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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01 Aug 1974
TL;DR: Analytical modeling of communication receivers to account for their nonlinear response to multiple input signals is discussed, based on the application of the Wiener-Volterra analysis of nonlinear functionals.
Abstract: Analytical modeling of communication receivers to account for their nonlinear response to multiple input signals is discussed. The method is based on the application of the Wiener-Volterra analysis of nonlinear functionals. The derived analytical relations were embodied in a computer program which provides nonlinear transfer functions of large circuits specified by their parameters. This method was applied to the prediction of behavior of communication receivers in the presence of interference. Examples illustrate the method and demonstrate its validity in the small-signal region.
425 citations
TL;DR: A modified prototype repetitive controller is applied as a plug-in module to a Winchester disk drive with a preexisting analog feedback controller to demonstrate its efficacy in the reduction of this periodic component.
Abstract: Tracking errors in disk drive systems have a significant repetitive component that is not explicitly taken into account in conventional servo controllers. A modified prototype repetitive controller is applied as a plug-in module to a Winchester disk drive with a preexisting analog feedback controller to demonstrate its efficacy in the reduction of this periodic component. A review of the Winchester disk drive system is included. >
317 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, Hillerstr¨om, 1996, Chew, & Tomizuka, 1990 ]....
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TL;DR: A robust repetitive controller structure is proposed that uses multiple memory-loops in a certain feedback configuration, such that small changes in period-time do not diminish the disturbance rejection properties.
313 citations
"Measuring the higher order sinusoid..." refers background in this paper
...The repetitive controller M is an addon device which generates infinite amplification at the harmonics of the excitation frequency ω0 [Steinbuch, 2002]....
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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 article, the authors proposed a data-driven model of stiction, which can be directly related to real valves in the process industry and validated the simulation results generated using the proposed model with that from a physical model of the valve.
288 citations