Continuous Stirred Tank Reactor Research Articles

Estimation of quality variables in a continuous train of reactors using recurrent neural networks-based soft sensors

The first stage in the industrial production of Styrene-Butadiene Rubber (SBR) typically consists in obtaining a latex from a train of continuous stirred tank reactors. Accurate real-time estimation of some key process variables is of paramount importance to ensure the production of high-quality rubber. Monitoring the mass conversion of monomers in the last reactor of the train is particularly important. To this effect, various soft sensors (SS) have been proposed, however they have not addressed the underlying complex dynamic relationships existing among the process variables. In this work, a SS based on recurrent neural networks (RNN) is developed to estimate the mass conversion in the last reactor of the train. The main challenge is to obtain an adequate estimate of the conversion both in its usual steady-state operation and during its frequent transient operating phases. Three architectures of RNN: Elman, GRU (Gated Recurrent Unit), and LSTM (Long Short-Term Memory) are compared to critically evaluate their performances. Moreover, a comprehensive analysis is conducted to assess the ability of these models to represent different operational modes of the train. The results reveal that the GRU network exhibits the best performance for estimating the mass conversion of monomers. Then, the performance of the proposed model is compared with a previously-developed SS, which was based on a linear estimation model with a Bayesian bias adaptation mechanism and the use of Control Charts for decision-making. The model proposed here proved to be more efficient for estimating the mass conversion of monomers, particularly during transient operating phases. Finally, to evaluate the methodology utilized for designing the SS, the same RNN architectures were trained to online estimate another quality variable: the mass fraction of Styrene bound to the copolymer. The obtained results were also acceptable.

Highly efficient maximum-likelihood identification methods for bilinear systems with colored noises

This paper mainly discussed the highly efficient iterative identification methods for bilinear systems with autoregressive moving average noise. Firstly, the input-output representation of the bilinear systems is derived through eliminating the unknown state variables in the model. Then based on the maximum-likelihood principle, a maximum-likelihood gradient-based iterative (ML-GI) algorithm is proposed to identify the parameters of the bilinear systems with colored noises. For improving the computational efficiency, the original identification model is divided into three sub-identification models with smaller dimensions and fewer parameters, and a hierarchical maximum-likelihood gradient-based iterative (H-ML-GI) algorithm is derived by using the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Finally, the algorithms are verified by a simulation example and a practical continuous stirred tank reactor (CSTR) example. The results show that the proposed algorithms are effective for identifying bilinear systems with colored noises and the H-ML-GI algorithm has a higher computational efficiency and a faster convergence rate than the ML-GI algorithm and the GI algorithm.

Source separation and anaerobic co-digestion of blackwater and food waste for biogas production and nutrient recovery.

Anaerobic co-digestion of source-separated blackwater (BW) and food and kitchen waste (FW) offers decentralized circular economy solutions by enabling local production of biogas and nutrient-rich byproducts. In this study, a 2 m3 pilot-scale continuously stirred tank reactor (CSTR) operated under mesophilic conditions was utilized for co-digestion of BW and FW. The process obtained a CH4 yield of 0.7 ± 0.2 m3/kg influent-volatile solid (VS), reaching a maximum yield of 1.1 ± 0.1 m3/kg influent-VS, with an average organic loading rate of 0.6 ± 0.1 kg-VS/m3/d and HRT of 25 days. The CH4 production rate averaged 0.4 ± 0.1 m3/m3/d, peaking at 0.6 ± 0.1 m3/m3/d. Treatment of digestate through flocculation followed by sedimentation recovered over 90% of ammonium nitrogen and potassium, and 80-85% of total phosphorus in the liquid fraction. This nutrient-rich liquid was used to cultivate Chlorella vulgaris, achieving a biomass concentration of 1.2 ± 0.1 g/L and 85 ± 3% and 78 ± 5% ammonium nitrogen and phosphorus removal efficiency, respectively. These findings not only highlight the feasibility of anaerobic co-digestion of source-separated BW and FW in local biogas production but also demonstrate the potential of microalgae cultivation as a sustainable approach to converting digestate into nutrient-rich algae biomass.

A fascinating exploration into nitrite accumulation into low concentration reactors using cutting-edge machine learning techniques

In the last couple decades, more use of nitrogenous chemical fertilizers and improper disposable of wastewater has harmed water and it cause water pollution. Low concentrated Nitrite (NO2) is the one of hazardous pollution and it is difficult to remove through biological processes, while it occurs in low concentration. Many technologies have been developed to accumulate NO2 in the mainstream. However, most of them use chemical inhibitors for nitrite oxidizing bacteria (NOB). In past studies high concentrated reactor performance have been modeled using mathematical models. In this study, machine learning application (MLA) was applied to model the performance of reactors. The reactor was low concentrated, continuous stirred tank reactor (CSTR) with in-fluent total ammonia nitrogen (TAN) concentration was (∼30PPM-TAN and ∼50PPM-TAN) and lower output TAN concentration was (∼1PPM-TAN). However, 216 days of water treatment data from CSTR were used, and the CSTR’s efficiency (%) of nitrite accumulation was estimated using in-fluent and effluent quantities. Then efficiency is predicted with 70 % of the data that is used to train the algorithms. Confusion matrix was used to access the performance of algorithms and actual and predicted classes (efficiencies) were compared. The DTC and XGB over-performed other algorithms.

In-situ biomethanation of high CO content syngas in agricultural biogas digesters

To meet global energy demands, syngas with high CO content (>50 %) generated from hydrothermal gasification of agricultural residues or wood, could be utilized as a co-substrate in anaerobic digestion (AD) processes for conversion into CH4. This study investigated in-situ biomethanation using synthetic gas (55 % CO, 35 % H2, and 15 % CO2), mimicking wood gasification syngas, during AD of cow manure, the most abundant agricultural waste. A continuously stirred tank reactor (CSTR) served as a control and was fed only cow manure, while the other two reactors were fed syngas with or without gas recirculation at different gas loading rates (GLRs).In-situ syngas injection in AD of cow manure at GLRs ≤0.3 L LRV−1 d−1 improved overall CH4 productivity compared to the control (0.35 ± 0.1 vs. 0.29 ± 0.1 L LRV−1 d−1), though the CH4 content (45 ± 5 %) was lower than the control reactor (62 ± 3 %), indicating a need for biogas upgrading. Gas recirculation enabled higher CO and H2 conversion efficiencies of 99–100 % but considerably decreased CH4 productivity from cow manure. In-situ biomethanation enhanced the relative abundance of hydrogenotrophic methanogens, highlighting their role in syngas conversion to CH4.

Quantitative Online Monitoring of an Immobilized Enzymatic Network by Ion Mobility-Mass Spectrometry.

The forward design of in vitro enzymatic reaction networks (ERNs) requires a detailed analysis of network kinetics and potentially hidden interactions between the substrates and enzymes. Although flow chemistry allows for a systematic exploration of how the networks adapt to continuously changing conditions, the analysis of the reaction products is often a bottleneck. Here, we report on the interface between a continuous stirred-tank reactor, in which an immobilized enzymatic network made of 12 enzymes is compartmentalized, and an ion mobility-mass spectrometer. Feeding uniformly 13C-labeled inputs to the enzymatic network generates all isotopically labeled reaction intermediates and products, which are individually detected by ion mobility-mass spectrometry (IMS-MS) based on their mass-to-charge ratios and inverse ion mobilities. The metabolic flux can be continuously and quantitatively monitored by diluting the ERN output with nonlabeled standards of known concentrations. The real-time quantitative data obtained by IMS-MS are then harnessed to train a model of network kinetics, which proves sufficiently predictive to control the ERN output after a single optimally designed experiment. The high resolution of the time-course data provided by this approach is an important stepping stone to design and control sizable and intricate ERNs.

Enhanced wastewater treatment with an AnF-AAO system for improved internal carbon source utilization

The main challenge in removing nutrients from municipal wastewater in China is the lack of available carbon sources. While hydrolysis acidification tanks can improve wastewater biodegradability by effectively utilizing internal carbon sources, high sludge concentrations are difficult to control in traditional tank variants. In this study, an innovative anaerobic filter (AnF) hydrolysis acidification reactor composed of a continuously stirred tank reactor (CSTR) and cloth media filter was designed to regulate and maintain high sludge concentrations in the hydrolysis acidifier. The reactor was used as a pretreatment unit for the anaerobic/anoxic/oxic (AAO) units and combined into an AnF-AAO system to explore the effectiveness of internal carbon source utilization in wastewater. The results indicate that as the sludge concentration in the hydrolysis acidifier increased, the hydrolysis and acidification processes became more efficient. The optimal sludge concentration was 40 g/L, which significantly increased the production of soluble chemical oxygen demand and volatile fatty acids. Above this concentration, the efficiency decreased. Compared to traditional AAO processes, the AnF-AAO system achieved superior total nitrogen and phosphorus removal with shorter hydraulic retention times and reduced sludge production by a significant amount of 35%. Due to its capacity for enhancing internal carbon source utilization, the AnF-AAO system constitutes a promising approach for sustainable urban wastewater treatment.

A dynamic compartmental model of a sequencing batch reactor (SBR) for biological phosphorus removal

ABSTRACT Bioreactors are usually modelled as continuous stirred tank reactors (CSTRs) or CSTRs connected in series (Tanks-In-Series configuration). In large systems with non-ideal mixing, such approaches do not sufficiently capture the complex hydrodynamics, leading to model inaccuracies due to the lumping of spatial gradients. Highly detailed computational fluid dynamics (CFD) models provide insight into complex hydrodynamics but are computationally too expensive for flow-sheet models and digital twin applications. A compartmental model (CM) can be a middle-ground by providing a more realistic representation of the hydrodynamics and still being computationally affordable. However, the hydrodynamics of a plant can be very different under varying flow conditions. Dynamic CMs can capture these changes in an elegant way. So far, the application of CMs has been limited mostly to continuous flow systems. In this study, a dynamic CM of a sequencing batch reactor (SBR) is developed for a bio-P removal process. The SBR comes with challenges for CM development due to its distinct operational stages. The dynamic CM shows significant improvements over the CSTR model (using the same biokinetic parameters) for dissolved oxygen and phosphate predictions reducing the need for model recalibration that can lead to over-fitting and limited extrapolation capability of the model.

Rapid Start-up of Continuous Autotrophic Nitrogen Removal Reactor by Hybrid-inoculating PN and PN/A Granular Sludges

The rapid cultivation of partial nitritation/ANAMMOX （PN/A） granular sludge in a continuous-flow mode is one of the key technologies for efficient biological nitrogen removal in domestic wastewater treatment. Compared with that in PN/A granular sludge, PN granular sludge demonstrates a shorter incubation period and suitability for batch culture. It is also a good carrier for enriching ANAMMOX （AMX） bacteria. In this study, we established a continuous-flow autotrophic nitrogen removal process in three continuously stirred tank reactors （CSTR） （R1-R3） by hybrid-inoculating PN/A and PN granular sludge at the mass ratios of 3∶1, 1∶1, and 1∶3, respectively. By implementing high ammonium nitrogen loading and short hydraulic retention time, continuous autotrophic nitrogen removal processes were successfully started up in the three CSTRs. The results showed that compared with that of R1 and R2, R3 had a longer start-up time but a similar steady-state nitrogen removal performance. The total nitrogen removal load of R3 could be more than 2.6 kg·（m3·d）-1. Intriguingly, the inoculated PN granular sludge served as a precursor for PN/A granular sludge cultivation. This approach facilitated the enrichment of anaerobic ammonia-oxidizing bacteria （AMX） by introducing abundant ammonium-oxidizing bacteria （AOB） and nitrite nitrogen substrates into the CSTR. According to the results of high-throughput sequencing, the microbial abundance and diversity of the mature granules in R1-R3 were significantly higher than those of the inoculation sludge. AOB （genus Nitrosomonas）, AMX （genera Candidatus Kuenenia and Candidatus Brocadia）, and symbiotic heterotrophs, such as Chloroflexi, Bacteroidetes, and Chlorobi, drove the autotrophic nitrogen removal process and maintained the stability of the granular structure. In summary, a novel start-up strategy of hybrid-inoculating granular sludge was provided for a continuous-flow autotrophic nitrogen removal in engineering application.

Data‐driven nonlinear state observation for controlled systems: A kernel method and its analysis

AbstractThis work proposes a data‐driven state observation algorithm for nonlinear dynamical systems, when the true state trajectory is not measurable and hence the states information needs to be reconstructed from input and output measurements. Such a reduction is formed by kernel canonical correlation analysis (KCCA), which (i) implicitly maps the available input–output data into a higher‐dimensional feature space, namely the reproducing kernel Hilbert space (RKHS); (ii) finds a projection of the past input–output data and a projection of the future input–output data with maximal correlation; and (iii) identifies the projected inputs and outputs, namely the canonical variates, as the observed states. We adopt a least squares support vector machine (LS‐SVM) formulation for KCCA, which imposes regularization on the vectors that specify the projections and is amenable to convex optimization. We prove theoretically that, based on the statistical consistency of KCCA, the observed states determined by the proposed state observer has a guaranteed correlativity with the actual states (when properly transformed). Furthermore, such observed states, when supplemented with the information of succeeding inputs, can be used to predict the succeeding outputs with guaranteed upper bound on the prediction error. Case studies are performed on two numerical examples and an exothermic continuously stirred tank reactor (CSTR).

Physics-informed neural networks with hard linear equality constraints

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are data-driven models and devoid of any physics. The incorporation of physics into neural networks can improve generalization and data efficiency. The physics-informed neural network (PINN) is an approach to leverage known physical constraints present in the data, but it cannot strictly satisfy them in the predictions. This work proposes a novel physics-informed neural network, KKT-hPINN, which rigorously guarantees hard linear equality constraints through projection layers derived from KKT conditions. Numerical experiments on Aspen models of a continuous stirred-tank reactor (CSTR) unit, an extractive distillation subsystem, and a chemical plant demonstrate that this model can further enhance the prediction accuracy.

Scaling study of miniaturised continuous stirred tank reactors via residence time distribution analysis and application in the production of iron oxide nanoparticles

Magnetically agitated miniaturised continuous stirred tank reactors (mCSTRs) are an attractive platform for the intensification of chemical reactions involving solids by combining active stirring and intensified heat and mass transfer due to their small dimensions. This work investigated the operation of mCSTRs at flowrates up to 60 ml/min (space time of 3 s per tank) as a means of increasing the throughput of fast reactions. Investigation of the residence time distribution under varying operational (flowrate, stirrer rotational speed) and reactor geometrical (stirred volume, stir bar size) parameters, showed deviation from the ideal CSTR behaviour at increasing flowrates, which could be mitigated by keeping the stir bar length close to the tank diameter, increasing stirrer rotational speed, and using larger tank sizes. Assembling mCSTRs into cascades did not amplify non-ideal behaviour and allowed narrowing the residence time distribution at high throughput. Various configurations of mCSTR cascades were evaluated for the synthesis of iron oxide nanoparticles (IONPs) via iron chloride co-precipitation with NaOH, demonstrating the importance of residence time distribution (RTD) control when increasing the throughput of nanoparticle production. Using a 5 × 3 ml mCSTR cascade for the core formation followed by a 5 × 3 ml mCSTR cascade for deagglomeration/stabilisation, the IONP flow synthesis was scaled successfully, producing high quality nanoparticles (7.3 ± 2 nm) at 60.5 ml/min (l/h scale).

Simultaneous state‐estimator tuning and parameter estimation for systems with nonstationary disturbances, multi‐rate data, and measurement delays

AbstractModel‐based monitoring and control of chemical and biochemical processes rely on state estimators such as extended Kalman filters (EKFs) to ensure accurate online model predictions. Accurate predictions depend on appropriate model parameters and suitable state‐estimator tuning factors. Extensions to our previously developed simultaneous parameter estimation and tuning (SPET) method are proposed so that SPET can be used for systems with nonstationary disturbances, time‐varying parameters, multi‐rate data, and measurement delays. A continuous stirred tank reactor (CSTR) case study with simulated data is used to illustrate and test the proposed method. Superior online model predictions and state‐estimator performance are achieved using SPET compared to a traditional approach for parameter estimation and EKF tuning, with improvements in the average sum‐of‐squared prediction errors ranging from 3% to 52% for the scenarios tested. The SPET approach will also be useful for more‐advanced state estimators that require the same tuning information as EKFs.

Process Parameter Optimization of Waste Polyethylene Terephthalate Bottle Neutral Hydrolysis Depolymerisation Using Process Simulation and Response Surface Methodology

The global surge in plastic production has led to a concerning accumulation of durable plastic waste in landfills and the environment. To address this issue, the depolymerization of waste polyethylene terephthalate (PET) through neutral hydrolysis has been proposed as a chemical recycling solution. Despite its potential environmental benefits, the endothermic nature of this process at high temperatures has raised doubts about its commercial feasibility. In response, this study was conducted to assess optimal conditions for waste PET depolymerization using neutral hydrolysis in a continuous stirred tank reactor with zinc acetate as a catalyst. Process simulation, aimed to manufacture pure terephthalic acid (TPA) and ethylene glycol from pelletized post-consumer PET bottles, was conducted with Aspen Plus Version 11. Sensitivity analysis explored the impact of factors such as reaction temperature, reaction time, PET flake size, and catalyst to PET ratio on both PET conversion and TPA yield. The study found that PET depolymerization increased with decreasing particle size, longer reaction times, increasing catalyst to PET ratio and reaction temperatures within the range of 200–240°C. Optimizing the process through response surface modelling revealed that key parameters for neutral hydrolysis considering a mean particle size of 20 mm were the ratio of water to PET, temperature, pressure, and reaction time with optimal values of 5:1, 225°C, 30 bar, and 67.5 min respectively. The model's reliability was confirmed through variance analysis, emphasizing the significance of main and interaction effects in the regression model.

Pilot-scale evaluation of cascade anaerobic digestion of mixed municipal wastewater treatment sludges.

This work assessed the performance of a pilot-scale cascade anaerobic digestion (AD) system when treating mixed municipal wastewater treatment sludges. The cascade system was compared with a conventional continuous stirred tank reactor (CSTR) digester (control) in terms of process performance, stability, and digestate quality. The results showed that the cascade system achieved higher volatile solids removal (VSR) efficiencies (28-48%) than that of the reference (25-41%) when operated at the same solids residence time (SRT) in the range of 11-15 days. When the SRT of the cascade system was reduced to 8days the VSR (32-36%) was only slightly less than that of the reference digester that was operated at a 15-day SRT (39-43%). Specific hydrolysis rates in the first stage of the cascade system were 66-152% higher than those of the reference. Additionally, the cascade system exhibited relatively stable effluent concentrations of volatile fatty acids (VFAs: 100-120 mg/l), while the corresponding concentrations in the control effluent demonstrated greater fluctuations (100-160 mg/l). The cascade system's effluent pH and VFA/alkalinity ratios were consistently maintained within the optimal range. During a dynamic test when the feed total solids concentration was doubled, total VFA concentrations (85-120 mg/l) in the cascade system were noticeably less than those (100-170 mg/l) of the control, while the pH and VFA/alkalinity levels remained in a stable range. The cascade system achieved higher total solids (TS) content in the dewatered digestate (19.4-26.8%) than the control (17.4-22.1%), and E. coli log reductions (2.0-4.1 log MPN/g TS) were considerably higher (p < 0.05) than those in the control (1.3-2.9 log MPN/g TS). Overall, operating multiple CSTRs in cascade mode at typical SRTs and mixed sludge ratios enhanced the performance, stability digesters, and digestate quality of AD. PRACTITIONER POINTS: Enhanced digestion of mixed sludge digestion with cascade system. Increased hydrolysis rates in the cascade system compared to a reference CSTR. More stable conditions for methanogen growth at both steady and dynamic states. Improved dewaterability and E. coli reduction of digestate from the cascade system.

The effects of drag models and operating condition on the simulation of photocatalytic degradation of pesticides in a fluidized bed reactor.

Fluidized bed reactor can enhance mass transfer and increase reaction rate. Numerical simulation helps to optimize fluidized bed reactors. The present paper models the photocatalytic oxidation of 2,4-dichlorophenoxy acetic acid in a fluidized bed reactor using the Eulerian-Eulerian model. The drag models have influences on the distribution of catalysts particles. The bed expands under the fluid flow and reaches a quasi-steady height at approximately 3s. The asymmetric distribution of catalysts with respect to the axis plane is predicted. The Gidaspow model predicts the nearly same bed expansion with the experimental data, whereas the Syamlal-O Brien model overestimates it. The simulation results at two pH values are in accordance with the experimental data. The removal in the continuous stirred tank reactor decreases with the increase in flow rate.

DEVELOPMENT AND ASSESSMENT OF MANUAL AND AUTOMATED PID CONTROLLERS FOR THE OPTIMUM PRODUCTION OF ETHYLENE GLYCOL IN A CSTR

Industrially, one of the techniques used to enhance the optimum production of petrochemicals is the configuration of process control units such as gas chromatography (G.C. Analyzer) for concentration and thermocouple for temperature in the production system. This research focused on the application of the principles of mass and energy conservation in the development of dynamic or unsteady state models for predicting the behaviour of the system or process involved in the production of ethylene glycol from a reaction involving oxidation of ethylene-to-ethylene oxide which further undergoes hydrolysis to produce ethylene glycol in a continuous stirred tank reactor (CSTR). The high mathematical complexities of the mass and energy balance models of the Process as a result of the reaction kinetic scheme of the non-elementary reaction of the process which integrated both linear and non-linear terms into the models were resolved by the application of the principles of Taylor’s series expansion, Laplace Transform, partial fraction and matrix in the development of the dynamic models. Process simulation tool (Simulink) was utilized in the configuration of closed-loop systems with thermocouple and G. C. Analyzer, at the feed point of the reactor for process variables (temperature and concentration) control during the process using proportional, integral and derivative (PID) as controller parameters. The results of the process behaviour showed that manual tuning of different controller parameters experienced a high level of fluctuations and would not attain its stability or steady state even at a processing time above 16 seconds. Whereas, automatic tuning of desired controller gains of 1.361, 1.056 and 0.4109 for K P, K I and K D for temperature and pressure with a tuning time of 143.9 Seconds, requires a maximum time of 8 seconds for the system to attain stability. This study showed that automated tuning of the controller resulted in better performance characteristics for optimum production of ethylene glycol in a non-isotheral continuous stirred tank reactor within the shortest possible time.

Genome-centric metagenomics and methanogenic pathway analysis for acclimated anaerobic digestion of chicken manure with high ammonia stressed under thermophilic condition

Thermophilic anaerobic digestion (AD) of animal manure offers various environmental benefits but the process requires a microbial community acclimatized to high ammonia. In current study, a lab-scale continuous stirred tank reactor (CSTR) fed with chicken manure was operated under thermophilic condition for 450 days in total. Results showed that the volumetric methane production decreased from 445 to 328 and sharply declined to 153 mL L−1·d−1 with feeding total solid (TS) step increased from 5% to 7.5% and 10%, respectively. While, after a long-term stop feeding for 80 days, highly disturbed reactor was able to recover methane generation to 739 mL L−1·d−1 at feeding TS of 10%. Isotope analysis indicted acetate converted to methane through the syntrophic acetate oxidation and hydrogenotrophic methanogenesis (SAO-HM) pathway increased from 33% to 63% as the concentration of ammonium increased from 2493 to 6258 mg L−1. Significant different in the genome expression of the SAO bacterial from 0.09% to 1.23%, combining with main hydrogenotrophic partners (Methanoculleus spp. and Methanothermobacter spp.) contented of 2.1% and 99.9% during inhibitory and recovery stages, respectively. The highly expressed KEGG pathway in level 3 (enzyme genes) for the Recovery sludge combining with the extraordinary high abundance of genera Halocella sp. suggested that Halocella sp. might be a highly efficient hydrolytic and acidogenic microorganism and enhance the process of SAO during carbon metabolic flow to methane. This report will be a basis for further study of AD studies on high nitrogen content of poultry manure.

Manifold embedding stationary subspace analysis for nonstationary process monitoring with industrial applications

Industrial processes frequently exhibit nonstationary characteristics due to factors like load fluctuations and external interference. Accurate monitoring of nonstationary industrial processes is of vital importance in ensuring production stability and safety. Unfortunately, most existing monitoring methods overlook the manifold structure presented in nonstationary data due to nonstationary features, causing the loss of critical information and poor interpretability. As a consequence, monitoring performance is compromised. To address this issue, this paper proposes a manifold embedding stationary subspace analysis (MESSA) algorithm. By embedding a neighborhood preservation term into the objective function of SSA, MESSA effectively mitigates the impact of nonstationarity on manifold structure. The extracted features incorporate both global stationarity and local manifold characteristics, facilitating a more comprehensive reconstruction of the intricate underlying mechanisms in industrial processes. This contributes to a substantial enhancement in the accuracy and reliability of process monitoring. A set of nonstationary swiss-roll dataset is designed to visually demonstrate the capability of MESSA in extracting manifold structure. Case studies including a numerical case, a continuous stirred tank reactor system and a real industrial roasting process validate the superior monitoring performance of the proposed method.

Stable predictive control of continuous stirred-tank reactors using deep learning

In this work, a Lyapunov-based predictive control method utilizing deep learning techniques is proposed for driving continuous-time nonlinear processes towards the desired equilibrium point. Initially, a neural ordinary differential equation model is developed to learn the continuous-time dynamics from discrete-time sampling data. Subsequently, the theoretical conditions that the control Lyapunov function (CLF) developed on the learned continuous-time system is feasible to act on the actual system through a zero-order-holder are analyzed. Building upon the theoretical analysis and the constructed continuous-time dynamics, a deep neural network control Lyapunov function (DNN-CLF) controller is developed. Importantly, the DNN-CLF is independent of the affine system formulation, effectively addressing the challenge of designing the CLF. Benefiting from the stability guarantee provided by the established DNN-CLF, it is integrated into the model predictive control (MPC) framework to develop Lyapunov-based MPC to further improve the control performance. To ensure safety, considering error propagation and associated risks with enlarging the feasible region of the CLF, tubes are constructed and integrated into the MPC scheme. Finally, a numerical simulation of a chemical process is conducted to validate the efficiency of the proposed method.