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.

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.

Robust stabilization of a chemical reactor

2009 ◽  
Vol 63 (5) ◽  
Author(s):  
Monika Bakošová ◽  
Dalibor Puna ◽  
Petr Dostál ◽  
Jana Závacká
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Exothermic Reaction ◽  
Robust Stabilization ◽  
Output Feedback Control ◽  
Chemical Reactor ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Continuous Stirred Tank Reactor ◽  
Static Output

AbstractRobust static output feedback control was applied to a continuous stirred tank reactor with parametric uncertainty and multiple steady states in which exothermic reaction takes place. The problem of robust controller design was converted to a solution of linear matrix inequalities and a computationally simple non-iterative algorithm is presented. The possibility of using robust static output feedback for stabilization of reactors with uncertainty and comparison of robust P and PI controllers with an optimal controller is demonstrated by simulation results.

scholarly journals Robust constrained MPC stabilization of a CSTR

2012 ◽  
Vol 5 (2) ◽  
pp. 153-158 ◽  
Author(s):  
Juraj Oravec ◽  
Monika Bakošová
Keyword(s):  
Predictive Control ◽  
Exothermic Reaction ◽  
Robust Stabilization ◽  
Optimization Methods ◽  
Linear Matrix ◽  
Continuous Stirred Tank Reactor ◽  
Control Approach ◽  
Model Based ◽  
Constrained Model ◽  
Input Variables

Abstract The paper addresses a case study of robust stabilization of a continuous stirred tank reactor using robust model-based predictive control with constrained input variables. One exothermic reaction runs in the reaction mixture and the reactor is modelled in the form of an uncertain polytopic system. The control approach is based on solution of a set of linear matrix inequalities. This formulation enables to use convex optimization methods to design a gain matrix of a state feedback controller in each control step. The task of stabilization is solved in assumed control conditions with respect to symmetric constraints on control inputs. The control performance achieved by robust constrained model-based predictive control is studied via simulations. Obtained results confirm that the robust constrained model-based predictive control ensures the stability demands and the quality requirements represented by chosen quadratic cost function.

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.

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 Novel Multiplicity and Stability Criteria for Non-Isothermal Fixed-Bed Reactors

2021 ◽  
Vol 8 ◽  
Author(s):  
Jens Bremer ◽  
Kai Sundmacher
Keyword(s):  
Exothermic Reaction ◽  
Fixed Bed ◽  
Operating Conditions ◽  
Continuous Stirred Tank Reactor ◽  
Stability Criteria ◽  
Fixed Bed Reactors ◽  
Continuous Stirred Tank ◽  
Back Mixing ◽  
State Multiplicity ◽  
New Criteria

With the increasing need to utilize carbon dioxide, fixed-bed reactors for catalytic hydrogenation will become a decisive element for modern chemicals and energy carrier production. In this context, the resilience and flexibility to changing operating conditions become major objectives for the design and operation of real industrial-scale reactors. Therefore steady-state multiplicity and stability are essential measures, but so far, their quantification is primarily accessible for ideal reactor concepts with zero or infinite back-mixing. Based on a continuous stirred tank reactor cascade modeling approach, this work derives novel criteria for stability, multiplicity, and uniqueness applicable to real reactors with finite back-mixing. Furthermore, the connection to other reactor features such as runaway and parametric sensitivity is demonstrated and exemplified for CO2 methanation under realistic conditions. The new criteria indicate that thermo-kinetic multiplicities induced by back-mixing remain relevant even for high Bodenstein numbers. In consequence, generally accepted back-mixing criteria (e.g., Mears’ criterion) appear insufficient for real non-isothermal reactors. The criteria derived in this work are applicable to any exothermic reaction and reactors at any scale. Ignoring uniqueness and multiplicity would disregard a broad operating range and thus a substantial potential for reactor resilience and flexibility.

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.

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