Effects of Extra Sinusoidal Inputs to Nonlinear Systems
01 Dec 1962-Journal of Basic Engineering (American Society of Mechanical Engineers Digital Collection)-Vol. 84, Iss: 4, pp 559-569
About: This article is published in Journal of Basic Engineering.The article was published on 1962-12-01. It has received 48 citations till now. The article focuses on the topics: Nonlinear system.
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TL;DR: Five existing methods for mitigating the effects of element mismatch are compared: physical level calibration, dynamic element matching, noise-shaping with digital calibration, large periodic high-frequency dithering, and large stochastic high-pass dithering.
Abstract: The performance of digital-to-analog converters is principally limited by errors in the output voltage levels. Such errors are known as element mismatch and are quantified by the integral non-linearity. Element mismatch limits the achievable accuracy and resolution in high-precision applications as it causes gain and offset errors, as well as harmonic distortion. In this article, five existing methods for mitigating the effects of element mismatch are compared: physical level calibration, dynamic element matching, noise-shaping with digital calibration, large periodic high-frequency dithering, and large stochastic high-pass dithering. These methods are suitable for improving accuracy when using digital-to-analog converters that use multiple discrete output levels to reconstruct time-varying signals. The methods improve linearity and therefore reduce harmonic distortion and can be retrofitted to existing systems with minor hardware variations. The performance of each method is compared theoretically and confirmed by simulations and experiments. Experimental results demonstrate that three of the five methods provide significant improvements in the resolution and accuracy when applied to a general-purpose digital-to-analog converter. As such, these methods can directly improve performance in a wide range of applications including nanopositioning, metrology, and optics.
8 citations
TL;DR: Using a power series, Fourier transform, and Fourier series, respectively, to represent the non-linear input-output characteristic, three formulas for the amplitude of any output frequency component are derived and shown that the formula for any output amplitude is given by a series which converges rapidly, allowing efficient numerical computation.
8 citations
TL;DR: In this article, a bounded-input, bounded-output type of stability criterion for systems with non-linearities that do not satisfy the sector condition was obtained, based on the nature of the operation of the elements of the system on the derivatives of the input and output functions.
Abstract: The object of this paper is to obtain a bounded-input, bounded-output type of stability criterion for systems with non-linearities that do not satisfy the sector condition. A criterion is obtained that is based on the nature of the operation of the elements of the system on the derivatives of the input and output functions. This criterion has the following form when applied to a feedback system made up of a time-invariant linear element in cascade with a nonlinear element. If the slope of the input-output characteristic of the nonlinear element is bounded, and if the linear element satisfies a circle or Popov condition for these bounds, then the system maps input functions whose derivatives belong to the space \{x(t)/
i \sigma > 0
i e^{\sigma t} x(t) \in L_{2}[0, \infty)\} into output functions of the same class. This class of functions is a subspace of the space L_{\infty} [0, \infty) , and as a consequence, a bounded-input, bounded-output type of stability criterion is established. Experiments were performed with feedback systems containing hysteresis-type nonlinear elements, and the feedback limit gain for stability so determined was compared with that predicted by the stability criterion. For different experimental systems and for different assumptions, the theoretically predicted limit gain ranged from about 1/3 to about 9/10 the limit gain observed experimentally.
8 citations
TL;DR: A description is given of a computer-aided control system design package, NLCON, that supports analysis and design functions for single-input/single-output nonlinear control systems with a single nonlinearity.
Abstract: A description is given of a computer-aided control system design package, NLCON, that supports analysis and design functions for single-input/single-output nonlinear control systems with a single nonlinearity. The single nonlinearity can be one of seven nonlinearities commonly encountered in mechanical systems, and its location within the system is not restricted. The controller design benefits from designer experience, but it is facilitated by the software package, since program operation is highly interactive and the interface is user friendly. The analysis functions supported include sinusoidal-input describing functions and limit-cycle analysis, frequency-response determination, and jump-resonance analysis. Design functions include procedures for compensator modification to modify limit-cycle and jump-resonance behavior. A design advisory is provided for some simple design situations. Examples to illustrate various facets of program operation are presented. >
6 citations
TL;DR: In this paper, the suppression of limit-cycle oscillations in unity-feedback control systems with an on-off type nonlinearity in cascade with a linear transfer function is presented.
Abstract: A procedure is presented for the suppression of limit-cycle oscillations in unity-feedback control systems which have an on-off type nonlinearity in cascade with a linear transfer function. The procedure is based on the introduction of a minor loop into the system. This produces a high-frequency periodic signal at the input of the nonlinearity, and thereby limit-cycle oscillations are suppressed.
5 citations