[PDF] The Analysis Of Nonlinear Feedback Sampled Data Systems eBook

Author : Mangalore Anantha Pai
Publisher :
Page : 226 pages
File Size : 35,77 MB
Release : 1961
Category : Data transmission systems
ISBN :

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Various techniques are available for the analysis of nonlinear sampled-data systems. Most of these methods use either the phase plane approach or the describing function technique. Since the performance of such a system is described, at sampling instants, by means of a difference equation, an approach based on the difference equation would seem to be both natural and direct. The principle of complex convolution for a transform is explained and its geometrical interpretation is given. It is shown how the application of the convolution transform is both direct and simple with respect to solving nonlinear difference equations when the equation is given in scalar form. Dependence of the convergence of the solution on the initial value and the degree of nonlinearity is pointed out. It is concluded that for difference equations of second order and higher, this method involves too much laborious computation to justify its use. A simple method is presented for examining free oscillations in a sampled-data system containing either relay or a saturating amplifier. In addition, a certain analytical technique, analogous to that for differential equations, is developed to investigate the stability of forced oscillations for certain types of nonlinear difference equations. (Author).

Author : Juan I. Yuz
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 44,75 MB
Release : 2013-10-17
Category : Technology & Engineering
ISBN : 1447155629

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Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: · the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; · although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and · the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either partially or completely erroneous. They also deal with linear and nonlinear, deterministic and stochastic cases. The impact of the ideas presented on several standard problems in signals and systems is illustrated using a number of applications. Academic researchers and graduate students in systems, control and signal processing will find the ideas presented in Sampled-data Models for Linear and Nonlinear Systems to be a useful manual for dealing with sampled-data systems, clearing away mistaken ideas and bringing the subject thoroughly up to date. Researchers in statistics and economics will also derive benefit from the reworking of ideas relating a model derived from data sampling to an original continuous system.

Author : Hossein Beikzadeh
Publisher :
Page : 160 pages
File Size : 27,36 MB
Release : 2014
Category : Discrete-time systems
ISBN :

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This thesis concerns with a common practical problem in the area of sampled-data control systems where the plant is described by nonlinear dynamics and input and output signals are sampled at different rates. We first follow the continuous-time (emulation) approach to propose a general stabilization framework for multirate nonlinear systems in presence of disturbances. This provides a multirate H_infinity synthesis scheme which can be used to tackle the intrinsic difficulty of unknown exact discrete-time model in nonlinear sampled-data control systems. Moreover, an alternative performance criterion is introduced based on the L_2 incremental gain as a stronger form of the usual L_2 gain that quantifies whether or not small changes in exogenous inputs such as disturbances or noise will result in small changes at the output. The second part of the thesis investigates the discrete-time approach based on model approximation to the problem of multirate nonlinear sampled-data systems. First, we establish prescriptive design principles for single-rate sampled-data nonlinear observer that is input-to-state stable in the presence of unknown exact discrete-time model as well as disturbance inputs. Our results are then applied to the so-called one-sided Lipschitz nonlinearities to develop constructive design techniques via tractable (linear matrix inequalities) LMIs. Taking the idea of input-to-state stable observer into account, we propose a general framework for multirate observer design that exploits a single-rate observer working at the base sampling period of the system together with modified sample and hold devices to reconstruct the missing intersample signals. Finally, in order to verify the advantages of multirate sampling we extend our results to the area of networked-control systems (NCSs). A general output-feedback structure is developed which utilizes the same idea as that of our multirate observer to predict the missing outputs between measured samples. The proposed multirate network-based controller is shown to be capable of preserving the dissipation inequality slightly deteriorated by some additive terms, in spite of network-induced uncertainties and disturbance inputs. By this means a stable NCS can be obtained under much lower data rate and a significant saving in the required bandwidth.