Measuring the higher order sinusoidal input describing functions of a non-linear plant operating in feedback
TL;DR: In this article, two measuring techniques are presented for measuring the higher order sinusoidal input describing functions (HOSIDF) of a non-linear plant operating in feedback.
About: This article is published in Control Engineering Practice.The article was published on 2008-01-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Harmonic & Harmonics.
Citations
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Journal Article•
TL;DR: In this paper, a modification of the integrated friction model structure proposed by Swevers et al. called the Leuven model is presented, which allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function.
Abstract: This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.
288 citations
TL;DR: In this paper, a linear dynamic time-invariant model is identified to describe the relationship between the reference signal and the output of the system, and the power spectrum of the unmodeled disturbances are identified to generate uncertainty bounds on the estimated model.
Abstract: Linear system identification [1]?[4] is a basic step in modern control design approaches. Starting from experimental data, a linear dynamic time-invariant model is identified to describe the relationship between the reference signal and the output of the system. At the same time, the power spectrum of the unmodeled disturbances is identified to generate uncertainty bounds on the estimated model.
83 citations
TL;DR: A linear dynamic time-invariant model is identified to describe the relationship between the reference signal and the output of the system and the power spectrum of the unmodeled disturbances are identified to generate uncertainty bounds on the estimated model.
Abstract: This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be retrieved without a significant increase in the amount of measured data. 2) Next it is studied if it is safe to use a linear system identification approach, even if the presence of nonlinear distortions is detected. The properties of the linear system identification approach under these conditions are studied, and the reliability of the uncertainty bounds is checked. 3) Eventually, tools are provided to check how much can be gained if a nonlinear model were identified instead of a linear model.
Addressing these three questions forms the outline of this article. The possibilities and pitfalls of using a linear identification framework in the presence of nonlinear distortions will be discussed and illustrated on lab-scale and industrial examples.
In this article, the focus is on nonparametric and parametric black box identification methods, however the results might also be useful for physical modeling methods. Knowing the actual nonlinear distortion level can help to choose the required level of detail that is needed in the physical model. This will strongly influence the modeling effort. Also, in this case, significant time can be saved if it is known from experiments that the system behaves almost linearly. The converse is also true. If the experiments show that some (sub-)systems are highly nonlinear, it helps to focus the physical modeling effort on these critical elements.
61 citations
TL;DR: In this paper, a frequency domain based method for controller design for nonlinear systems is presented, which is applied to optimally design a feed forward friction compensator for an industrial motion stage in a transmission electron microscope.
50 citations
Additional excerpts
...Finally, the Higher Order Sinusoidal Input Describing Functions (HOSIDF) [16,18,26] are used to analyze nonlinear effects in the following....
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TL;DR: A mapping from the parameters defining the nonlinear and LTI dynamics to the output spectrum is derived, which allows analytic description and analysis of the corresponding higher order sinusoidal input describing functions.
29 citations
References
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TL;DR: In this paper, an extension to higher-order describing functions is realized by introducing the concept of the harmonics generator, which relates the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude of a sinusoidal excitation.
100 citations
TL;DR: The aim of this paper is to present an adaptive solution to suppression of vibrations that has its roots in repetitive control based on models of isolated frequencies rather than the commonly used delay model.
Abstract: The aim of this paper is to present an adaptive solution to suppression of vibrations. Adaptation is appropriate whenever the fundamental frequency is unknown or drifting, e.g., when the vibration is caused by a rotational machine with unknown rotational speed. The approach presented here has its roots in repetitive control based on models of isolated frequencies rather than the commonly used delay model. The relationship between different modeled frequencies is fixed by the model structure, and the fundamental frequency is obtained by gradient descent or Newton's method. To show the feasibility of this approach, it was used to reduce the vibrations on a lever that were caused by a motor with imbalance in its rotation. As an actuator, a standard loudspeaker was used, and the vibration was sensed by an accelerometer.
100 citations
"Measuring the higher order sinusoid..." refers methods in this paper
...Stability In order to successfully apply the memory loop as an add-on device under measurement conditions, overall system stability must be preserved [Tomizuka, Tsao, & Chew, 1988, Hillerström, 1996, Chew, & Tomizuka, 1990]....
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TL;DR: In this paper, the interpretation and properties of the non-linear frequency response functions are discussed and illustrated by example, and new methods of parametric spectral analysis for a wide class of nonlinear systems were introduced.
99 citations
15 Sep 1996
TL;DR: In this paper, the exact analysis of limit cycles caused by friction is presented, where necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles.
Abstract: This paper presents techniques that admit an exact analysis of limit cycles caused by friction. Necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles. There are two types of limit cycles, one where motion sticks for a time interval and another where the velocity is zero only at single time instants. The results are applied to an example with a resonant servo. Comparisons with describing function analysis are also made.
69 citations
18 May 1993
TL;DR: In this paper, a theoretical framework for the distortion generated by odd power nonlinearities when using multisine test signals for frequency domain identification is presented, and it is shown that the distortion is a function of the number of test harmonics, their harmonic values and their phases.
Abstract: The errors introduced into linear system identification by nonlinear distortions are examined. A theoretical framework is presented for the distortion generated by odd power nonlinearities when using multisine test signals for frequency domain identification. It is shown that the distortion is a function of the number of test harmonics, their harmonic values and their phases. An explanation of previously published practical results is then given. This leads to the definition of a novel class of signals, termed no interharmonic distortion (NID) multisines, with interesting properties. The application of NID multisines to system testing with a recently proposed method of compensating for nonlinearities is examined. This allows the identification of the linear system and the straightforward calculation of the coefficient of the nonlinear term. >
56 citations