Continuous Stirred Tank Reactor System Research Articles

Adaptive Robust Control of Nonlinear Constrained Stirred‐Tank Reactors via Self‐Organizing Fuzzy Neural Network

ABSTRACTThis paper presents an adaptive robust constraint controller for a continuous stirred tank reactor (CSTR) system based on a self‐organizing fuzzy neural network (SOFNN). Due to the high complexity of the chemical reactions, the CSTR system contains many strong nonlinearities and uncertainties. This is the first time to introduce the SOFNN into the adaptive controller design of the CSTR system, which improves the adaptability to dynamic system changes through the adjustment of the fuzzy network structure. Meanwhile, the time‐varying integral barrier Lyapunov functions (TVIBLFs) are employed to ensure the dimensionless reactant concentration and mixture temperature within a reasonable scope, which can improve the stability and safety of the CSTR system. Based on Lyapunov stability analysis, all the signals in a closed‐loop system are ultimately bounded. Simulation results substantiate the efficacy of the proposed control scheme.

Advanced Control Strategies for Continuous Stirred Tank Reactors:

This paper investigates the control of a Continuous Stirred Tank Reactor (CSTR), with a primary emphasis on achieving temperature stability and optimizing reactant conversion. The CSTR poses challenges due to its nonlinear and exothermic behavior. To address these challenges, Model Predictive Control (MPC) is employed, a powerful strategy for handling complex systems. Additionally, Particle Swarm Optimization (PSO) is introduced to fine-tune MPC parameters, ensuring optimal performance. By integrating PSO with MPC, this study enhances control capabilities, specifically targeting the intricate demands of CSTR systems.

Performance of High-Gain Observer (HGO) For Level Estimation in Continuous Stirred Tank Reactor (CSTR)

This paper presents an estimation of level in CSTR system. Due to the non-linearity in the model of the CSTR system, our focus is on observers capable of handling this non-linearity. We proposed to use a High Gain Observer (HGO) for performing level estimation. The desired characteristics for estimation include minimal error, fast convergence time, and robustness in the presence of noisy measurements. A comprehensive analysis of the observers, including the evaluation of their effectiveness and robustness, is presented through simulation

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.

Data-driven auto-tuning strategy for RTO-MPC based on Bayesian optimization

Real-time optimization (RTO) and model predictive control (MPC) are extensively employed in industrial processes to enhance economic objectives. However, the tuning of the system remains a challenge, in particular, for cases where an explicit model relating the RTO objective and the process dynamics is unknown. To address this issue, an online data-driven auto-tuning strategy leveraging two Bayesian optimization (BO) techniques is proposed. This strategy is useful for situations where the RTO objective and the process dynamics are detectable but their exact functional forms are unclear. The proposed strategy views the RTO objective as a black-box objective and interprets the steady-state conditions as black-box equality constraints within the RTO layer. In this context, the upper-trust-bound based constrained BO (UTB-CBO) method is adopted to optimize the setpoints and enhance solution feasibility. Additionally, the proposed approach can take into account measurable disturbance inputs explicitly and account for their consequential influence on objective optimization by considering disturbance variations as contextual information. Simultaneously, another contextual BO scheme is implemented to automatically tune the MPC controller parameters for improving tracking performance upon accepting the setpoints optimized by the RTO. Simulation results based on a continuous stirred-tank reactor system are given to illustrate the effectiveness of the proposed approach.

Data-driven economic MPC with asymptotic stability and strong duality verification using Hankel matrix

We consider the problem of dynamic regulation with an economic cost function to control unknown linear systems, in which improving the economic performance and guaranteeing the stability of economical optimal equilibrium point are control objectives. A data-driven economic MPC scheme is presented using measured input-output trajectories without a prior system identification step. Our method uses Hankel matrices which include one input-output data trajectory for prediction in economic MPC, while persistently exciting of the input generating the data is needed. One of the novelties of the presented framework is directly verifying the strong duality property from input-output trajectory with the general cost function, considered as the supply rate. This is used to find a Lyapunov function for data-driven economic MPC. Under the strong duality assumption, asymptotic stability of the economical optimal equilibrium point for the closed-loop system with terminal equality constraint is guaranteed. The proposed data-driven economic MPC approach needs only persistently exciting data trajectory along with an upper bound on the system order and need no model description and no online parameter estimation. The proposed scheme applicability compared to the existing model-based economic MPC and data-driven MPC is illustrated for continuous stirred tank reactor (CSTR) and a numerical example and the robustness of the proposed scheme is evaluated in the case of measurement noise, as well as nonlinear model for CSTR system.

Optimal Tracking Neuro-Control of Continuous Stirred Tank Reactor Systems: A Dynamic Event-Driven Approach

Optimal Tracking Neuro-Control of Continuous Stirred Tank Reactor Systems: A Dynamic Event-Driven Approach

ANFIS and Takagi–Sugeno interval observers for fault diagnosis in bioprocess system

This paper develops a data-driven approach for incipient fault diagnosis based on ANFIS and Takagi–Sugeno (TS) interval observers. First, the nonlinear bioreactor system is identified using an adaptive neuro-fuzzy inference system (ANFIS), which results in a set of polytopic TS models derived from measurement data. Second, a bank of TS interval observers is deployed to detect sensor and process faults using adaptive thresholds. Unlike other works that require training fault data, only fault-free data is considered for ANFIS learning in this work. Fault insolation is based on residual generation and evaluated on a fault signal matrix (FSM). Parametric uncertainty and measurement noise are considered to guarantee the method’s robustness. The effectiveness of the proposed method is tested on a well-known bioreactor Continuous stirred tank reactor system (CSTR) reference simulator.

Causality-embedded reconstruction network for high-resolution fault identification in chemical process

Fault identification is essential for analyzing the root causes and propagation of faults. Traditional identification based on contribution plots often suffer from the smearing effect, a phenomenon where the residuals of fault variables smearing over other non-fault process variables due to the complex interconnections within the processes, potentially leading to ambiguous or inaccurate diagnosis. To address this, we propose the Causality-Embedded Reconstruction Network (CERN) based high-resolution fault identification for chemical process. CERN is an advanced graph network model that embeds causality, featuring a dual-decoding scheme comprising a causal decoder and an attribute decoder. This design ensures that feature reconstruction is guided by variables with established causal relationships, effectively isolating the feature representations of normal variables from the influence of fault variables that lack a causal connection. By leveraging this causality-embedded reconstruction, the smearing effect can be alleviated. Experiments conducted on a Continuous Stirred-Tank Reactor system and a real-world Continuous Catalytic Reforming process to demonstrate that the proposed CERN-based fault identification method not only improves the accuracy in identifying fault variables but also offers explanatory insights and traceability for fault diagnosis, showing prospects for industrial process safety.

A Cross-Layer Game-Theoretic Approach to Resilient Control of Networked Switched Systems Against DoS Attacks.

This article investigates the resilient control strategies of networked switched systems (NSSs) against denial-of-service (DoS) attacks and external disturbance. In the network layer, both the defender and the attacker allocate energy over multiple channels. Considering the impact of switching characteristic in the physical layer on the network layer, a dynamic regulating factor is proposed to adjust the total energy of the defender. To optimize the signal-to-interference-noise ratio and energy consumption simultaneously at each player's side, a multiobjective game problem is formulated. Furthermore, a nondominated sorting genetic algorithm framework is employed, incorporating the knee point selection mechanism to attain the Pareto-Nash equilibrium, based on which the optimal defense strategy can be derived to achieve resilience against DoS attacks. In the physical-layer, taking the dynamic packet loss caused by DoS attacks and external disturbance into account, an H∞ minimax controller containing control inputs and the switching signal is designed to guarantee the optimal performance for NSSs through the dynamic game-theoretic approach. Finally, the networked continuous stirred tank reactor system is provided to verify the effectiveness of the proposed method.

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.

Multiphase photochemistry in flow mode via an integrated continuous stirred tank reactor (CSTR) approach.

A new photochemical CSTR system capable of handling solids in scaled continuous processes is presented. High-power UV-LEDs are integrated in these CSTRs containing an insoluble base that aids in generating pyrazolines via cycloaddition between alkenes and in situ generated diazo species. Contrary to reported batch methods product degradation via ring contraction is suppressed whilst generating gram quantities of spirocyclic pyrazolines.

Recursive Delta-Operator-Based Subspace Identification with Fixed Data Size

This paper proposes a recursive delta-operator-based subspace identification method with fixed data size. The majority of existing subspace identification methods are constrained to discrete-time systems because of the disparity in Hankel matrices. Additionally, due to the storage cost, LQ-factorization and singular value decomposition in identification methods are best suited for batch processing rather than online identification. The continuous-time systems are transformed into state space models based on the delta-operator to address these issues. These models approach the original systems when the sampling interval approaches zero. The size of the data matrices is fixed to reduce the computing load. By fading the impact of past data on future data, the amount of data storage can be decreased. The effectiveness of the proposed method is illustrated by the continuous stirred tank reactor system.

Exploring the viability of a floating photocatalyst in a continuous stirred tank reactor system for continuous water treatment.

The use of photocatalysts in continuous stirred tank reactor (CSTR) systems allows for efficient and continuous water treatment, thus meeting the demand for scalable technology and comparative data in large-scale implementations. Hence, this study aims to explore the feasibility of a floating photocatalyst within a CSTR system for continuous water treatment. An expanded polystyrene (EPS)-TiO2 composite was synthesized following established methodologies, and their efficacy in removing the water pollutant methylene blue (MB) was compared for both batch and CSTR systems. A nonlinear first-order model was identified as the most suitable approach to accurately simulate MB degradation under experimental conditions, and the calculated pseudo-first-order degradation rate constant (k') for the CSTR system (0.0126-0.0172/min) was found to be superior to that observed for the batch system (0.0113/min). In addition, an increase in the flow rate reduced the retention time, leading to lower MB removal efficiency for the CSTR system. In addition, the EPS-TiO2/UV system with a CSTR configuration was found to efficiently use light and energy based on the calculated quantum yield (Φ = 2.86 × 10-4) and electrical energy per order (EEO = 857.46 kWh/m3/order). The findings of this study contribute to the development of sustainable and efficient water treatment strategies, offering valuable insight into the implementation of practical water treatment processes.

Residual neural network-based observer design for continuous stirred tank reactor systems

Continuous stirred tank reactor (CSTR) is a common reactor in the chemical industry. The accurate observation of the concentration conversion rate of the mixture and the internal temperature of the reaction vessel is a prerequisite for obtaining the desired mixture. This paper proposes a novel observer based on residual neural networks for CSTR systems. Firstly, the mathematical model of the CSTR reaction is given, as well as a detailed description of the structure and equations of the residual neural networks and the designed observer. Then the matrix method is used for the nonlinear isolation of the residual neural networks and the theory of quadratic constraints for nonlinear activation functions of the neural networks is applied. Thus, the convergence of the proposed observer is analyzed theoretically in detail. Finally, the numerical simulations are implemented to demonstrate that the proposed residual neural network-based observer can quickly and accurately observe the state changes during the CSTR reaction.

Decentralized $H_{\infty }$ Control for Switched Interconnected Large-Scale Systems: A Computationally Attractive Method

This article investigates the decentralized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controller design problems for switched interconnected large-scale systems (ILSSs). The designed decentralized controllers are dependent on the switching modes which can reduce the conservatism. Sufficient conditions are established for ensuring the asymptotic stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance of the studied switched ILSSs. Novel computationally attractive mode-dependent controller deign method is derived. The established controller design conditions eliminate the computationally expensive matrix inversion terms and are given in terms of linear matrix inequalities. Finally, the validness of the proposed decentralized controller design method is verified by the interconnected continuous stirred-tank reactor systems. Other three numerical examples are also performed to show the advantages and superiorities of the derived theoretical results.

A hybrid event-triggered stabilization approach for switched systems under asynchronous switching and its application

This paper investigates the stabilization problem of switched systems with mismatched modes by an event-triggered control approach. A hybrid event-triggered scheme (HETS) with a dynamically adjustable threshold is newly proposed, which combines periodic sampling, continuous event-trigger and slow switching. It is assumed that the modes and states of the controller are updated only at each triggering instant, so the situation of asynchronous switching could arise. Compared with the control strategy under static HETS, the proposed hybrid event-triggered control strategy has the advantage of potentially speeding up the stabilization while reducing the communication burden. To ease the analysis, the closed-loop system is accordingly represented as a combination of the switched system with a periodically sampled control input and the one with a continuously event-triggered control input. By considering input delay information in the construction of multiple Lyapunov–Krasovskii functional (LKF), a discontinuous and non-positive definite LKF is developed to establish sufficient conditions on the exponential stability for the closed-loop switched system. The design method of the desired controller and HETS is then provided. Finally, the result obtained in this paper is applied to a networked continuous stirred tank reactors system.

Adaptive Almost Passivity and Boundedness for Uncertain Switched Nonlinear Systems

This article proposes an almost passivity concept to describe the practical passivity property of switched nonlinear systems, whose subsystems are only passive outside a ball on their active time intervals. Based on this almost passivity concept, adaptive almost passification and boundedness property of a class of switched nonlinearly parameterized systems are studied. First, adaptive almost passification is achieved by the design of adaptive controllers and a switching law dependent on state for the systems whose subsystems have the relative degree one, even if each subsystem is not adaptive feedback almost passive. Second, for the system with any relative degree, the constructive design methods of adaptive controllers and switching law dependent on state are provided to achieve almost passivity by recursive feedback almost passification technique. Third, the ultimate boundedness of adaptive feedback almost passive system is proved using multiple storage functions method under the restricted condition on the energy changing of inactive subsystems. Finally, a continuous stirred tank reactor system is taken as an example to illustrate the effectiveness of the established theory.

An integrated structure of operational performance-oriented monitoring and degradation recovery based on iterative adaptive dynamic programming

Driven by the increasing industrial demands for process safety and product quality, this paper is devoted to operational performance monitoring and performance degradation recovery for closed-loop control systems under abnormal working conditions. To this end, a new operational performance indicator is designed and its benchmark with an explicit sensitivity criteria for selecting historical data, to detect the system degradation timely and accurately. Then, by embedding the operational performance indicator as a trigger condition, a data-driven performance degradation recovery method with the aid of iterative adaptive dynamic programming (ADP) algorithm is investigated. This implementation shows that iterative ADP can be applied efficiently by utilizing both value iteration and measurement data to recover the anomaly induced system performance degradation. Finally, a case study on the continuous stirred tank reactor system is provided to validate the effectiveness of these proposed methods.

Optimization of Levenberg Marquardt Algorithm Applied to Nonlinear Systems

As science and technology advance, industrial manufacturing processes get more complicated. Back Propagation Neural Network (BPNN) convergence is comparatively slower for processing nonlinear systems. The nonlinear system used in this study to evaluate the optimization of BPNN based on the LM algorithm proved the algorithm’s efficacy through a MATLAB simulation analysis. This paper examined the application impact of the enhanced approach using the Continuous stirred tank reactor (CSTR) control system as an example. The study’s findings demonstrate that the LM optimization algorithm’s identification error exceeds 10-5. The research’s suggested control approach for reactant concentration CA in CSTR systems provides a better tracking effect and a stronger anti-interference capacity. Compared to the PI control method, the overall control effect is superior. As a result, the optimization model for nonlinear systems has a greatly improved processing accuracy. With some data support for the accuracy study of neural network models and the application of nonlinear systems, the suggested LM-BP optimization algorithm is evidently more appropriate for nonlinear systems.