Van De Vusse Reaction Research Articles

Non-Smooth Optimization for Robust Control of Infinite-Dimensional Systems

We use a non-smooth trust-region method for $H_\infty$-control of infinite-dimensional systems. Our method applies in particular to distributed and boundary control of partial differential equations. It is computationally attractive as it avoids the use of system reduction or identification. For illustration the method is applied to control a reaction-convection-diffusion system, a Van de Vusse reactor, and to a cavity flow control problem.

ROBUST DATA RECONCILIATION IN A CHEMICAL REACTOR THROUGH SIMULATED ANNEALING OPTIMIZATION

Robust data reconciliation (RDR) is an effective technique designed to minimize/annul gross errors drawbacks over estimated process variables. In the present work, a brief review on heuristic optimization methods devoted to RDR in chemical processes is performed. Twelve robust estimators were evaluated, including Smith and Bell estimators, which were never before used within this context. The performance of these estimators was evaluated in a Van de Vusse reaction system, described by a nonlinear system of equations. The problem was solved by both the simulated annealing method and the IPOPT framework. The results showed the efficiency and consistency of both schemes and, despite the relevance of gross errors, the redescending estimators exhibited better global performance.

Sequential state inference of engineering systems through the particle move-reweighting algorithm

Intractable sequential inference arises in several applications in the physical engineering process. One of the most successful and efficient stochastic simulation techniques that is appropriate to perform the Bayesian inference (inversion decision) in complex dynamic models is the sequential Monte Carlo (SMC) methods. Although, these methods have become widely accepted among researchers and practitioners, in practice the manifestation of the path degeneracy implies a poor approximation of the target measures. This is an unavoidable deep problem when approximating sequence target models, and it becomes evident when strong non-linearity is presented. To deal with this drawback of the SMC methods, a promise mechanism is used to create particle diversity to move the particle according some kernel perturbation. In this article, we apply in three non-linear engineering dynamical systems (reservoir dynamics, van de Vusse reaction and pipe-in-pipe), a class of move algorithms, without the need to change the computational complexity called the move-regweighting scheme proposed by Marques and Storvik [(Particle move-reweighting strategies for online inference. Preprint series. Statistical Research Report (1), 2013]. Numerical simulations with different number of particles are performed to demonstrate the accuracy of the algorithm.

Inference of chemical reaction networks using mixed integer linear programming

Abstract The manual determination of chemical reaction networks (CRN) and reaction rate equations is cumbersome and becomes workload prohibitive for large systems. In this paper, a framework is developed that allows an almost entirely automated recovery of sets of reactions comprising a CRN using experimental data. A global CRN structure is used describing all feasible chemical reactions between chemical species, i.e. a superstructure. Network search within this superstructure using mixed integer linear programming (MILP) is designed to promote sparse connectivity and can integrate known structural properties using linear constraints. The identification procedure is successfully demonstrated using simulated noisy data for linear CRNs comprising two to seven species (modelling networks that can comprise up to forty two reactions) and for batch operation of the nonlinear Van de Vusse reaction. A further case study using real experimental data from a biodiesel reaction is also provided.

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.

An Efficient Measure for Quantification of Nonlinearity in Chemical Engineering Processes Based on I/O Steady-State Loci

Nonlinearity is virtually ubiquitous in chemical engineering plants, and assessing the degree of nonlinearity involved in a process is of special interest for process control purposes. In this paper, we introduce a simple nonlinearity measure to quantify the extent of nonlinearity in a dynamic system based on its normalized steady-state input/output loci. Our nonlinearity measure obviates the limitations of previous metrics in terms of computational effort and correct identification of highly nonlinear relationships. The measure is satisfactorily applicable to various I/O relationships—from truly linear to sinusoidal, for instance. In order to illustrate the efficiency of the proposed measure, four numerical examples concerning a double-effect evaporator, a jacketed continuously stirred tank reactor (CSTR) with an irreversible reaction, a CSTR involving van de Vusse reactions, and the Henson–Seborg–Pottmann CSTR are presented.

Constrained reachability and trajectory generation for flat systems

We consider the problem of trajectory generation for constrained differentially flat systems. Based on the topological properties of the set of admissible steady state values of a flat output we derive conditions which allow for an a priori verification of the feasibility of constrained set-point changes. We propose to utilize this relation to generate feasible trajectories. To this end we suggest to split the trajectory generation problem into two stages: (a) the planning of geometric reference paths in the flat output space combined with (b) an assignment of a dynamic motion to these paths. This assignment is based on a reduced optimal control problem. The unique feature of the approach is that due to the specific construction of the paths the optimal control problem to be solved is guaranteed to be feasible. To illustrate our results we consider a Van de Vusse reactor as an example.

Tuning of NMPC controllers via multi-objective optimisation

Nonlinear Model Predictive Control (NMPC) is a powerful technique that can be used to control many industrial processes. Different and often conflicting control objectives, e.g., reference tracking, disturbance rejection and minimum control effort, are typically present. Most often these objectives are translated into a single weighted sum (WS) objective function. This approach is widespread because it is easy to use and understand. However, selecting an appropriate set of weights for the objective function is often non-trivial and is mainly done by trial and error. The current study proposes a systematic procedure for tuning Nonlinear MPC based on multi-objective optimisation methods. Advanced methods allow an efficient solution of the multi-objective problem providing a systematic overview of the controller behaviour. Moreover, through analytic relations it is possible to link a solution obtained with these novel methods to a set of weights for a weighted sum objective function. Applying this set of weights causes the WS to generate the same solution as obtained with the advanced method. Hence, an appropriate controller can be selected based on the alternatives generated by the advanced method, while the corresponding weights for a WS can be derived for implementing the controller in practice. The procedure is successfully tested on two benchmark applications: the Van de Vusse reactor and the Tennessee Eastman plant.

Integrated OBF-NN models with enhanced extrapolation capability for nonlinear systems

This paper proposes a nonlinear system identification using parallel linear-plus-neural network models that provide more accurate predictions on the process behavior even on extrapolated regions. For this purpose, a residuals-based identification algorithm using parallel integration of linear orthonormal basis filters (OBF) and neural networks model is developed and analyzed under range extrapolations. Results on the van de Vusse reactor case study show enhanced extrapolation capability when compared to the conventional neural network (NN) and the series Wiener-NN models.

Selectivity engineering with single-feed hybrid reactive distillation columns

Reactive distillation (RD) can be advantageously used to improve the selectivity of the desired product in the multi-reaction system. Process synthesis and design of RD systems to attain the desired selectivity is a challenging task. Our previous work in this field (e.g. Amte et al., 2011, 2012) was restricted to fully reactive RD models and their networks. In this work, we examine the potential of a hybrid reactive distillation column, with both reactive and non-reactive sections, through an example of a single reactant complex reaction scheme (e.g. van de Vusse reaction) in which reactant is intermediate boiling. An algorithm for conceptual design of such columns is presented. It is based on the boundary value method (BVM) that utilizes the concept of operation leaves of rectifying and stripping sections; the overlap of which indicates the potential feasible split. Based on the desired selectivity, we determine the locus of reactive stage compositions in the RD column. Its intersections with the non-reactive stage composition lines (SCL) allow rapid screening of feasible designs of hybrid reactive distillation (HRD) columns. The approach generates multiple designs and allows one to compare them in terms of energy and catalyst requirement. The proposed method is applicable to single reactant single-feed hybrid columns, and because of its graphical representation, it cannot be directly used for systems with a large number of components. More work is therefore necessary to extend this approach to the multi-reactant double-feed hybrid configurations.

Tuning of PID Controllers for Continuous Stirred Tank Reactors

Tuning of proportional integral and derivative (PID) controllers for stable SOPTDZ (second order plus time delay with a zero) systems is proposed. The PID controller was designed based on internal model control and stability analysis principles. The proposed controllers were applied to the various stable transfer function models of jacketed CSTR, isothermal CSTR carrying out Van de Vusse reaction and a bioreactor. Simulation results on various transfer function models and on non-linear model equations of jacketed CSTR carrying first-order exothermic reaction, isothermal constant volume CSTR carrying out Van de Vusse reaction and a bioreactor are given to show the effectiveness of the proposed PID controllers. The performance under model uncertainty is also studied considering perturbation in one parameter at a time. The performance of the proposed controllers is compared with the controller designed by direct synthesis method.

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.

Nonlinear extended output feedback control for CSTRs with van de Vusse reaction

This paper developed an output-feedback control system for regulation of continuous stirred tank reactors (CSTRs) with van de Vusse reaction. The reactors are often used as benchmark representatives of nonminimum-phase processes. Control of such nonlinear processes is difficult because they exhibit the inverse response. Linear controllers usually give unsatisfactory results in this case and thus nonlinear control approaches are more suitable. The proposed control system consists of a nonlinear observer and an extended nonlinear state feedback controller. The extension consists in adding the integrator to the controller for improving steady state performance of the control system. Stability of the control system including the observer dynamics is guaranteed, thanks to the existence of an input-to-state Lyapunov function. Simulation studies are conducted to illustrate the effectiveness of the proposed control system and its robustness.

Attainable regions of reactive distillation—Part III. Complex reaction scheme: Van de Vusse reaction

The main underlying principle behind the application of reactive distillation (RD) for selectivity enhancement is to facilitate the separation of selected components and favorably manipulate the composition profiles in the reactive zone to expedite the desired reaction. In this paper, a geometric approach of attainable region (AR), which is already developed for conventional reactor network, is extended further to include few representative RD configurations. We define new RD building blocks and the corresponding composition vectors that indicate a need of networking of RD units among themselves and with conventional reactors to enlarge the set of attainable compositions. A model reaction scheme of van de Vusse type ( A ⟹ k 1 B ⟹ k 2 C , 2 A ⟹ k 3 D ) is studied as an illustrative example and an algorithm is developed to obtain the attainable region for the given kinetics, feed composition and relative volatilities. In almost all the different cases, which are studied by varying the kinetics and volatility pattern, network consisting of RD units performs better than the conventional reactor network.

Continuous stirred tank coalescence/redispersion reactor: A simulation study

This paper presents an analysis and detailed numerical study of the continuous stirred tank coalescence/redispersion reactor (CSTCRR), developed as a multidimensional population balance model combining a well-stirred reactor with the generalized coalescence/redispersion (gCR) model of micromixing. The gCR micromixing model is based on the concept of interactive population of fluid elements, identified as Kolmogorov microscale eddies under the given turbulence conditions, and represents mixing of chemical species on microscale by collision induced mass exchange processes. This model allows modelling diverse micromixing rates for different chemical species depending on their molecular diffusion properties. An infinite order multivariate moment equation model was elaborated by applying the joint moments of concentrations of chemical species from which a second order moment equation reduction was obtained by means of the cumulant-neglect closure method. The simulation results obtained by the second order moment equation model for the irreversible quasi-linear bimolecular and quadratic autocatalytic with linear decay reactions, and for the Van de Vusse reaction network revealed that the CSTCRR spans the whole range of variation of the micromixing intensity between the two micromixing extremes, i.e. perfect mixing and complete segregation, and it produces a smooth monotone sequence of product yields in the mixing space as the micromixing intensity is varied between these two extremes by modulating the rate determining parameters.

Robust H∞ control for Van de Vusse reactor via T–S fuzzy bilinear scheme

This paper proposes a fuzzy bilinear scheme including a fuzzy modeling method and a fuzzy controller for a class of uncertain nonlinear systems with an additive disturbance input. Firstly, this procedure of modeling describes how to transform a nonlinear system into a fuzzy bilinear system (FBS). For controller design problem, the parallel distributed compensation (PDC) method is adopted to design a fuzzy controller which ensures the robust asymptotic stability of the uncertain T–S FBS with an additive disturbance input and guarantees an H∞ norm bound constraint on disturbance attenuation. Besides, some sufficient conditions are derived to guarantee the robust stabilization of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, the Van de Vusse reactor (Chen, Lin, Lin, & Tong, 2008; Chong & Zak, 1996; Kashiwagi & Rong, 2002; Li, Tsai, Lee, Hsiao, & Chao, 2008; Perez, Ogunnaike, & Devasia, 2000) with additive disturbance input is utilized to demonstrate the validity and feasibility of the proposed control scheme.

Introduction to the special issue on optimal process control

Process engineers routinely use optimization in designing and operating complex systems as a means to improve their performance. Optimization has thus become a major enabling area over the years, where it has evolved from a methodology of academic interest into a technology that has and continues to make a significant impact on industry. To date, most rigorous optimization implementations have been for the design and operation of lumped systems using steady-state simulation and optimization technologies. However, a majority of natural as well as industrial systems either are inherently transient, have important transients between steady-state phases, and/or are spatially distributed. Interest in dynamic optimization and optimal control of process systems has grown significantly over the last few decades and much progress has been achieved in solution strategies. Despite its great potential, however, seldom has this technology made an impact on the process industry sector yet. Its implementation does not come without a cost. It requires a thorough understanding of the underlying phenomena, which is hardly compatible with the limited effort and time that can usually be spent for modeling. Moreover, a high level of expertise is still needed for the solution of optimal control problems (OCPs), which is itself a consequence of the lack of sufficiently fast and reliable numerical solution techniques. In this special issue of Optimal Control Applications and Methods, we have provided a selection of articles that address some of these issues and apply advanced techniques for the optimal operation, control and estimation of complex process systems. Bonilla et al. [1] propose a new method for solving nonconvex OCPs. Their method relies on a homotopy-based approach, whereby the original nonconvex OCP is gradually transformed into a simpler convex OCP by varying an homotopy parameter. A special structure is assumed for the nonconvex OCP, namely the dynamic system is control-affine and the cost function penalizes deviations from a given reference trajectory, which makes the method well suited for model predictive control (MPC) applications. They demonstrate their methodology on two case studies, a simple parameter estimation problem and the optimal control of an isothermal chemical reactor with Van de Vusse reactions and input multiplicities. They find that the likelihood of finding a global solution to the original nonconvex OCP is greatly improved compared to standard local optimization techniques. The paper by Aliyev and Gatzke [2] presents a nonlinear MPC formulation with prioritized constraint handling. This formulation is particularly relevant for control problems that have relatively limited degrees of freedom compared to the number of control objectives of interest. It ensures that the constrained optimization problem remains feasible at each MPC execution. They develop an implementation of prioritized MPC that is computationally efficient. A closed-loop test on multivariate refinery facility simulation with significant nonlinearity and input multiplicity is investigated. Because first principles’ models are difficult to obtain for such processes, second-order

A convexity‐based homotopy method for nonlinear optimization in model predictive control

AbstractThis paper presents a convexity‐based homotopy solution procedure to non‐convex optimal control problems (OCPs) arising in model predictive control. The approach deals with a special class of OCP formulations, where the dynamic system involved is control‐affine and the objective is a penalty on deviations from a state reference trajectory. The non‐convex OCP is modified by introducing a penalized pseudo state and a homotopy parameter which gradually transforms the original problem into a convex one. The method solves first this convex formulation and uses the result to initialize the solution of the next problem on the zero path, recovering the original OCP. The proposed methodology is evaluated for the benchmark control problem of an isothermal chemical reactor with Van de Vusse reactions and input multiplicity. For the simple case with control horizon one, the method is able to find the global solution due to the convex initialization, while local optimization techniques only lead to a local minimum. Copyright © 2010 John Wiley & Sons, Ltd.

Towards synthesis of an optimal thermal cracking reactor

To develop new reactor options for thermal cracking of ethane or other light hydrocarbons to lower olefins a fundamental process synthesis approach is taken. Firstly, an optimal reaction path and conditions are targeted, starting from a mechanistic reaction network. Secondly, to implement the optimal reaction path the reactor geometry and equipment are designed. This contribution focuses on the development of a targeting approach, for which a new distributive reaction-mixing synthesis model is formulated and applied. The mixing kernel in the model provides freedom to redistribute the reaction mixture along a continuous reaction coordinate to optimize product yield. The model was validated for two applications. It reproduces the results for the Van de Vusse reaction network as obtained by the attainable region theory. When applied to a small reaction network for the conversion of ethane into ethylene, it reconfirms the existing result that for this network the plug flow mode at maximum temperature and minimum pressure gives the optimal olefin yield.

Adaptive extremum-seeking control of convection-reaction distributed reactor with limited actuation

In this paper, we pose and solve an adaptive extremum control problem to optimize the productivity of a van de Vusse reaction taking place in a tubular reactor governed by a set of nonlinear hyperbolic partial differential equations. Estimation and control algorithms that take into account control input constraints are developed by using a Lyapunov-based procedure, ensuring stability and convergence under a persistency of excitation condition. Here, we assume that the temperature information along the reactor is the only available on-line measurement to estimate the unmeasured objective function at the reactor exit. Numerical application of the proposed method shows that the resulting feedback algorithm steers the system to its optimum using a non-distributed jacket temperature actuation. The time evolution of the cost function is compared with an idealized distributed version of the algorithm presented previously.