scholarly journals The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 178
Author(s):  
Sebastian Plamowski ◽  
Richard W Kephart
Keyword(s):  
Predictive Control ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Order ◽  
Double Precision ◽  
Model Order ◽  
Numerical Errors ◽  
Multiple Input ◽  
Multidimensional Objects ◽  
Order Reduction Method

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.

Fluid of multidimensional objects in cosmology

1991 ◽  
Vol 32 (11) ◽  
pp. 3141-3147 ◽  
Author(s):  
Roman A. Maszczyk
Keyword(s):  
Multidimensional Objects

scholarly journals Applying of intergral parameters of multidimensional objects to solve the medical and biological problems.

Morphologia ◽  
2016 ◽  
Vol 10 (4) ◽  
pp. 84-87
Author(s):  
K. I. Dyagovets ◽  
D. G. Marchenko ◽  
S. B. Morozova ◽  
N. S. Petruk ◽  
L. A. Romanenko ◽  
...  
Keyword(s):  
Multidimensional Objects

Use of Mechanisms Marking Centers of Simplexes in Their 2-Dimensional Projections as Axonographs of Multidimensional Spaces

2021 ◽  
Vol 8 (4) ◽  
pp. 13-23
Author(s):  
Sherzod Abdurahmanov
Keyword(s):  
Dimensional Space ◽  
Spatial Location ◽  
Straight Line Segment ◽  
Barycentric Coordinates ◽  
Parallel Projection ◽  
Problem Solution ◽  
Similarity Coefficients ◽  
Translational Movement ◽  
Straight Line ◽  
Multidimensional Objects

A brief historical excursion into the graphics of geometry of multidimensional spaces at the paper beginning clarifies the problem – the necessary to reduce the number of geometric actions performed when depicting multidimensional objects. The problem solution is based on the properties of geometric figures called N- simplexes, whose number of vertices is equal to N + 1, where N expresses their dimensionality. The barycenter (centroid) of the N-simplex is located at the point that divides the straight-line segment connecting the centroid of the (N–1)-simplex contained in it with the opposite vertex by 1: N. This property is preserved in the parallel projection (axonometry) of the simplex on the drawing plane, that allows the solution of the problem of determining the centroid of the simplex in its axonometry to be assigned to a mechanism which is a special Assembly of pantographs (the author's invention) with similarity coefficients 1:1, 1:2, 1:3, 1:4,...1:N. Next, it is established, that the spatial location of a point in N-dimensional space coincides with the centroid of the simplex, whose vertices are located on the point’s N-fold (barycentric) coordinates. In axonometry, the ends of both first pantograph’s links and the ends of only long links of the remaining ones are inserted into points indicating the projections of its barycentric coordinates and the mechanism node, which serves as a determinator, graphically marks the axonometric location of the point defined by its coordinates along the axes х1, х2, х3 … хN.. The translational movement of the support rods independently of each other can approximate or remote the barycentric coordinates of a point relative to the origin of coordinates, thereby assigning the corresponding axonometric places to the simplex barycenter, which changes its shape in accordance with its points’ occupied places in the coordinate axes. This is an axonograph of N-dimensional space, controlled by a numerical program. The last position indicates the possibility for using the equations of multidimensional spaces’ geometric objects given in the corresponding literature for automatic drawing when compiling such programs.

Fractal Geometry as a Bridge between Realms

2013 ◽  
pp. 25-43 ◽  
Author(s):  
Terry Marks-Tarlow
Keyword(s):  
Fractal Geometry ◽  
Open Systems ◽  
Autonomous Systems ◽  
Mathematical Notation ◽  
Deep Space ◽  
The Unconscious ◽  
Self And Other ◽  
Branching Structures ◽  
Self Similar ◽  
Multidimensional Objects

This chapter describes fractal geometry as a bridge between the imaginary and the real, mind and matter, conscious and the unconscious. Fractals are multidimensional objects with self-similar detail across size and/or time scales. Jung conceived of number as the most primitive archetype of order, serving to link observers with the observed. Whereas Jung focused upon natural numbers as the foundation for order that is already conscious in the observer, I offer up the fractal geometry as the underpinnings for a dynamic unconscious destined never to become fully conscious. Throughout nature, fractals model the complex, recursively branching structures of self-organizing systems. When they serve at the edges of open systems, fractal boundaries articulate a paradoxical zone that simultaneously separates as it connects. When modeled by Spencer-Brown’s mathematical notation, full interpenetration between inside and outside edges translates to a distinction that leads to no distinction. By occupying the infinitely deep “space between” dimensions and levels of existence, fractal boundaries contribute to the notion of intersubjectivity, where self and other become most entwined. They also exemplify reentry dynamics of Varela’s autonomous systems, plus Hofstadter’s ever-elusive “tangled hierarchy” between brain and mind.

scholarly journals Measuring Subgroup Preferences in Conjoint Experiments

2019 ◽  
Vol 28 (2) ◽  
pp. 207-221 ◽  
Author(s):  
Thomas J. Leeper ◽  
Sara B. Hobolt ◽  
James Tilley
Keyword(s):  
Conjoint Analysis ◽  
Best Practice ◽  
Causal Interpretation ◽  
Reference Category ◽  
Subgroup Differences ◽  
Political Preferences ◽  
Randomized Design ◽  
Marginal Means ◽  
Arbitrary Sign ◽  
Multidimensional Objects

Conjoint analysis is a common tool for studying political preferences. The method disentangles patterns in respondents’ favorability toward complex, multidimensional objects, such as candidates or policies. Most conjoints rely upon a fully randomized design to generate average marginal component effects (AMCEs). They measure the degree to which a given value of a conjoint profile feature increases, or decreases, respondents’ support for the overall profile relative to a baseline, averaging across all respondents and other features. While the AMCE has a clear causal interpretation (about the effect of features), most published conjoint analyses also use AMCEs to describe levels of favorability. This often means comparing AMCEs among respondent subgroups. We show that using conditional AMCEs to describe the degree of subgroup agreement can be misleading as regression interactions are sensitive to the reference category used in the analysis. This leads to inferences about subgroup differences in preferences that have arbitrary sign, size, and significance. We demonstrate the problem using examples drawn from published articles and provide suggestions for improved reporting and interpretation using marginal means and an omnibus F-test. Given the accelerating use of these designs in political science, we offer advice for best practice in analysis and presentation of results.

Identification of Multidimensional Objects and Multiple Observation Intervals

2021 ◽  
pp. 231-250
Author(s):  
Michael J. Hautus ◽  
Neil A. Macmillan ◽  
C. Douglas Creelman
Keyword(s):  
Multidimensional Objects

PC-based devices for immittance control of multidimensional objects

2002 ◽  
Vol 51 (5) ◽  
pp. 1133-1136 ◽  
Author(s):  
E. Pohodylo ◽  
P. Stolyarchuk ◽  
M. Chyrka
Keyword(s):  
Multidimensional Objects
Sign in / Sign up

Export Citation Format

Share Document