scholarly journals Modified Optimal Class of Newton-Like Fourth-Order Methods for Multiple Roots

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 526 ◽  
Author(s):  
Munish Kansal ◽  
Ramandeep Behl ◽  
Mohammed Ali A. Mahnashi ◽  
Fouad Othman Mallawi
Keyword(s):  
Fourth Order ◽  
Numerical Experiments ◽  
Chemical Reactor ◽  
Multiple Roots ◽  
Continuous Stirred Tank Reactor ◽  
Fractional Conversion ◽  
Special Cases ◽  
Continuous Stirred Tank ◽  
Two Stages ◽  
Good Number

Here, we propose optimal fourth-order iterative methods for approximating multiple zeros of univariate functions. The proposed family is composed of two stages and requires 3 functional values at each iteration. We also suggest an extensive convergence analysis that demonstrated the establishment of fourth-order convergence of the developed methods. It is interesting to note that some existing schemes are found to be the special cases of our proposed scheme. Numerical experiments have been performed on a good number of problems arising from different disciplines such as the fractional conversion problem of a chemical reactor, continuous stirred tank reactor problem, and Planck’s radiation law problem. Computational results demonstrates that suggested methods are better and efficient than their existing counterparts.

scholarly journals A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Young Ik Kim ◽  
Young Hee Geum
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Harmonic Mean ◽  
Optimal Order ◽  
Multiple Roots ◽  
Multiple Zeros ◽  
Asymptotic Error ◽  
Two Parameter

We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximate multiple roots of nonlinear equations. They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the developed methods.

Sliding-mode Observer for Uncertainty Estimation in a Class of Chemical Reactor: A Differential-Algebraic Approach

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Ricardo Aguilar-López
Keyword(s):  
Sliding Mode ◽  
Algebraic Approach ◽  
Chemical Reactor ◽  
Uncertainty Estimation ◽  
Temperature Measurements ◽  
Continuous Stirred Tank Reactor ◽  
Reaction Heat ◽  
On Line ◽  
Continuous Stirred Tank ◽  
Noisy Measurements

The problem of the on-line estimation of the reaction heat in a continuous stirred tank reactor from temperature measurements is addressed in this paper. The proposed uncertainty observer is based on differential algebraic techniques, such that the algebraic observability condition of the uncertainty from noisy temperature measurements is easily verified and the observer structure is very simple, which lead to feasible implementation. The observer proposed is robust against noisy measurements and sustained disturbances. The good performance of the observer is shown by means of numerical simulations and is compared with a nonlinear Luenberger-type observer.

scholarly journals The Kronecker Summation Method for Robust Stabilization Applied to a Chemical Reactor

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Radek Matušů ◽  
Jana Závacká ◽  
Roman Prokop ◽  
Monika Bakošová
Keyword(s):  
Exothermic Reaction ◽  
Robust Stabilization ◽  
Algebraic Approach ◽  
Rational Functions ◽  
Chemical Reactor ◽  
Theoretical Background ◽  
Summation Method ◽  
Continuous Stirred Tank Reactor ◽  
Interval System ◽  
Continuous Stirred Tank

The paper focuses on robust stabilization where the suitable parameters of a simple continuous-time PI controller are determined through a combination of the Kronecker summation method, sixteen plant theorem, and an algebraic approach to control design in the ring of proper and stable rational functions. The initial theoretical background is followed by an illustrative experiment which includes computation of the controller and verification of control results for a continuous stirred tank reactor with exothermic reaction modelled as a fourth-order interval system.

scholarly journals An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1809 ◽  
Author(s):  
Ramandeep Behl ◽  
Samaher Khalaf Alharbi ◽  
Fouad Othman Mallawi ◽  
Mehdi Salimi
Keyword(s):  
Nonlinear Equations ◽  
Real Life ◽  
Higher Order ◽  
Multiple Roots ◽  
Continuous Stirred Tank Reactor ◽  
Computational Mathematics ◽  
Life Problems ◽  
Derivative Free ◽  
Continuous Stirred Tank ◽  
Ostrowski’S Method

Finding higher-order optimal derivative-free methods for multiple roots (m≥2) of nonlinear expressions is one of the most fascinating and difficult problems in the area of numerical analysis and Computational mathematics. In this study, we introduce a new fourth order optimal family of Ostrowski’s method without derivatives for multiple roots of nonlinear equations. Initially the convergence analysis is performed for particular values of multiple roots—afterwards it concludes in general form. Moreover, the applicability and comparison demonstrated on three real life problems (e.g., Continuous stirred tank reactor (CSTR), Plank’s radiation and Van der Waals equation of state) and two standard academic examples that contain the clustering of roots and higher-order multiplicity (m=100) problems, with existing methods. Finally, we observe from the computational results that our methods consume the lowest CPU timing as compared to the existing ones. This illustrates the theoretical outcomes to a great extent of this study.

Robust model-based predictive control of exothermic chemical reactor

2015 ◽  
Vol 69 (10) ◽  
Author(s):  
Juraj Oravec ◽  
Monika Bakošová
Keyword(s):  
Predictive Control ◽  
Chemical Reactor ◽  
Continuous Stirred Tank Reactor ◽  
Total Consumption ◽  
Quality Of Control ◽  
Model Based ◽  
Robust Model ◽  
Continuous Stirred Tank

AbstractA case study of the robust model-based predictive control (MPC) of an exothermic continuous stirred tank reactor (CSTR) with uncertain parameters is presented. Three robust MPC approaches are considered and the simulation results are compared in terms of quality of control performance and total consumption of coolant. The results reveal the main benefits of the considered approaches and confirm that the robust MPC can bring about a reduction in consumption of the coolant.

scholarly journals A TITO Control Strategy to Increase Productivity in Uncertain Exothermic Continuous Chemical Reactors

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 873
Author(s):  
Ricardo Aguilar-López ◽  
Juan Luis Mata-Machuca ◽  
Valeria Godinez-Cantillo
Keyword(s):  
Control Strategy ◽  
Chemical Reactor ◽  
Operating Conditions ◽  
Stirred Tank ◽  
Optimal Controller ◽  
Continuous Stirred Tank Reactor ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Continuous Stirred Tank ◽  
Continuous Chemical

In this manuscript, a two-input two-output (TITO) control strategy for an exothermic continuous chemical reactor is presented. The control tasks of the continuous chemical reactor are related to temperature regulation by a standard proportional-integral (PI) controller. The selected set point increases reactor productivity due to the temperature effect and prevents potential thermal runaway, and the temperature increases until it reaches isothermal operating conditions. Then, an optimal controller is activated to increase the mass reactor productivity. The optimal control strategy is based on a Euler-Lagrange framework, in which the corresponding Lagrangian is based on the model equations of the reactor, and the optimal controller is coupled with an uncertainty estimator to infer the unknown terms required by the proposed controller. As a benchmark, a continuous stirred tank reactor (CSTR) with a Van de Vusse chemical reaction is considered as an application case study. Notably, the proposed methodology is generally applicable to any continuous stirred tank reactor. The results of numerical experiments verify the satisfactory performance of the proposed control strategy.

scholarly journals Neural network based explicit MPC for chemical reactor control

2019 ◽  
Vol 12 (2) ◽  
pp. 218-223 ◽  
Author(s):  
Karol Kiš ◽  
Martin Klaučo
Keyword(s):  
Neural Network ◽  
Predictive Control ◽  
Chemical Reactor ◽  
Control Input ◽  
Continuous Stirred Tank Reactor ◽  
The Neural Network ◽  
Approach Training ◽  
Continuous Stirred Tank ◽  
And Control

Abstract In this paper, implementation of deep neural networks applied in process control is presented. In our approach, training of the neural network is based on model predictive control, which is popular for its ability to be tuned by the weighting matrices and for it respecting the system constraints. A neural network that can approximate the MPC behavior by mimicking the control input trajectory while the constraints on states and control input remain unimpaired by the weighting matrices is introduced. This approach is demonstrated in a simulation case study involving a continuous stirred tank reactor where a multi-component chemical reaction takes place.

On the Influence of Fluctuating Flow Rate Upon the Performance and Behaviour of Isothermal Reacting Systems

1998 ◽  
Vol 63 (6) ◽  
pp. 881-898
Author(s):  
Otakar Trnka ◽  
Miloslav Hartman
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Fluidized Bed Reactor ◽  
Computational Techniques ◽  
Continuous Stirred Tank Reactor ◽  
Gas Flow Rate ◽  
Solid Reaction ◽  
Continuous Stirred Tank ◽  
And Performance ◽  
Reacting Systems

Three simple computational techniques are proposed and employed to demonstrate the effect of fluctuating flow rate of feed on the behaviour and performance of an isothermal, continuous stirred tank reactor (CSTR). A fluidized bed reactor (FBR), in which a non-catalytic gas-solid reaction occurs, is also considered. The influence of amplitude and frequency of gas flow rate fluctuations on reactant concentrations at the exit of the CSTR is shown in four different situations.

Sign in / Sign up

Export Citation Format

Share Document