Continuous Stirred Tank Reactor System Research Articles

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.

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.

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.

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

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.

Continuous cultivation of Debaryomyces hansenii (LAF‐3 10 U) on dodecane in synthetic desalter effluent at varying dilution rates on dodecane

AbstractDesalter effluent (DE) is typically discharged into a petroleum wastewater treatment plant, but its high salt concentration deteriorates the biological treatment. This study used various dilution rates to investigate the treatment of a synthetic DE containing dodecane under saline conditions using a halotolerant yeast, Debaryomyces hansenii, to determine the optimum substrate concentration for use in continuous stirred‐tank reactors (CSTRs). A literature review indicated that this study was the first to examine the biological treatment of DE using D. hansenii in a CSTR system. At a low dodecane substrate concentration, DE did not inhibit D. hansenii growth, and the experimental data approached the Monod model, with μmax and Ks selected as 0.08 h−1 and 1575 mg L−1, respectively. The optimum removal of chemical oxygen demand (95.7% and 85%) was obtained at dilution rates of 0.007 and 0.026 d−1. Using D. hansenii in a CSTR system appeared to be a sustainable approach for the biological treatment of DE. Scale‐up of these laboratory findings to the industrial scale is required to confirm that petroleum DE can be treated using equalization and filtration tanks as a continuous bioreactor. Adjusting the dilution rate can provide sufficient time for biodegradation and hydrocarbon removal from high salt DE by halotolerant yeasts like D. hansenii.

Dynamic Event-Triggered Adaptive NN Control for Switched Uncertain Nonlinear Systems.

This article is concerned with the problem of dynamic event-triggered adaptive neural network (NN) control for a class of switched strict-feedback uncertainty nonlinear systems. A novel switched command filter-based dynamic event-triggered adaptive NN control approach is set up by exploiting the backstepping and command filter and the common Lyapunov function method. Since adaptive controllers of subsystems are event triggered, then if the switching happens between any two consecutive triggering instants, asynchronous switching will arise between candidate controllers of subsystems and subsystems. Unlike the existing literature, where maximum asynchronous time is restricted, without any strict limitations on maximum asynchronous time being needed in this article, the asynchronous switching problem is directly handled by proposing a novel switching dynamic event-triggered mechanism (DETM) and event-triggered adaptive controllers of subsystems. Moreover, a piecewise constant variable is introduced into the switching DETM, which overcomes the difficulty of switched measurement error being discontinuous. Also, a strictly positive lower bound of interevent times is obtained. Finally, a continuous stirred tank reactor system and a numerical example are presented to demonstrate the effectiveness of the developed approach.

Computing control invariant sets of cascade nonlinear systems: Decomposition and distributed computing

In this work, we present a distributed framework based on the graph algorithm for computing control invariant set for nonlinear cascade systems. The proposed algorithm exploits the structure of the interconnections within a process network. First, the overall system is decomposed into several subsystems with overlapping states. Second, the control invariant set for the subsystems are computed in a distributed manner. Finally, an approximation of the control invariant set for the overall system is reconstructed from the subsystem solutions and validated. We demonstrate the efficacy and convergence of the proposed method to the centralized graph-based algorithm using several numerical examples including a six dimensional continuous stirred tank reactor system.

A novel learning-based asynchronous sliding mode control for discrete-time semi-Markov jump systems

In this paper, a novel asynchronous sliding mode-based learning control is proposed for a class of discrete-time semi-Markov jump systems, in which the probability density function of sojourn-time is dependent on two consecutive modes. The asynchronous switching characteristic is employed for the nonsynchronization between the controller and the jump modes. Based on the discrete-time semi-Markov kernel and multiple-Lyapunov functions, sufficient conditions are provided to guarantee the σ-error mean-square stability of the sliding mode dynamics. Furthermore, a recursive sliding mode learning controller is designed such that the sliding modes can be driven onto the designed sliding surface and the chattering caused by the asynchronous switching and mode jump can be effectively suppressed. Finally, numerical simulations on the continuous stirred tank reactor system are given to demonstrate the effectiveness and potential of the proposed techniques.

Towards automated hazard analysis for CPS security with application to CSTR system

Hazard analysis to identify risks due to cyber attacks is crucial to ensure cyber–physical systems’ safety and correct their behavior. This study proposes a framework to analyze cyber–physical systems (CPS) risks using system dynamics to identify the critical physical components and hazardous interactions. We divide the input space into three regions, namely safe, alarm, and hazard zones, based on some given information and the dynamics of the CPS. These regions show how by manipulation of the critical inputs system can be driven to some predefined region. Moreover, using the concept of gap metric, we refine the list of the input value of vulnerable components to update the regions. Also, as a part of hazard analysis, we study and obtain the time needed to operate the system from a safe region to a hazard region by manipulating the inputs. The proposed framework uses the physical system’s model dynamics to simulate safe, alarm, and hazard mode activity. This framework’s primary goal is to provide decision-makers with a framework to evaluate CPS safety measures to implement adequate safety mechanisms. Model dynamics of continuous stirred tank reactor system (CSTR) has been employed to simulate the process under different manipulation of the input signal based on the proposed framework to identify the critical inputs and hazardous scenarios.

An Improved Particle Swarm Optimization with Multiple Strategies for PID Control System Design

In this paper, an improved particle swarm optimization (PSO) with multiple subpopulations is developed for PID control system designs. The original single population needs to be divided into several subpopulations, and each subpopulation then tackles a corresponding performance index of the system. Under this proposed structure, several PID controllers can be simultaneously designed to meet different performance indexes when the algorithm is executed only one time. It is a great improvement because the general PSO algorithm with a single population can only deal with one performance index. To demonstrate the feasibility of the proposed scheme, a complicated chemical nonlinear process called the continuously stirred tank reactor (CSTR) is illustrated. Three different kinds of control operations are simulated including the step response control, set-point tracking control, and unstable equilibrium point control. For each control case five different performance indexes are assigned to guide the PID controller design combined with the nonlinear CSTR system. Simulation results will sufficiently confirm the superiority of the proposed algorithm.

Incipient fault detection for dynamic chemical processes based on enhanced CVDA integrated with probability information and fault-sensitive features

Recently, canonical variate dissimilarity analysis (CVDA) has emerged as an efficient incipient fault monitoring method for dynamic chemical processes. Nevertheless, the basic CVDA method omits the mining of the probability information hidden in the canonical variate vectors and does not make full use of the fault-sensitive features provided by the prior fault data. Aiming at these two limitations, this paper presents an enhanced CVDA method, called fault-sensitive probability-related CVDA (FSPRCVDA), for better monitoring incipient faults. Firstly, the traditional CVDA is improved to the probability-related CVDA (PRCVDA) by applying the Kullback–Leibler divergence to measure the probability distribution changes of canonical variates. Secondly, fault-sensitive features are extracted by local Fisher discriminant analysis on the normal and prior fault data. The extracted fault-sensitive features are used to construct the auxiliary model for assisting the primary PRCVDA model, which leads to the holistic FSPRCVDA model. The case study on a continuous stirred tank reactor system shows that the proposed FSPRCVDA method has higher incipient fault detection rate than the basic CVDA method.