scholarly journals Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 7190
Author(s):  
Dominik Łuczak

Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.

Author(s):  
Ran Zhao ◽  
Chengying Xu

In this paper, we present a systematic modeling method of direct drive systems. Experiments are designed to decouple and model friction and force ripple separately, which are two major sources of tracking error. Three different optimization methods, least square method, nonlinear least square method and particle swarm optimization are used for parameter optimization. The analytical form of the model makes it easy to use in engineering practices. All results are obtained and verified experimentally. The method presented in this paper can also be used to model other mechanical systems.


Author(s):  
A. F. Beardon

AbstractThe unwinding number of a complex number was introduced to process automatic computations involving complex numbers and multi-valued complex functions, and has been successfully applied to computations involving branches of the Lambert W function. In this partly expository note we discuss the unwinding number from a purely topological perspective, and link it to the classical winding number of a curve in the complex plane. We also use the unwinding number to give a representation of the branches $$W_k$$ W k of the Lambert W function as a line integral.


Radio Science ◽  
2008 ◽  
Vol 43 (4) ◽  
pp. n/a-n/a
Author(s):  
Jie Yang ◽  
Mary C. Taylor ◽  
Yu Zhang ◽  
Tapan K. Sarkar

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dongju Chen ◽  
Shuai Zhou ◽  
Lihua Dong ◽  
Jinwei Fan

This paper presents a new identification method to identify the main errors of the machine tool in time-frequency domain. The low- and high-frequency signals of the workpiece surface are decomposed based on the Daubechies wavelet transform. With power spectral density analysis, the main features of the high-frequency signal corresponding to the imbalance of the spindle system are extracted from the surface topography of the workpiece in the frequency domain. With the cross-correlation analysis method, the relationship between the guideway error of the machine tool and the low-frequency signal of the surface topography is calculated in the time domain.


2021 ◽  
Vol 2010 (1) ◽  
pp. 012121
Author(s):  
Chuanyun Wang ◽  
Guowei Yang ◽  
Dongdong Sun ◽  
Jiankai Zuo ◽  
Ershen Wang

2021 ◽  
Vol 11 (17) ◽  
pp. 8236
Author(s):  
Le Zhang ◽  
Hongguang Ji ◽  
Liyuan Liu ◽  
Jiwei Zhao

To study the crack evolution law and failure precursory characteristics of deep granite rocks in the process of deformation and failure under high confining pressure, granite samples obtained from a depth of 1150 m are tested using a TAW-2000 triaxial hydraulic servo testing machine and a PCI-II acoustic emission monitoring system. Based on the stress–strain curve and IET function, the loading process of the sample is divided into five stages: crack closure, linear elastic deformation, microcrack generation and development, macroscopic fracture generation and energy surge, and post-peak failure. The evolution trend and fracture evolution law of the acoustic emission signal event interval function in different stages are analyzed. In particular, the signals with an amplitude greater than 85 dB, a peak frequency greater than 350 kHz, and a frequency centroid greater than 275 kHz are defined as the failure precursor signals before the rock reaches the peak stress. The defined precursor signal conditions agree well with the experimental results. The time–frequency analysis and wavelet packet decomposition of the precursor signal are performed on the extracted characteristic signal of the failure precursor. The results show that the time-domain signal is in the form of a continuous waveform, and the frequency-domain waveform has multi-peak coexistence that is mainly concentrated in the high-frequency region. The energy distribution obtained by the wavelet packet decomposition of the characteristic signal is verified with the frequency-domain waveform. The energy distribution of the signal is mainly concentrated in the 343.75–375 kHz frequency band, followed by the 281.25–312.5 kHz frequency band. The energy proportion of the high-frequency signal increases with the confining pressure.


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