scholarly journals Extension of First Order Predictive Functional Controllers to Handle Higher Order Internal Models

2008 ◽  
Vol 18 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Mohamed Khadir ◽  
John Ringwood
Keyword(s):  
Higher Order ◽  
Internal Models ◽  
Input Output ◽  
Model Decomposition ◽  
First Order ◽  
The Family ◽  
Armax Model ◽  
Cascaded Model ◽  
Process Plants ◽  
Functional Control

Extension of First Order Predictive Functional Controllers to Handle Higher Order Internal ModelsPredictive Functional Control (PFC), belonging to the family of predictive control techniques, has been demonstrated as a powerful algorithm for controlling process plants. The input/output PFC formulation has been a particularly attractive paradigm for industrial processes, with a combination of simplicity and effectiveness. Though its use of a lag plus delay ARX/ARMAX model is justified in many applications, there exists a range of process types which may present difficulties, leading to chattering and/or instability. In this paper, instability of first order PFC is addressed, and solutions to handle higher order and difficult systems are proposed. The input/output PFC formulation is extended to cover the cases of internal models with zero and/or higher order pole dynamics in an ARX/ARMAX form, via a parallel and cascaded model decomposition. Finally, a generic form of PFC, based on elementary outputs, is proposed to handle a wider range of higher order oscillatory and non-minimum phase systems. The range of solutions presented are supported by appropriate examples.

Higher Order Predictive Functional Control Versus Dynamical Matrix Control for a Milk Pasteurisation Process: Transfer Function Versus Finite Step Response Internal Models

2013 ◽  
Vol 10 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Tarek Mohamed Khadir ◽  
John Vincent Ringwood
Keyword(s):  
Internal Model ◽  
Industrial Applications ◽  
Higher Order ◽  
Step Response ◽  
Dynamical Matrix ◽  
First Order ◽  
Predictive Functional Control ◽  
Functional Control ◽  
Milk Pasteurisation ◽  
Matrix Control

Abstract Predictive functional control (PFC), a model predictive control algorithm, has been proven to be very successful in a wealth of industrial applications due to its many laudable attribute, such as its simplicity and intuitive appeal. For simple single input single output processes, PFC applications use a first-order plus delay internal model and, as long as such models improve the control over classical control strategies, then their use remains justified. In this paper, a higher order internal PFC model is considered in order to reduce any possible plant-model mismatch, where the internal model is formulated as a series of cascaded or parallel first-order systems. The control approach is compared to a more conventional over parameterized dynamical matrix control (DMC) approach, used extensively for Multi-Input Multi-Output systems in the petrochemical industry. This paper demonstrates the benefits of the PFC higher order formulation for a typical milk pasteurisation plant, with significant improvements in the variances of both controlled and manipulated variables when compared to a first-order PFC. In this aspect, the higher order controller competes well with DMC performances, however, using a much more simpler and compact internal model form.

scholarly journals Semi-Local Analysis and Real Life Applications of Higher-Order Iterative Schemes for Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 92
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Ioannis K. Argyros ◽  
Sanjeev Kumar
Keyword(s):  
Nonlinear Systems ◽  
Applied Mathematics ◽  
Real Life ◽  
Higher Order ◽  
Local Analysis ◽  
First Order ◽  
The Family ◽  
Lipschitz Constants ◽  
Theoretical Results ◽  
Real World Problems

Our aim is to improve the applicability of the family suggested by Bhalla et al. (Computational and Applied Mathematics, 2018) for the approximation of solutions of nonlinear systems. Semi-local convergence relies on conditions with first order derivatives and Lipschitz constants in contrast to other works requiring higher order derivatives not appearing in these schemes. Hence, the usage of these schemes is improved. Moreover, a variety of real world problems, namely, Bratu’s 1D, Bratu’s 2D and Fisher’s problems, are applied in order to inspect the utilization of the family and to test the theoretical results by adopting variable precision arithmetics in Mathematica 10. On account of these examples, it is concluded that the family is more efficient and shows better performance as compared to the existing one.

Higher Order Two-Point Efficient Family of Halley Type Methods for Simple Roots

2016 ◽  
Vol 13 (04) ◽  
pp. 1641016 ◽  
Author(s):  
Ramandeep Behl ◽  
S. S. Motsa
Keyword(s):  
Nonlinear Equations ◽  
Computational Cost ◽  
Basins Of Attraction ◽  
Higher Order ◽  
The Other ◽  
Sixth Order ◽  
Order Derivative ◽  
Initial Value ◽  
First Order ◽  
The Family

In this paper, we proposed a new highly efficient two-point sixth-order family of Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. In terms of computational cost, each member of the family requires two-function and two first-order derivative evaluations per iteration. On the account of the results obtained, it is found that our proposed methods are efficient and show better performance than existing sixth-order methods available in the literature. Further, it is also noted that larger basins of attraction belong to our methods as compared to the existing ones. On the other hand, the existing methods are slower and have darker basins while some of them are too sensitive upon the choice of the initial value.

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.

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

Generalized Frequency Domain Robust Tuning of a Family of Fractional Order PI/PID Controllers to Handle Higher Order Process Dynamics

2011 ◽  
Vol 403-408 ◽  
pp. 4859-4866 ◽  
Author(s):  
Saptarshi Das ◽  
Amitava Gupta ◽  
Shantanu Das
Keyword(s):  
Frequency Domain ◽  
Fractional Order ◽  
Test Bench ◽  
Standard Test ◽  
Higher Order ◽  
Pid Controllers ◽  
Order Process ◽  
Controller Tuning ◽  
Process Dynamics ◽  
The Family

Generalization of the frequency domain robust tuning has been proposed in this paper for a family of fractional order (FO) PI/PID controllers. The controller tuning is enhanced with two new FO reduced parameter templates which are capable of capturing higher order process dynamics with much better accuracy. The paper validates the proposed methodology with a standard test-bench of higher order processes to show the relative merits of the family of FO controller structures.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

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