Van De Vusse Reaction Research Articles

Nonideal mixing effect based on Cholette’s model on Van de Vusse reaction selectivity dynamics in an isothermal continuous stirred-tank reactor

Abstract The nonideal mixing effect on the Van de Vusse reaction dynamic in a continuous stirred-tank reactor (CSTR) has rarely been studied in literature. This work presents the mixing operation condition and kinetic reaction constant effects on the Van de Vusse reaction selectivity dynamic in an isothermal CSTR based on Cholette’s model. The mixing condition effect is defined using the parameter μ = n/m, where n is the flow fraction to the reactor and m is the dead space fraction in the reactor. In Cholette’s model, μ = 1 and μ ≠ 1 represent, respectively, the ideal and nonideal mixing operations. Herein, the final desired product yield steady state in the phase plane is first constructed under reaction constant and mixing condition combinations, indicating that the larger the μ values, the higher the desired product steady-state yield. In the selectivity dynamic simulations, the phase plane is divided into transient extreme yield region and region of monotonic variation in yield. It is found for the first time that a higher μ value leads to a decrease in the transient maximum selectivity region area and an increase in the transient minimum selectivity region area in the phase plane. Moreover, the trajectory from the start up to the final steady state will be changed due to nonideal mixing. These results have not been published and have direct applications in real reactor design and operation. Since a CSTR with ideal mixing is hardly attainable in practice, our results benefit the real reactor design and startup policy development in the desired product transient maximum yield.

On the development of steady-state and dynamic mass-constrained neural networks using noisy transient data

This paper presents the development of algorithms for mass-constrained neural network models that can exactly satisfy mass conservation laws of chemical process systems, even if the training data violates the same. As opposed to approximately satisfying mass balance constraints of a system by considering additional penalty terms in the objective function, algorithms have been developed to solve an equality-constrained optimization problem, thus ensuring the exact satisfaction of the overall mass conservation laws. For developing dynamic mass-constrained networks, hybrid series and parallel all-nonlinear static-dynamic neural network models are leveraged. The proposed algorithms for solving both the inverse and forward problems are tested by considering both steady-state and dynamic data in presence of varieties of noise characterizations. The proposed structures and algorithms are applied to the development of data-driven models of two nonlinear dynamic chemical processes, namely the Van de Vusse reactor system as well as a solvent-based post-combustion CO2 capture process.

Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

Influence of Estimators and Numerical Approaches on the Implementation of NMPCs

Advanced control strategies, together with state-estimation methods, are frequently applied to nonlinear and complex systems. It is crucial to understand which of these are the most efficient methods for the best use of these approaches in a chemical process. In the current work, nonlinear model predictive control (NMPC) approaches were developed that considered three numerical methods: single shooting (SS), multiple shooting (MS), and orthogonal collocation (OC). Their performance was compared against the Van de Vusse reactor benchmark while considering set-point changes, unreachable set-point, disturbances, and mismatches. The results showed that the NMPC based on OC presented less computational cost than the other approaches. The extended Kalman filter (EKF), constrained extended Kalman filter (CEKF), and the moving horizon estimator (MHE) were also developed. The estimators’ performance was compared for the same benchmark by considering the computational cost and the mean squared error (MSE) for the estimated variables, thereby verifying the CEKF as the best option. Finally, the performance of the nine combinations of estimators and control approaches was compared to consider the Van de Vusse reactor and the same scenarios, thereby verifying the best performance of the CEKF with the OC. The present work can help with choosing the numerical method and the estimator for controlling chemical processes.

Economic MPC with modifier adaptation using transient measurements

This paper presents a method to estimate process dynamic gradients along the transient that combined with the idea of Modifier Adaptation (MA) improves the economic cost fuction of the examples presented. The gradient estimation method, called TMA, aims to reduce the large convergence time required for traditional MA in processes of slow dynamics. TMA is used with an economic predictive control with MA (eMPC+TMA) and was applied in two case studies: a simulation of the Williams-Otto reactor and a hybrid laboratory plant based on the Van de Vusse reactor. The results show that eMPC+TMA could reach the plant real steady-state optimum despite process-model mismatch, due to the inclusion of the effect of process dynamics in the TMA algorithm. Despite the estimation errors, the proposed methodology improved the profit of the experimental case study, with respect to the use of an eMPC with no modifiers, by about 20% for the unconstrained case, and by 130% in the constrained case.

Hybrid Series/Parallel All-Nonlinear Dynamic-Static Neural Networks: Development, Training, and Application to Chemical Processes

This paper presents the development of data-driven hybrid nonlinear static-nonlinear dynamic neural network models and addresses the challenges of optimal estimation of parameters for such hybrid networks. A parallel static-dynamic neural network and two variants of series networks, specifically, nonlinear static-nonlinear dynamic and nonlinear dynamic-nonlinear static networks, are investigated in this work. Performances of the proposed fully nonlinear hybrid series and parallel network models are compared with the existing state-of-the-art data-driven models like long–short-term memory networks and gated recurrent unit models as well as DABNet-type linear-dynamic-nonlinear-static neural network. Algorithms are developed for training the series and parallel hybrid networks where the static and dynamic networks can be trained independently by different algorithms. These algorithms offer flexibility for incorporating different types of static and dynamic network architectures and their training algorithms thus offering tradeoff between computational expense and accuracy for highly nonlinear systems. In addition to the typical training objective that minimizes some squared error, an objective function is considered that penalizes overfitting and uncertainty in parameter estimates. Performances of the proposed algorithms are evaluated for three nonlinear example problems─a two-tank pH neutralization reactor, the widely used Van de Vusse reactor, and a pilot plant for postcombustion CO2 capture using monoethanolamine solvent. Computational expense and convergence performance of the proposed network architectures and their training algorithms are presented.

One-Layer Real-Time Optimization Using Reinforcement Learning: A Review with Guidelines

This paper reviews real-time optimization from a reinforcement learning point of view. The typical control and optimization system hierarchy depend on the layers of real-time optimization, supervisory control, and regulatory control. The literature about each mentioned layer is reviewed, supporting the proposal of a benchmark study of reinforcement learning using a one-layer approach. The multi-agent deep deterministic policy gradient algorithm was applied for economic optimization and control of the isothermal Van de Vusse reactor. The cooperative control agents allowed obtaining sufficiently robust control policies for the case study against the hybrid real-time optimization approach.

Trajectory tracking for nonlinear systems using extended quadratic port-Hamiltonian models without input and state coordinate transformations

In this note, an enhanced trajectory tracking (or equivalently, tracking-error) approach is developed for the control of nonlinear systems whenever the stage of feedback passivation design prior to synthesizing state feedback controllers is impossible. To achieve this purpose while using the original state vector to retain its interpretation, it is possible without the use of input and state coordinate transformations to combine the system dynamics with the so-called extended quadratic port-Hamiltonian (PH) models (including possibly the quadratic pseudo PH models) which are then divided into non-relaxing and relaxing ones for further study on control benefits. Interestingly, both cases are associated to a unifying quadratic Hamiltonian storage function similar to that of electrical, mechanical, or electromechanical systems with a specific insight. Sufficient conditions for the global asymptotic or exponential convergence of the system trajectory to the reference one are shown. In addition, a Proportional–Integral action can be added to the tracking control for improving the closed-loop performance and robustness. The proposed approach is illustrated via two case studies, including the non-minimum phase Van de Vusse reaction system and the 3-DOF SCARA robot.

Sparse Identification and SDRE based MRAC Scheme for a Van de Vusse Reactor

Sparse Identification and SDRE based MRAC Scheme for a Van de Vusse Reactor

Spiking PID Control Applied in the Van de Vusse Reaction

Artificial neural networks (ANN) can approximate signals and give interesting results in pattern recognition; some works use neural networks for control applications. However, biological neurons do not generate similar signals to the obtained by ANN. The spiking neurons are an interesting topic since they simulate the real behavior depicted by biological neurons. This paper employed a spiking neuron to compute a PID control, which is further applied to the Van de Vusse reaction. This reaction, as the inverse pendulum, is a benchmark used to work with systems that has inverse response producing the output to undershoot. One problem is how to code information that the neuron can interpret and decode the peak generated by the neuron to interpret the neuron's behavior. In this work, a spiking neuron is used to compute a PID control by coding in time the peaks generated by the neuron. The neuron has as synaptic weights the PID gains, and the peak observed in the axon is the coded control signal. The neuron adaptation tries to obtain the necessary weights to generate the peak instant necessary to control the chemical reaction. The simulation results show the possibility of using this kind of neuron for control issues and the possibility of using a spiking neural network to overcome the undershoot obtained due to the inverse response of the chemical reaction.

Advanced Construction of the Dynamic Matrix in Numerically Efficient Fuzzy MPC Algorithms

A method for the advanced construction of the dynamic matrix for Model Predictive Control (MPC) algorithms with linearization is proposed in the paper. It extends numerically efficient fuzzy algorithms utilizing skillful linearization. The algorithms combine the control performance offered by the MPC algorithms with nonlinear optimization (NMPC algorithms) with the numerical efficiency of the MPC algorithms based on linear models in which the optimization problem is a standard, easy-to-solve, quadratic programming problem with linear constraints. In the researched algorithms, the free response obtained using a nonlinear process model and the future trajectory of the control signals is used to construct an advanced dynamic matrix utilizing the easy-to-obtain fuzzy model. This leads to obtaining very good prediction and control quality very close to those offered by NMPC algorithms. The proposed approach is tested in the control system of a nonlinear chemical control plant—a CSTR reactor with the van de Vusse reaction.

Towards Necessary and Sufficient Stability Conditions for NMPC

Abstract The analysis of convergence and stability conditions for Non-linear Model Predictive Control (NMPC) schemes has seen significant progress during the last decades. Numerous results in the literature state sufficient conditions for convergence and/or stability of NMPC. Yet, necessary and sufficient conditions are—to the best of the author’s knowledge—not known and, given the variety of choices for MPC design, seemingly appear to be difficult. This paper analyzes the convergence of NMPC of continuous-time systems in time-invariant settings. We introduce the receding-horizon Hamiltonian—i.e., the value of the optimal control Hamiltonian along the sequence of OCPs—as a novel tool for stability/convergence analysis. Based on the assumption of strict dissipativity, we prove necessary and sufficient conditions for asymptotic convergence of the closed loop to the optimal steady state. Numerical results obtained for the Van de Vusse reactor illustrate the proposed conditions.

Robust data reconciliation in chemical reactors

Robust data reconciliation is an effective technique designed to minimize gross errors drawbacks over estimated process variables. This work presents a review focusing on chemical reactor problems, which generate a challenging scenario due to strongly nonlinear constraints and have not been compared in terms of several robust estimators. The main contribution is to present a comparative analysis of 16 robust estimators, including since Smith estimator, developed in the XIX century, until the newly Jin, Correntropy and Xie ones. The performance of these estimators was analyzed in three case studies under steady-state conditions, including a non-isothermal CSTR reactor with a Van de Vusse reaction system. It was used IPOPT and simulated annealing optimizers implemented in Scilab software. The results showed the efficiency and consistency of the implemented methods, and although the influence of gross errors was significant, the redescending type estimators like Correntropy, Xie and Biweight showed a better overall performance.

Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction—Application to a Chemical Reactor

In Model Predictive Control (MPC) algorithms, control signals are generated after solving optimization problems. If the model used for prediction is linear then the optimization problem is a standard, easy to solve, quadratic programming problem with linear constraints. However, such an algorithm may offer insufficient performance if applied to a nonlinear control plant. On the other hand, if a model used for prediction is nonlinear, then non–convex optimization problem must be solved at each algorithm iteration. Then the numerical problems may occur during solving it and the time needed to calculate the control signals cannot be determined. Therefore approaches based on linearized models are preferred in practical applications. A fuzzy algorithm with an advanced generation of the prediction is proposed in the article. The prediction is obtained in such a way that the algorithm is formulated as a quadratic optimization problem but offers performance very close to that of the MPC algorithm with nonlinear optimization. The efficiency of the proposed approach is demonstrated in the control system of a nonlinear chemical control plant—a CSTR (Continuous Stirred–Tank Reactor) with van de Vusse reaction.

Liquid Level System Realizing Van de Vusse Reactor Dynamics and its Control Experiments

Liquid Level System Realizing Van de Vusse Reactor Dynamics and its Control Experiments

Design and application of nonlinear model‐based tracking control schemes employing DEKF estimation

SummaryThis paper deals with the design and application of nonlinear model‐based control schemes for stable and nonlinear benchmark industrial processes. The primary control objective is to facilitate set‐point (constant/time‐varying) tracking in the presence of external disturbances, process noise, measurement noise, parametric uncertainty, and model mismatch. We first propose a “noninferential‐type” model‐based control scheme which involves a finite‐dimensional, nonlinear, and deterministic process model to generate the model states. Secondly, an “inferential‐type” model‐based control scheme has been introduced particularly to take into account the stochastic uncertainties such as process noise and measurement noise. The second scheme exploits the dual extended Kalman filter for estimating the immeasurable states and the process parameters through which disturbance is injected. Unlike fixed‐parameter controllers, the proposed schemes update the controller gains at each step depending on the real‐time process gains. In order to demonstrate the usefulness of the proposed closed‐loop tracking control schemes, two exhaustive case studies have been carried out on the CSTR and Van de Vusse reactor processes, which are considered to be benchmark industrial processes due to highly nonlinear and unpredictable behaviour and due to nonminimum phase property. Finally, the performance of the proposed schemes are compared with an EKF‐based adaptive PI control framework and the simulation results reveal that the transient performance of the proposed schemes are better than that of the aforementioned PI technique especially in perturbed condition (ie, in presence of model mismatch and measurement noise).

A comment on thermodynamically consistent feasibility condition of asymptotic observers

In this note, an extension of the design of asymptotic observers is proposed for the thermodynamically consistent non-isothermal continuous stirred tank reactor (involving nc active chemical species with nr independent reactions) that has incomplete state information. The two well-known constraints for the implementations of the asymptotic observer are the process operating conditions and the availability of temperature measurement together with (nr-1) concentration measurements. However, even though the process operating conditions are justified, the requirement of having good estimation performances and high accuracy of (nc-nr+1) state estimates may only be guaranteed if a so-called feasibility condition of the observer is fulfilled. This feasibility condition is formulated via the full rank constraint of a structural matrix, which is related to the stoichiometric coefficient matrix. A sufficient condition for the fulfilment of the full rank constraint shows that the process estimation selection is not made arbitrarily. Interestingly, as the designed observer is based on thermodynamic information only and does not require knowledge of reaction kinetics, the solution proposed to the feasibility condition has a clear physical meaning. Numerical simulations considered for Van de Vusse reaction system illustrate the application of the theoretical results.

Design of robust <i>H</i><SUB align="right">∞ fuzzy output feedback controller for affine nonlinear systems: fuzzy Lyapunov function approach

In this paper, we propose a new systematic approach based on non-quadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.

Design of robust H_ fuzzy output feedback controller for affine nonlinear systems: Fuzzy Lyapunov function approach

In this paper, we propose a new systematic approach based on non-quadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.

Tracking error plus damping injection control of non-minimum phase processes

This work proposes a passivity-based approach to deal with the output-tracking-error problem for a large class of nonlinear chemical processes including non-minimum phase systems. More precisely, in that framework, the system dynamics is firstly written into the relaxing (pseudo) port-Hamiltonian representation which does not necessarily require the positive semi-definite property of the damping matrix. Then, a reference trajectory associated with a certain structure passing through a desired equilibrium point (i.e., the set-point) is chosen so that the error dynamics can be globally asymptotically stabilized at the origin thanks to the assignment of an appropriate damping injection. This method is subsequently illustrated for a benchmark of multiple reactions systems, namely Van de Vusse reaction system. The numerical simulations show the applications of the proposed approach.