Back-stepping stabilization of chaotic systems based on triangular form

2019 ◽  
Vol 33 (12) ◽  
pp. 1950153
Author(s):  
Chenchen Peng
Keyword(s):  
Chaotic Systems ◽  
Physical Models ◽  
The Other ◽  
Control Problems ◽  
Coordinate Transformations ◽  
Triangular System ◽  
Triangular Form ◽  
Triangular Structure ◽  
State Component

This paper investigates the stabilization of a class of chaotic systems. On the basis of triangular system, chaotic systems which have triangular structure, can be converted into such structure and can be converted into such structure partly by appropriate coordinate transformations are considered. Different with the previous works, triangular system studied in this work has simpler structure and more applications. Moreover, back-stepping technique is used to obtain the stabilization controllers which are single controllers without judging which state component should be stabilized. It should be emphasized that the triangular structure studied in this paper is feasible not only for the stabilization of chaotic systems but for the other control problems of chaotic systems and other physical models as long as the system satisfies one of the above three cases. Several examples are selected to verify the correctness and effectiveness of the obtained results.

On the factorization of rotations with examples in diffractometry

1990 ◽  
Vol 428 (1875) ◽  
pp. 451-472 ◽  
Keyword(s):  
Rotation Angle ◽  
Rotation Axis ◽  
Axial Direction ◽  
The Other ◽  
Rotation Vector ◽  
Coordinate Transformations ◽  
Rotation Axes ◽  
Analytic Expressions ◽  
Direction Cosines

An analysis of compound rotations, such as occur in eulerian cradles, is presented in terms of a calculus of rotation axes, without reference to the associated coordinate transformations. The general case of three rotation shafts mounted on one another, with any relation between them at datum zero, is presented. The problem and its solution may be represented entirely in terms of a plane octagon in which four sides have directions that are instrumental constants and the other four sides have lengths that are instrumental constants. When the first four sides are given lengths that express both the rotation angle and the axial direction of the required rotation, then the remaining four sides have directions that directly express the rotations in the drive shafts, that will generate the required rotation. Analytic expressions are given for the shaft setting angles in the general case. If the first and third axes are parallel and the intermediate one perpendicular to these at datum zero (as in the four-circle diffractometer) then these reduce to θ 1 = arctan ( μ, σ ) + [arctan ( λ , v ) - ψ -½8π], θ 2 = 2 s arcsin ( λ 2 + v 2 )½, θ 3 = ( μ, σ ) - [arctan ( λ , v ) - ψ - ½8π], s = ± 1, 0 ≤ arcsin ( λ 2 + v 2)½ ≤ ½π, in which λ, μ, v and σ are the four components of a rotation vector constructed such that λ, μ and v are the direction cosines of the rotation axis multiplied by sin½ θ for a rotation angle θ and σ is cos½ θ . ψ is a constant determined by the choice of directions to which λ and v are measured. The results for the general case are also expressed in terms of more conventional variables.

Physical Models and Physiological Concepts: Explanation in Nineteenth-Century Biology

1965 ◽  
Vol 2 (3) ◽  
pp. 201-219 ◽  
Author(s):  
Everett Mendelsohn
Keyword(s):  
Nineteenth Century ◽  
Concept Formation ◽  
Explanatory Models ◽  
Physical Models ◽  
The Other ◽  
Biological Phenomena ◽  
Claude Bernard ◽  
French School ◽  
Biological Laws ◽  
Analytical Tools

SynopsisThe response to physics and chemistry which characterized mid-nineteenth century physiology took two major directions. One, found most prominently among the German physiologists, developed explanatory models which had as their fundamental assumption the ultimate reducibility of all biological phenomena to the laws of physics and chemistry. The other, characteristic of the French school of physiology, recognized that physics and chemistry provided potent analytical tools for the exploration of physiological activities, but assumed in the construction of explanatory models that the organism involved special levels of organization and that there must, in consequence, be special biological laws.The roots of this argument about concept formation in physiology are explored in the works of Theodor Schwann, Johannes Müller, François Magendie and Claude Bernard among others.

scholarly journals Early Stage Digital Twins for Early Stage Engineering Design

2019 ◽  
Vol 1 (1) ◽  
pp. 2557-2566 ◽  
Author(s):  
David Edward Jones ◽  
Chris Snider ◽  
Lee Kent ◽  
Ben Hicks
Keyword(s):  
Life Cycle ◽  
Product Life Cycle ◽  
Early Stage ◽  
Physical Models ◽  
The Other ◽  
Digital Twin ◽  
Digital Twins ◽  
Design Cycle ◽  
Revision Control ◽  
First Time

ABSTRACTWhile extensive modelling - both physical and virtual - is imperative to develop right-first-time products, the parallel use of virtual and physical models gives rise to two interrelated issues: the lack of revision control for physical prototypes; and the need for designers to manually inspect, measure, and interpret modifications to either virtual or physical models, for subsequent update of the other. The Digital Twin paradigm addresses similar problems later in the product life-cycle, and while these digital twins, or the “twinning” process, have shown significant value, there is little work to date on their implementation in the earlier design stages. With large prospective benefits in increased product understanding, performance, and reduced design cycle time and cost, this paper explores the concept of using the Digital Twin in early design, including an introduction to digital twinning, examination of opportunities for and challenges of their implementation, a presentation of the structure of Early Stage Twins, and evaluation via two implementation cases.

The Influence of Aircraft Characteristics on A.T.C. Problems

1961 ◽  
Vol 65 (606) ◽  
pp. 418-423 ◽  
Author(s):  
B. N. Tomlinson
Keyword(s):  
Traffic Control ◽  
Air Traffic Control ◽  
Supersonic Jet ◽  
Air Traffic ◽  
The Other ◽  
Control Problems ◽  
Operating Characteristics ◽  
Transport Aircraft

To provide a basis for discussion of air traffic control problems some of the operating characteristics of long haul subsonic and supersonic jet transport aircraft are examined. Two trans-Atlantic aircraft are compared, one designed to cruise at 500 knots (Mach 0·85) and the other at 1,250 knots (Mach 2·2).

scholarly journals TENTHREDO (?) DELTA, PROV.

1886 ◽  
Vol 18 (2) ◽  
pp. 32-33
Author(s):  
W. Hague Harrington
Keyword(s):  
Posterior Margin ◽  
The Other ◽  
Careful Examination ◽  
Triangular Form ◽  
Past Season ◽  
The Past ◽  
Typical Form

Among the Tenthredinidæ captured by me during the past season was a good series of Tenthredo delta Prov, consisting of 12 females and 26 males. In pinning them I was frequently struck by the evident irregularity of the venation of the wings, and on a more careful examination of the specimens I find these irregularities to be both numerous and remarkable. No other species represented in my cabinet show any such divergencies from the typical form, except in rare instances. Provancher describes the female (page 210, “Petite Faune Entomologique du Canada”) as having two discoidal cells in under wings, and Cresson (“Trans. Am. Ent. Soc.,” vol. viii., page 44) as having one or two middle cells. One middle cell appears to be the rule, and any deviation therefrom to be an exception. Of my 12 specimens, 10 have one middle cell each, one has two middle cells, and the other none. The males are more uniform apparently in their venation, as none of my 26 specimens have middle cells in the under wings, thus agreeing with the description given by Cresson (loc. cit). Apart from the varying number of middle cells, the under wing of the females have the cells varying much in shape, especially the middle one, which ranges from a small triangular form to a large foursided (square or irregular) one. There are also occasionally small additional cells on the posterior margin.

Numerical Simulation of Heat and Fluid Flow in a Basic Pulse-Tube Refrigerator

2004 ◽  
Author(s):  
Takao Koshimizu ◽  
Hiromi Kubota ◽  
Yasuyuki Takata ◽  
Takehiro Ito
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Heat Exchange ◽  
Surface Heat ◽  
Physical Models ◽  
The Other ◽  
Pulse Tube ◽  
Working Principle ◽  
Pulse Tube Refrigerators ◽  
Heat And Fluid Flow

The working principle of refrigeration in basic pulse-tube refrigerators (BPTR) has been explained by the mechanism called surface heat pumping (SHP) that heat is conveyed from the cold end to the hot end of the pulse tube by the successive heat exchange between the working gas and the wall. In this study, a numerical simulation has been performed to clarify the effect of the wall in BPTRs by comparing the numerical results in two physical models; one is the model considering the heat exchange between the working gas and the wall (HE model), and the other is the model ignoring that (AW model). As a result, the importance in the effect of the wall was shown clearly. In addition, the mechanism of refrigeration other than the SHP was made clear in the AW model.

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