis of measurements that contain some degree of contamination due to noise or non-linear effects. It is based on a set of rules that may be more successful than a direct approach based on a least squares criteria.