On the monotonicity of higher-order interval iterations for bounding the inverse matrix

Computing ◽  
1988 ◽  
Vol 40 (4) ◽  
pp. 367-372
Author(s):  
J. Herzberger
Keyword(s):  
Higher Order ◽  
Inverse Matrix ◽  
Order Interval ◽  
Interval Iterations

scholarly journals Design of Robust Controller for Higher Order Interval System using Differential Evolutionary Algorithm

2018 ◽  
Vol 7 (4) ◽  
pp. 232
Author(s):  
D. Srinivasa Rao ◽  
M. Siva Kumar ◽  
M. Ramalinga Raju
Keyword(s):  
Pid Controller ◽  
Higher Order ◽  
Stability Conditions ◽  
Order Interval ◽  
Order Model ◽  
Robust Controller ◽  
Interval System ◽  
Interval Model ◽  
Reduced Order ◽  
De Algorithm

This paper describes the design of the robust PI/PID controller for the higher order interval system via its reduced order model using the differential evolution (DE) algorithm. A stable reduced interval model is generated from a higher order interval system using the DE in order to minimize the cost and reduce the complexity of the system. This reduced order interval numerator and denominator polynomials are determined by minimizing the Integral Squared Error (ISE) using the DE. Then, using reduced order interval model, a robust PI/PID controller is designed based on the stability conditions for determining robust stability of interval system. Finally, using these stability conditions, a set of inequalities in terms of controller parameters is obtained from the reduced order closed loop characteristic polynomial. Then these inequalities are solved to obtain robust controller parameters with the help of a DE algorithm. The designed, robust controller from the reduced order interval model will be attributed to the higher order interval system. The designed PI/PID controller from our proposed method not only stabilizes the reduced order model, but also stabilizes the original higher order system. The viability of the proposed methodology is illustrated through the numerical example of its successful implementation. The efficacy of the proposed methodology is also evaluated against the available approaches presented in the literature and the results were successfully implemented.

scholarly journals Design of FOPID controller for higher order continuous interval system using improved approximation ensuring stability

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
P. D. Dewangan ◽  
V. P. Singh ◽  
S. L. Sinha
Keyword(s):  
Controller Design ◽  
Test System ◽  
Higher Order ◽  
Phase Margin ◽  
Order Interval ◽  
Single Input Single Output ◽  
Single Output ◽  
Multipoint Padé Approximation ◽  
Single Input ◽  
Reduce Order Modeling

AbstractThis contribution deals with the design of a fractional-order proportional-integral-derivative (FOPID) controller through reduce-order modeling for continuous interval systems. First, a higher order interval plant (HOIP) is considered. The reduced-order interval plant (ROIP) for considered HOIP is derived by multipoint Padé approximation integrated with Routh table. Then, FOPID controller is designed for ROIP to satisfy the phase margin and gain cross over frequency. Thus obtained FOPID controller is implemented on HOIP also to validate the performance of designed FOPID on HOIP. A single-input-single-output (SISO) test system is taken up to elaborate the entire process of controller design. The outcomes affirm the validity of the designed FOPID controller. The designed FOPID controller produced stable results retaining the phase margin and gain cross-over frequency when implemented on HOIP. The results further proved that FOPID controller is working efficiently for ROIP and HOIP.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

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