Continuous Stirred Tank Reactor Model Research Articles

End-to-end reinforcement learning of Koopman models for economic nonlinear model predictive control

(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic models that are sufficiently accurate and computationally tractable. Data-driven surrogate models for mechanistic models can reduce the computational burden of (e)NMPC; however, such models are typically trained by system identification for maximum prediction accuracy on simulation samples and perform suboptimally in (e)NMPC. We present a method for end-to-end reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We apply our method to two applications derived from an established nonlinear continuous stirred-tank reactor model. The controller performance is compared to that of (e)NMPCs utilizing models trained using system identification, and model-free neural network controllers trained using reinforcement learning. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC, and that, in contrast to the neural network controllers, the (e)NMPC controllers can react to changes in the control setting without retraining.

Numerical Simulation of the Thermal Destruction of Organophosphorous

The organophosphorus class of compounds has several usages nowadays. Some halogenated organophosphorus are used as flame retardants, and others are used as pesticides worldwide. In the last case, those compounds are subject to law regulation. They are now used as chemical weapons in many wars and terrorist attacks. Due to this variety of usages and the high toxicity of such compounds, the study of the proper treatment for residues containing those substances is significant to prevent the degradation of soil, water, and the atmosphere. For these reasons, the present study conducted numeric simulations of the incineration of organophosphorus compounds using kinetic models of combustion and pyrolysis found in the literature. The study of the degradation of this class of substances and the pollutant formation was made by simulating a homogeneous zeroth-order reactor and a continuous stirred tank reactor model. Due to the results of the simulations, the degradation made with the batch mode operation is efficient in the degradation of the substances considered in this work. The stream-containing process products have CO2, CO, HF, HOPO, and HOPO2. The three last cited have no determination about the emission ranges in the legislation, but their concentrations indicate the necessity of treatment for them. Furthermore, it was possible to evaluate the negative influence of the hydrocarbon used as fuel and the presence of CO2 in the degradation of the organophosphate compounds.

Data-Driven Control of Highly Interactive Systems using 3DoF Model-On-Demand MPC: Application to a MIMO CSTR

This paper presents a Three-Degree-of-Freedom Model Predictive Control (3DoF MPC) framework based on Multi-Input-Multi-Output (MIMO) “Model-on-Demand” (MoD) estimation. MoD is a data-centric weighted regression algorithm that generates local models over adaptively varying neighborhoods of changing operating conditions. The 3DoF formulation enables individualized tuning of parameters relating to setpoint tracking and measured and unmeasured disturbance rejection. Online estimation of system dynamics using MIMO MoD and augmentation with the 3DoF MPC structure allows the generation of control laws based on efficient locally linear approximations of system nonlinearities. This paper evaluates the framework through a case study involving a nonlinear MIMO Continuous Stirred Tank Reactor (CSTR) model. The MIMO CSTR system is highly interactive, making data-driven estimation and control notably more challenging than its SISO counterpart. The generation of an informative database using modified “zippered” multisines is presented. The paper concludes with a case study demonstrating the effectiveness of 3DoF MoD MPC in achieving constrained MIMO control of reactor concentration and temperature in the presence of disturbances through a flexible and intuitive approach.

Exploring chlorination as a removal process for antiretroviral drugs (Nevirapine and Efavirenz) from water: Effect of operational parameters, kinetics, and trihalomethane formation

This study investigates the removal of antiretroviral drugs (ARVs), Nevirapine (NVP) and Efavirenz (EFV), from drinking water through chlorination, focusing on the influence of pH, temperature, chlorine concentration, and ARV initial concentration on the degradation kinetics and trihalomethane (THM) formation. At 25 °C and an initial concentration of 100 μg/L, the degradation trends for both ARVs were examined across varying pH levels. EFV exhibited greater pH sensitivity, with removal increasing from 37 % at pH 5.5 to 68 % at pH 8, while NVP removal increased only from 40 % at pH 5.5 to 48 % at pH 8. Temperature also played an essential role, as the removal of both ARVs increased with rising temperature, indicating an endothermic reaction. Higher chlorine concentrations resulted in increased removal, >90 % at 5 mg/L for both ARVs. Kinetic analysis revealed second-order behaviour, with higher rate constants observed at pH 5.5–7 for NVP and pH 7–8 for EFV. The intrinsic chlorination rate constants for both ARVs were estimated. The calculated half-lives indicated slow removal. The study also assessed contact time for NVP and EFV in a plug-flow reactor (PFR) and continuous stirred tank reactor model (CSTR). Also considering hydraulic residence time (HRT) rather than reaction time to assess the average amount of time that the ARVs spent in the selected reactors. The HRT for a CSTR was lower than the PFR, and the estimated HRT for a CSTR was a feasible value. The minimum HRT came out to 1.56 h (pH 7.5 and a temperature of 25 °C) for NVP and 1.07 h (pH 7 and a temperature of 25 °C) for EFV. Finally, THM formation was observed, with chloroform, dibromochloromethane and bromoform detected. Among the three THMs, the most significant change occurred between 4 and 6 h, with chloroform levels increasing from 31.59 μg/L to 63.49 μg/L. This study underscores the influence of operational parameters on ARV removal via chlorination. Highlighting pH sensitivity, temperature control, precise chlorine dosage, and environmental concerns such as trihalomethane formation ensures effective disinfection while minimizing negative impacts on both water quality and the environment. Emphasizing the importance of a comprehensive approach to ARV removal in water treatment processes is a proactive measure that integrates considerations of environmental impact, public health, regulatory compliance, and long-term sustainability into the design and operation of water treatment facilities.

Parameter optimization of nonlinear PID controller using RBF neural network for continuous stirred tank reactor

The temperature system of the Continuous Stirred Tank Reactor (CSTR) has the characteristics of strong nonlinearity and uncertain parameters. The linear PID controller makes it difficult to meet CSTR’s control requirements. Nonlinear PID (NPID) can improve the control effect of nonlinear controlled objects, but due to the influence of nonlinear function selection and manual parameter setting, when parameters are uncertain or subject to external interference, the control performance of the system will decrease. To improve the adaptive capability of the NPID controller, the RBF-NPID control algorithm is proposed. The learning ability of RBF neural network is used to adjust NPID parameters online to improve the control performance of the system. In order to verify the effectiveness of the proposed algorithm, a CSTR model was established in MATLAB and algorithm comparison research was carried out. Simulation results show the effectiveness and superiority of the proposed algorithm.

Extensibility of a Machine Learning Model for Stormwater Basin Design and Retrofit Optimization Through a User-Friendly Web Application

To sequester particulate matter (PM) and chemical loads, stormwater basins are a common infrastructure component of transportation land use systems in a planning/design or a retrofit phase. Basin design relies on residence time (RT), capacity–inflow ratio (CIR), and continuous stirred-tank reactor (CSTR) concepts to provide presumptive guidance for load reduction. For example, 14-day (or 21-day) RT is presumed to provide load reduction for total suspended solids (TSS) (e.g., commonly 80%), and for total phosphorus (TP) (e.g., commonly 60%). Despite such guidance, most existing basins are impaired—not meeting presumptive guidance, whether for TSS, nutrients, or chemicals (e.g., metals). RT guidance results in high initial basin design costs (land and construction). For impaired basin retrofit, RT guidance generates a significantly higher cost (area/volume increase), if such a retrofit is even feasible considering proximate infrastructure constraints. This study presents a computational fluid dynamics (CFD)-machine learning (ML) augmented web application, DeepXtorm, for cost–benefit optimization of basin design and retrofit. DeepXtorm is examined against basin costs from as-built data, RT, CIR, and CSTR (deployed in the Storm Water Management Model [SWMM]) over a range of load reduction levels of TSS (60%–90%) and TP (40%–60%). For a given load reduction requirement, DeepXtorm demonstrates up to an order of magnitude (or more) lower basin cost compared with RT, CIR, and CSTR models, and greater than an order of magnitude compared with as-built cost data. DeepXtorm represents a more robust and cost-effective tool for stormwater basin design and retrofit.

Transient heat transfer during startup of a thermal plasma chamber: Numerical insights

Thermal plasma pyrolysis of radioactive waste is a recommended technique to manage large volume of combustible radioactive waste comprising of rubber and plastics. A lumped parameter based numerical model, to predict the thermal behavior of a plasma pyrolysis chamber during startup, is reported in this work. The model takes into account the non-ideal flow conditions inside the plasma chamber which are specific to the geometry of the chamber. Three different non-ideal models – a Continuous Stirred Tank Reactor (CSTR) having exchange with a separate perfectly mixed CSTR like geometry, two parallel CSTRs, and two parallel CSTRs with exchange, as well as an ideal single CSTR model have been compared. The models consider heat transport from plasma chamber interior to the walls through convection as well as radiation. Resistance offered by five successive layers of insulation of different materials has been considered. The predictions from the models are compared against experimentally determined evolution of chamber temperature during startup for three different power ratings of the plasma torch. The model formulation of two parallel CSTRs with exchange (a two-parameter model) is observed to fit the experimental data the best. A detailed sensitivity analysis has been carried out and the optimum model parameters are determined. Temperature evolution of different insulation layers has also been obtained. The validated model has been used to study the temperature response of the chamber during two different types of operating transients, viz. step changes in torch power and sinusoidal variation in torch power.

Hydraulic characteristics of small-scale constructed wetland based on residence time distribution

ABSTRACT This paper designs and builds a small constructed wetland test site to study the internal hydraulic characteristics of different types of constructed wetlands, conducts NaCl pulse tracing experiments, and fits the residence time distribution (RTD) with the CSTRs+PFD model (Continuous Stirred-Tank Reactor model in parallel with Plug Flow with Dispersion model). The results showed that, among the six types of constructed wetlands, hydraulic parameters of horizontal subsurface flow constructed wetlands with baffles had the best performance, with a tracer recovery rate (F(t)) reaching 43.67% and hydraulic efficiency (λ) reaching 0.81. The addition of baffles slowed flow velocity, increased mean hydraulic retention time (Tm ) and peak residence time (Tp ), and reduced the short circuits phenomenon. The velocity of internal water flow increased during the horizontal and vertical deflections, which could well avoid the stagnation phenomenon caused by complicated flow state, thereby improving the hydraulic efficiency (λ). The CSTRs+PFD model can better fit the RTD of 6 different types of constructed wetlands. The peak value of the fitted curve, the time to reach the peak and the slope of the curve are all very similar to the measured RTD.

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

AbstractA continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.

Optimized Fuzzy-Based Wavelet Neural Network Controller for a Non-Linear Process Control System

One of the common non-linear process control problems is the continuous stirred tank reactor problem and the reactor is applied widely in chemical process industries. It is of high importance to develop a suitable controller scheme for the concentration and temperature control of the considered non-linear continuous stirred tank reactor (CSTR) model. In this paper, a novel wavelet neural network (WNN) controller model is developed to carry out the control action and to meet the performance requirements of the system model. The developed wavelet neural network model is tuned for its weights employing the proposed deterministic grey wolf optimizer algorithm and its input is fed from the Mamdani fuzzy model. The optimal number of rules to be formulated for the fuzzy rule base model is computed using the deterministic grey wolf optimizer (DGWO) which is the variant of the classic grey wolf optimizer (GWO). WNN controller devise, based on the inputs from the fuzzy model and weights from DGWO, is designed to perform control action on the non-linear CSTR model. The concentration and temperature control is carried out by the proposed controller and the responses are obtained. Also, the respective time response specifications are evaluated for the developed WNN controller. Simulation experiments prove the effectiveness of the proposed controller for the considered non-linear CSTR model in comparison with that of the existing controllers from the literature.

Glucose-oxygen biofuel cell based on laccase cathode and gold-modified carbon black anode: experimental research and mathematical modelling

This research studies processes in membraneless mediatorless biofuel cell (BFC), including the processes of oxygen reduction at the cathode with a laccase-based catalyst and glucose oxidation at gold-modified carbon black (20Au/XC-72R) as an anode catalyst. The influence of the glucose quantity in the nutrient solution on the electrochemical activity of BFC was investigated. At pH=4.7 the highest power density of 2.6 µW/cm2 was obtained for a solution containing 0.5 M of glucose. It was found that the concentration of glucose in the range of 0.2-0.5 M does not affect the electrochemical activity of immobilized laccase. The mathematical model of the studied BFC was based on the continuous stirred-tank reactor model, the electrochemical processes occurring on the electrodes were taken into account. The BFC’s output characteristics were calculated, profiles of the concentration of participants of electrode reactions on current density, the discharge curves, profiles of the power density dependence on current density at glucose concentration in the range of 0.1-1.5 M were obtained. The electrodes’ reactions rates dependences on the current density of BFC confirm that the cathodic reaction is limiting. Optimization of the BFC operation modes showed that the optimal glucose content at the nutrition solution is 0.546 M.

Optimal Iterative Learning Control for Batch Processes in the Presence of Time-Varying Dynamics

Optimal iterative learning control (OILC) has been recognized as an excellent model-based means for regulating batch process with abundant successful applications reported in the past decades but also received considerable criticisms for its poor robustness against model mismatch that is common for many industrial situations. Despite numerous attempts to address the issue, many of them are still not able to yield satisfactory control performance particularly in the presence of a possible combination of time-varying uncertainties and conservatively designed controllers, which may compromise the learning mechanism, hence rendering the robustness issue of OILC far from well explored. This article intends to investigate the aforementioned issue by proposing a new OILC method resting upon the minimization of a dynamic upper bound on tracking error which is distilled from better exploitation of the time variation of uncertainties. We also show that the problem can be formulated in the framework of convex–concave game that can be efficiently solved by a subgradient method with an excellent balance of optimality and computation time. Such a formulation enables us to gain: 1) guaranteed monotonic convergence on tracking error; 2) remarkably reduced conservatism on controller synthesis; and 3) controllable computation complexity. It is further shown that the proposed method is capable of handling nonlinearity, for example Volterra system, a classic representation of nonlinear process. The efficacy of the method is verified by numerical experiments on a continuous stirred tank reactor model.

Kinetic modelling and performance evaluation of vertical subsurface flow constructed wetlands in tropics

The design of vertical subsurface flow (VSSF) constructed wetlands (CWs) uses kinetic models to calculate the area based on the kinetic reaction rate constant (k) specific to local environmental conditions and target pollutants. Currently, kinetic modelling does not fully account for the impact of the hydraulic loading rate (HLR), which influences the wetland performance. This study used four experimental VSSF CWs operated at HLRs of 5, 10, 20 and 40 cm/day to investigate the applicability of three first order kinetic models combining plug-flow and continuous stirred tank reactor (CSTR) flow patterns. The target pollutants were BOD5, NH4+ and NO3-. For each pollutant, estimated k values varied between different HLRs and between plug flow and CSTR models. Assessment of uncertainty in kinetic modelling showed that all three models exhibit a similar trend in predicting the concentrations of BOD5 and NH4+ at 5–20 cm/day HLRs. A substantial removal of BOD5 (>88 %) and NH4+ (>70 %) were found for the investigated HLRs, although NO3- removal was not satisfactory. The HLR had a positive impact on mass removal rates (MRRs) for BOD5 and NH4+. Accordingly, 20 cm/day was deemed as the highest viable HLR for designing effective VSSF wetlands for the removal of BOD5 and NH4+. All three models can be employed to design VSSF wetlands at 20 cm/day HLR to treat BOD5 using k values of 0.352 (k-C), 0.380 (k-C*) and 0.996 (CSTR) m/day and to treat NH4+ using k values of 0.170 (k-C), 0.173 (k-C*) and 0.273 (CSTR) m/day.

Linear Model Predictive Control for a Coupled CSTR and Axial Dispersion Tubular Reactor with Recycle

This manuscript addresses a novel output model predictive controller design for a representative model of continuous stirred-tank reactor (CSTR) and axial dispersion reactor with recycle. The underlying model takes the form of ODE-PDE in series and it is operated at an unstable point. The model predictive controller (MPC) design is explored to achieve optimal closed-loop system stabilization and to account for naturally present input and state constraints. The discrete representation of the system is obtained by application of the structure properties (stability, controllability and observability) preserving Cayley-Tustin discretization to the coupled system. The design of a discrete Luenberger observer is also considered to accomplish the output feedback MPC realization. Finally, the simulations demonstrate the performance of the controller, indicating proper stabilization and constraints satisfaction in the closed loop.

Fault separation and detection algorithm based on Mason Young Tracy decomposition and Gaussian mixture models

PurposeFor the large-scale power grid monitoring system equipment, its working environment is increasingly complex and the probability of fault or failure of the monitoring system is gradually increasing. This paper proposes a fault classification algorithm based on Gaussian mixture model (GMM), which can complete the automatic classification of fault and the elimination of fault sources in the monitoring system.Design/methodology/approachThe algorithm first defines the GMM and obtains the detection value of the fault classification through a method based on the causal Mason Young Tracy (MYT) decomposition under each normal distribution in the GMM. Then, the weight value of GMM is used to calculate weighted classification value of fault detection and separation, and by comparing the actual control limits with the classification result of GMM, the fault classification results are obtained.FindingsThe experiment on the defined non-thermostatic continuous stirred-tank reactor model shows that the algorithm proposed in this paper is superior to the traditional algorithm based on the causal MYT decomposition in fault detection and fault separation.Originality/valueThe proposed algorithm fundamentally solves the problem of fault detection and fault separation in large-scale systems and provides support for troubleshooting and identifying fault sources.

Self-sustained Oscillations in Oxidation of Propane Over Nickel: Experimental Study and Mathematical Modelling

The regular reaction rate oscillations were observed by mass-spectrometry in the oxidation of propane over the Ni foil. CO, CO2, H2, and H2O were detected as products. The oscillations of products and reactants in the gas phase were accompanied by the oscillations of the catalyst temperature. It was shown by using isotopic labeling 18O2 that CO and CO2 formed simultaneously by the propane oxidation when the catalyst was in the highly active state. The non-isothermal model of a continuous stirred-tank reactor based on a microkinetic scheme including 50 reaction steps was developed. The model takes into account periodic oxidation and reduction of nickel and formation of main products. Using the method of quasi-steady-state approximations, it was shown that the observed self-sustained oscillations are associated with periodic changes in the coverage of the Ni surface by adsorbed oxygen and carbon as well as nickel oxide species. It was shown that the microkinetic scheme coupled with a continuous stirred-tank reactor model qualitatively describes the experimental data if the model also considers the periodic processes of oxidation and reduction of the Ni bulk.

Stormwater Efficiency of Bioretention Functions and Reactor Modelling Systems

Bioretention is a practical modern best management practices for stormwater control and are a conspicuous sort of vegetated stormwater foundation that functions for the different ecosystem. This paper discussion focusses on bioretention system functions (BSF) and reactor modeling (RM) review. Bioretention plays an essential role in carbon sequestration, as an alleviation process, to reduce global warming in the environment. Also, it functions for runoff infiltration, storage, and water uptake by vegetation. The base layer of a bioretention actively improves the denitrification capacity of the system and promotes the effective removal of phosphorus and nitrogen. Bioretention design soil ratio, plant types, and flow regime influence the efficiency of contaminants removal in the denitrification process. Bioretention beautifies the environment, and the utilization of compost in bioretention is on account of its water-holding and improved infiltration capacity, thereby improving water quality. The reactor modeling chemical description is through equations and kinetic models. The chemical computation of biological processes of pollutant nutrient removal from stormwater is in the form of a number equation. The models explored are first-order removal model, second order, plug flow patterns models, Monod and multiple Monod kinetics, continuous stirred-tank reactor model, and tank-in Series flow models.

Robust adaptive neural network prescribed performance control for uncertain CSTR system with input nonlinearities and external disturbance

In this paper, the control problem for continuously stirred tank reactor (CSTR) systems with input nonlinearities and unknown disturbances is addressed. To ensure constraints satisfaction on the input and the output of CSTR, we employ a system transformation technique to transform the original constrained model of CSTR into an equivalent unconstrained model, whose stability is sufficient to achieve the tracking control of the original CSTR system with a priori prescribed performance. To deal with two kinds of input nonlinearities, two neural networks (NNs)-based adaptive controllers are proposed. In the first approach, a robust control term is introduced to overcome the effects of the unknown input dead zone; however, in the second approach, an anti-windup compensator is designed to reduce the influence of the actuator saturation. In the proposed control methods, NNs are employed to approximate the unknown dynamics of CSTR and additional adaptive compensators are introduced to cope with NNs approximation errors and external disturbance. The proposed adaptive neural tracking controllers are designed with only one adaptive parameter by using the second Lyapunov stability method. In comparison with the traditional back-stepping-based techniques, usually used in CSTR control, the structures of the proposed controllers are much simpler with few design parameters since the causes for the problem of complexity growing are completely eliminated. Simulation results are presented to show the effectiveness of the proposed controllers.

Input Design for Continuous Time Output Error Models

In this paper, the problem of input design for identification of continuous time output error models is considered. The input design problem is formulated as maximization of a measure of the Fisher Information Matrix, which defines the accuracy with which the system parameters can be estimated. The optimization problem involving the Fisher Information matrix depends on the true system parameters, which are unknown. Existing methods use an iterative approach to tackle this circular dependency. In this paper, the system transfer function is represented using generalized orthonormal basis functions which makes the Fisher Information matrix independent of the true system parameters. Therefore, the input design problem reduces to solving a single optimization problem instead of a series of optimizations that are performed in existing methods. Further, in existing approaches, the computational complexity of the optimization grows with the length of the input vector to be identified. In the current paper, the input is also represented using smooth basis functions, thereby making the complexity independent of the length of the input vector. A least squares approach for parameter estimation is given and it is shown that the estimates are unbiased for the optimal inputs. The accuracy of the proposed method is demonstrated with the help of two examples. Further, input design for a continuous stirred tank reactor model and a quadruple tank experimental set up is considered in order to demonstrate the practical applicability of the new method.

A hybrid constructed wetland for organic-material and nutrient removal from sewage: Process performance and multi-kinetic models

A pilot-scale hybrid constructed wetland with vertical flow and horizontal flow in series was constructed and used to investigate organic material and nutrient removal rate constants for wastewater treatment and establish a practical predictive model for use. For this purpose, the performance of multiple parameters was statistically evaluated during the process and predictive models were suggested. The measurement of the kinetic rate constant was based on the use of the first-order derivation and Monod kinetic derivation (Monod) paired with a plug flow reactor (PFR) and a continuously stirred tank reactor (CSTR). Both the Lindeman, Merenda, and Gold (LMG) analysis and Bayesian model averaging (BMA) method were employed for identifying the relative importance of variables and their optimal multiple regression (MR). The results showed that the first-order–PFR (M2) model did not fit the data (P > 0.05, and R2 < 0.5), whereas the first-order–CSTR (M1) model for the chemical oxygen demand (CODCr) and Monod–CSTR (M3) model for the CODCr and ammonium nitrogen (NH4−N) showed a high correlation with the experimental data (R2 > 0.5). The pollutant removal rates in the case of M1 were 0.19 m/d (CODCr) and those for M3 were 25.2 g/m2∙d for CODCr and 2.63 g/m2∙d for NH4-N. By applying a multi-variable linear regression method, the optimal empirical models were established for predicting the final effluent concentration of five days' biochemical oxygen demand (BOD5) and NH4-N. In general, the hydraulic loading rate was considered an important variable having a high value of relative importance, which appeared in all the optimal predictive models.