Fitting Discrete-Time Models to Frequency Responses for Systems With Transport Delay

2011 ◽  
Author(s):  
Jeffrey A. Butterworth ◽  
Lucy Y. Pao ◽  
Daniel Y. Abramovitch
Keyword(s):  
Frequency Response ◽  
Discrete Time ◽  
Response Functions ◽  
Time Model ◽  
Frequency Response Functions ◽  
Transport Delay ◽  
Discrete Time Model ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Discrete Time Models

Fitting discrete-time models to frequency-response functions without addressing existing transport delay can yield higher-order models including additional non-physical nonminimum-phase (NMP) zeros beyond those that may appear as a result of sampling. These NMP zeros can be attributed to a discrete-time representation of a Pade´ approximation to account for the transport delay [1, 2]. Here, we explore this idea in greater detail and this discussion motivates the main contribution of this paper, the presentation of a procedure for fitting a discrete-time model to experimentally measured frequency response data. The appearance of NMP zeros in a system model can complicate controller design and limits the desired closed-loop performance. This discrete-time model-fitting procedure presents a technique that will help yield a model that reflects the measured frequency-response functions accurately, while minimizing the presence of non-physical NMP zeros. The key benefit being that, with respect to previous model fits, it may be possible to eliminate all NMP zeros in the discrete-time model. In the case of model-inverse-based control design, this will allow the stable inversion of the model without the use of approximation methods to account for NMP zeros.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

Detection of Local Damage of Flexural Member Using Measured Frequency Response Functions

2018 ◽  
Vol 23 (No 3, September 2018) ◽  
pp. 314-320
Author(s):  
Eun-Taik Lee ◽  
Hee-Chang Eun
Keyword(s):  
Damage Detection ◽  
Frequency Response ◽  
Damage Index ◽  
External Noise ◽  
Local Damage ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Proper Orthogonal

Measurements by sensors provide inaccurate information, including external noises. This study considers a method to reduce the influence of the external noise, and it presents a method to detect local damage transforming the measured frequency response functions (FRFs) to reduce the influence of the external noise. This study is conducted by collecting the FRFs in the first resonance frequency range from the responses in the frequency domain, taking the mean values at two adjacent nodes, and transforming the results to the proper orthogonal decomposition (POD). A damage detection method is provided. The curvature of the proper orthogonal mode (POM) corresponding to the first proper orthogonal value (POV) is utilized as the damage index to indicate the damage region. A numerical experiment and a floor test of truss bridge illustrate the validity of the proposed method for damage detection.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 1: Theory

1998 ◽  
Vol 120 (2) ◽  
pp. 503-508 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Component Mode Synthesis ◽  
New Method ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Experimental Implementation ◽  
Measured Frequency Response ◽  
Expansion Coefficients ◽  
Theoretical Developments

This paper presents a new method to calculate the so-called Craig-Bampton component mode synthesis (CMS) matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered. Experimental implementation of the method requires estimating the modal parameters corresponding to the measured free boundary modes and the Maclaurin series expansion coefficients corresponding to the omitted modes. Theoretical developments are presented in the present paper, Part 1. The performance of the new method is then demonstrated in Part 2 (Morgan et al., 1998) by comparison of experiment and analysis for a simple two-beam system.

Using Sherman–Morrison theory to remove the coupled effects of multi-transducers in vibration test

2018 ◽  
Vol 233 (4) ◽  
pp. 1364-1376 ◽  
Author(s):  
Rui Zhu ◽  
Qingguo Fei ◽  
Dong Jiang ◽  
Xiaochen Hang
Keyword(s):  
Frequency Response ◽  
Mass Loading ◽  
Response Functions ◽  
Modal Parameter ◽  
Mass System ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Target Values ◽  
Measured Frequency Response ◽  
The Relationship

Modal parameter identification is adversely affected by the mass loading of the transducer in experiments, especially when multi-transducers are arranged on the lightweight structure. In order to remove the coupling effects of transducers on each measurement point, a hierarchical multi-transducers eliminations method based on Sherman–Morrison theory is investigated. The method consists of two steps: (1) Decomposition: multiple elimination is decomposed into multi-levels, the relationship of the frequency response functions between each level is illustrated in the tree diagram; (2) Elimination: according to the relationship between each level, the measured frequency response functions are modified level by level. Numerical simulation is conducted by employing a three-degrees-of-freedom spring-mass system and the robustness is verified in the noise case. Experimental investigations are undertaken by employing a lightweight cantilever beam: Laser Doppler vibrometer is adopted to obtain measured frequency response functions without transducer mass loading effect, which are regarded as the target data. The initial frequency response functions are obtained in the case, in which multi-accelerometers are arranged and the effects should be removed. The result shows that the method can effectively decouple the frequency response functions due to transducers. In the elimination process, it is necessary to delete duplicate information (frequency response functions), which can greatly reduce the amount of calculation. And the effects of multi-transducers mass can be removed and the corrected frequency response functions are in quite good agreement with the target values.

Sign in / Sign up

Export Citation Format

Share Document