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Agent-based control of autocatalytic replicators in networks of reactors
Abstract
Spatially distributed systems such as reactor networks hosting multiple autocatalytic species demonstrate a rich spectrum of complex behavior. From a control systems perspective, spatially distributed systems offer a difficult control challenge because of their distributed nature, nonlinearity, and high order. Furthermore, manipulation of the network states may require simultaneous control actions in different parts of the system and may need transients through several operating regimes to achieve the desired operation. The lack of accurate and computationally efficient model-based techniques for large, spatially distributed systems results in complications in controlling the system, either in disturbance rejection or changing the operational regimes of the system. A hierarchical, agent-based control structure is presented whereby local control objectives may be changed in order to achieve the global control objective. The performance of the control system is demonstrated for several global objectives. The challenge posed is to control the spatial distribution of autocatalytic species in a network of five reactors hosting two species using the interaction flow rates as the manipulated variables. The multi-agent control system is able to effectively explore the parameter space of the network and intelligently manipulate the network flow rates such that the desired spatial distribution of species is achieved.
... Hybrid control systems that combine process dynamics and discrete control elements and include multiple models for different operating points are one way to develop control systems for spatially distributed systems (Morari et al., 2003;Christofides and El-Farra, 2005). An alternative approach is based on a hierarchical agent-based system with local and global control structures (Tatara et al., 2005c;Tatara et al., 2005b) that has been demonstrated on a network of interconnected continuous stirred tank reactors (CSTRs). Reactor networks exhibit highly complex behavior with multiple steady state operating regimes and have a large pool of candidates for manipulated variables (Tatara et al., 2004). ...
... Required agent types and roles are identified based on the requirements for controlling the physical system. The details of the hierarchical agent-based architecture (Tatara et al., 2005b;Tatara et al., 2005a) will not be repeated in detail here. The focus will rather be on the specific agent synthesis and instantiation for the presented examples. ...
... Therefore, the control agent for each reactor should prevent the invasion of the reactor for which it is responsible. For neighboring competitors, this control function can be achieved by the previously detailed methods of local agent control via the interaction rates (Tatara et al., 2005b). However, in the case where a new, more aggressive autocatalytic species is introduced to the network, these methods may fail. ...
Large-scale spatially distributed systems provide control challenges because of their nonlinearity, spatial distribution and generally high order. The control structure for these systems tend to be both discrete and distributed. A layered control structure interfaced with complex arrays of sensors and actuators provides a flexible supervision and control system that can deal with local and global challenges. An adaptive agent-based control structure is presented whereby local control objectives may be changed in order to achieve the global control objective. Information is shared through a global knowledge environment that promotes the distribution of ideas through reinforcement. The performance of the agent-based control approach is illustrated in a case study where the interaction front between two competing autocatalytic species is moved from one spatial configuration to another. The multi-agent control system is able to effectively explore the parameter space of the network and intelligently manipulate the network flow rates such that the desired spatial distribution of species is achieved.
... So-called hybrid control systems combine process dynamics and discrete control elements through the use of multiple linear models at different operating points [2,3]. One alternative approach is based on a hierarchical agent-based system with local and global control structures [4] that has been demonstrated on a network of interconnected continuous stirred tank reactors (CSTRs). These reactor networks can represent many population dynamics problems when specific types of chemical reactions take place in them. ...
... A hierarchical agent-based architecture has been recently developed for the control of spatially distributed chemical reactor networks [4]. The architecture consists of several sub-systems, each of which are highly modularized ( Figure 1). ...
Large-scale spatially distributed systems provide a unique and difficult control challenge because of their nonlinearity,
spatialdistribution and generally high order. The control structure for these systems tend to be both discrete and distributed
as well and contain discrete and continuous elements. A layered control structure interfaced with complex arrays of sensors
and actuators provides a flexible supervision and control system that can deal with local and global challenges. An adaptive
agent-based control structure is presented whereby local control objectives may be changed in order to achieve the global
control objective. Information is shared through a global knowledge environment that promotes the distribution of ideas through
reinforcement. The performance of the agent-based control approach is illustrated in a case study where the interaction front
between two competing autocatalytic species is moved from one spatial configuration to another. The multi-agent control system
is able to effectively explore the parameter space of the network and intelligently manipulate the network flow rates such
that the desired spatial distribution of species is achieved.
... In the literature, multi-agent systems have been used in many modeling and simulation applications. Agent-based systems are proposed for conceptual design and synthesis of chemical processes (Han et al. 1995), supply chain management (Julka et al. 2002a, b;Mele et al. 2007) and controller design (Tatara et al. 2005;Tetiker et al. 2008). However, concerning to multi-agent optimization for process systems engineering problems, very few articles have appeared, and they are limited to small-scale problems (Siirola et al. 2003(Siirola et al. , 2004. ...
Multi-agent optimization method is a nature-inspired framework that supports the cooperative search of an optimal solution of an optimization problem by a group of algorithmic agents connected through an environment with certain predefined information sharing protocol. In this work, we propose a novel heterogeneous multi-agent optimization (HTMAO) framework. The proposed framework is validated using a set of benchmark problems a real-world synthesizing radioactive waste blending problem. The optimal radioactive waste blending problem is formulated as a mixed integer nonlinear programming. The total frit used for vitrification process is minimized subject to thermodynamic properties and process model constraints. The model simultaneously determines the optimal decisions that include the combination of the waste tanks that form each waste blend and the amount of frit needed for the vitrification of each waste blend. In developing the HTMAO framework, efficient ant colony optimization algorithms; efficient simulated annealing; efficient genetic algorithm; and sequential quadratic programming solver are considered as algorithmic agents. We illustrate this approach through a real-world case study of the optimal radioactive waste blending of Hanford site in Southern Washington where nuclear waste is stored.
... Once the final configuration is found, the second sub problem is to decide on the actions to be taken in the correct order to move the system from its current state to the final state. Earlier works demonstrated autocatalytic reactions in CSTR networks to simulate population dynamics, multiple species of organisms that compete on same resources, or chemical manufacturing problems (Tatara et al., 2004;Tatara et al., 2005a;Tatara et al., 2005b). Controlling the spatial distribution of autocatalytic species that compete for the same resources in a network of reactors can be achieved by simultaneous manipulation of interconnection flow rates within the system. ...
Agent-based control structures provide flexible and emergent solutions to complex nonlinear problems benefiting from properties such as modularity, adaptability, scalability and robustness. One such problem is product grade transitions in distributed process. The framework proposed earlier (Tetiker, 2006a) is extended by adding several layers of agents to control species percentage distribution in autocatalytic reactor networks. A deadlock detection layer is implemented to detect and solve conflicting cases between local controller agents. An auctioning mechanism is employed to promote competition between local controller agents leading to emergent solutions satisfying global constraints. The proposed architecture performed successfully to change the species percentage distributions without specifying the final configuration.
... So-called hybrid control systems combine process dynamics and discrete control elements through the use of multiple linear models at different operating points Baotic et al., 2003). An alternative approach is based on a hierarchical agent-based system with local and global control structures (Tatara et al., 2004a). ...
From a control system perspective, spatially distributed systems offer challenges because of their distributed nature, nonlinearity, and high order. In addition, the control structure for these spatially distributed networks combine discrete and distributed components, in the form of complex arrays of sensors and actuators. Manipulation of the network states may require simultaneous control actions in different parts of the system and may need transients through several operating regimes to achieve the desired operation. A hierarchical, agent-based control structure is presented whereby local control objectives may be changed in order to achieve the global control objective. The performance of the hierarchical agent-based control approach is illustrated in a case study where the interaction front between two competing autocatalytic species is moved from one spatial configuration to another.The multi-agent control system is able to effectively explore the parameter space of the network and intelligently manipulate the network flow rates such that the desired spatial distribution of species is achieved.
... 27,28 The agent-based approach can provide an efficient solution to the scheduling problem, and it can tackle uncertainties in a real process. As a promising alternative for solving scheduling problems, a great number of agent-based techniques have been presented (see examples [29][30][31][32][33][34][35][36][37][38] ). Correspondingly, various toolkits and frameworks have been developed to facilitate the software development and administration of agent-based applications. ...
A novel efficient agent‐based method for scheduling network batch processes in the process industry is proposed. The agent‐based model is based on the resource‐task network. To overcome the drawback of localized solutions found in conventional agent‐based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function value by simulating another cloned agent‐based model. Global information is obtained, and the solution quality is improved. The solution quality of this approach is validated by detailed comparisons with the mixed‐integer programming (MIP) methods. A solution close to the optimal one can be found by the agent‐based method with a much shorter computational time than the MIP methods. As a scheduling problem becomes increasingly complicated with increased scale, more specifications, and uncertainties, the advantages of the agent‐based method become more evident. The proposed method is applied to simulated industrial problems where the MIP methods require excessive computational resources. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2884–2906, 2013
... The safe-parking framework has been extended to handle uncertainty and measurement unavailability in [8], and to handle faults for units in series in [9]. However, most processes in chemical industries use a complex integration of streams for many purposes, such as processing raw feedstock or improving the heat economy of the plant (see, e.g., [10] for control designs considering the networked nature of the system). The safe-parking mechanism for an isolated unit or units in series may not remain effective in the context of complex networked structures. ...
This work considers the problem of fault detection and isolation (FDI) and fault-handling for networked systems subject to actuator faults. The faults considered preclude the possibility of nominal operation in the affected unit. First, a model-based methodology is presented to detect and isolate faults with the explicit consideration of uncertainty. Then, an algorithm is developed to generalize the safe-parking approach for fault-tolerant control to account for complex interconnections such as parallel and recycle structures in networked systems. The efficacy of the integrated FDI and safe-parking framework is demonstrated through a chemical process example.
... Remark 1: By limiting the rate at which measurements from a given unit need to be communicated to the rest of the plant, the quasi-decentralized control structure offers a possible compromise (in terms of implementation) between the complexity of traditional centralized controllers and the performance limitations of fully decentralized control schemes (e.g., see [17], [18], [19] ). The problem of controlling large-scale multi-unit plants has also been studied within other frameworks, such as passivity-based control [20], distributed model predictive control (e.g., [21], [22]), agent-based systems [23] and singular perturbation for- mulations [24]. In these works, however, the problem of integrating WSNs into the plant-wide control structure and the subsequent communication issues that this raises have not been studied. ...
This paper develops a model-based networked control and scheduling framework for plants with interconnected units and distributed control systems that exchange information using a resource-constrained wireless sensor network (WSN). The framework aims to enforce closed-loop stability while simultaneously minimizing the rate at which each node in the WSN must collect and transmit measurements so as to conserve the limited resources of the wireless devices and extend the lifetime of the network as much as possible. Initially, the exchange of information between the local control systems is reduced by embedding, within each control system, dynamic models that provide forecasts of the evolution of the plant units when measurements are not transmitted through the WSN, and updating the state of each model when communication is re-established at discrete time instances. To further reduce WSN utilization, only a subset of the deployed sensor suites are allowed to transmit their data at any given time to provide updates to their target models. By formulating the networked closed-loop plant as a combined discrete-continuous system, an explicit characterization of the maximum allowable update period is obtained in terms of the sensor transmission schedule, the transmission times of the different sensor suites, the uncertainty in the models as well as the controller design parameters. It is shown that by judicious selection of the transmission schedule and the models, it is possible to enhance the savings in WSN resource utilization over what is possible with concurrent transmission condigurations. Finally, the results are illustrated using a network of chemical reactors with recycle.
... For nonlinear plants, on the other hand, results on this problem have been more limited . Examples of recent works include the development of a passivity-based framework for the analysis and stabilization of process networks using concepts from thermodynamics [9], the development of agent-based systems to control reactor networks [10], and the analysis and control of integrated process networks using time-scale decomposition and singular perturbations [11]. One of the key problems in the design of quasidecentralized control systems for multi-unit plants is the integration of communication issues and limitations in the formulation and solution of the plant-wide control problem. ...
This paper presents a quasi-decentralized nonlinear control methodology for multi-unit nonlinear plants whose constituent subsystems communicate over a shared, resource-constrained communication network. The objective is to stabilize the plant while keeping the communication requirements to a minimum in order to reduce the unnecessary utilization of network resources. To this end, an uncertain nonlinear model of the plant is initially used to design, for each unit, a stabilizing nonlinear feedback controller that requires state measurements from the neighboring units for implementation. To reduce the frequency at which the measurements are transmitted over the shared network, a copy of the stable compensated plant model is embedded in each unit to provide estimates of the states of the neighboring units when measurements are not available through the network. The state of the model is then updated at discrete time instances when communication is re-established. By analyzing the behavior of the model estimation error between updates, and exploiting the stability properties of the compensated model, a sufficient condition for practical stability of the networked closed-loop plant is obtained in terms of the update period, the plant-model mismatch and the controller design parameters. The stability condition can be used to obtain estimates of the maximum allowable update period and the size of the achievable residual set. Finally, the implementation of the networked control structure is demonstrated through an application to a chemical plant example.
... Significant research work has explored in depth the benefits and limitations of centralized and decentralized controllers as well as possible ways of overcoming some of their limitations (e.g., see [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and the references therein). Other examples of recent works on control of process networks include the analysis and stabilization of process networks based on passivity and concepts from thermodynamics ([12], [13]), the development of agent-based systems to control reactor networks ([14], [15]), and the analysis and control of integrated process networks using time-scale decomposition and singular perturbations ([16], [17]). An approach that provides a compromise between the complexity of traditional centralized control schemes, on the one hand, and the performance limitations of decentralized control approaches on the other, is quasi-decentralized control. ...
This paper develops a quasi-decentralized state estimation and control architecture for plants with limited state measurements and distributed, interconnected units that exchange information over a shared communication network. The objective is to stabilize the plant while minimizing network resource utilization and communication costs. The networked control architecture is composed of a family of local control systems that transmit their data in a discrete (on/off) fashion over the network. Each control system includes a state observer that generates estimates of the local state variables from the measured outputs. The estimates are used to implement the local feedback control law and are also shared over the network with the control systems of the interconnected units to account for the interactions between the units. To reduce the exchange of information over the network as much as possible without sacrificing stability, dynamic models of the interconnected units are embedded in the local control system of each unit to provide it with an estimate of the evolution of its neighbors when data are not transmitted through the network. The state of each model is then updated using the state estimate generated by the observer of the corresponding unit and transmitted over the network when communication is re-established. By formulating the networked closed-loop plant as a switched system, an explicit characterization of the maximum allowable update period (i.e., minimum cross communication frequency) between the distributed control systems is obtained in terms of plant-model mismatch, controller and observer design parameters. It is shown that the lack of full state measurements imposes limitations on the maximum allowable update period even if the models used to recreate the plant units? dynamics are accurate. The results are illustrated using a chemical process example and compared with other networked control strategies. The comparison shows that the minimum communic-
ation frequency required using quasi-decentralized control is less than what is required by a centralized control architecture indicating that the former is more robust with respect to communication suspension.
... In recent times, there has also been some interest in studying plant-wide control problems within the distributed model predictive control framework (e.g., [9], [10], [11]). Other examples of recent works on control of integrated process networks can be found in [12], [13], [14], [15]. To solve the problem where a decentralized control structure cannot provide the required stability and performance properties, and to avoid the complexity and lack of flexibility associated with traditional centralized control, a quasi-decentralized control strategy with cross communication between the plant units offers a suitable compromise. ...
This paper develops a quasi-decentralized control framework for plants with distributed, interconnected units that exchange information over a shared communication network. In this architecture, each unit in the plant has a local control system that communicates with the plant supervisor - and with other local control systems - through a shared communication medium. The objective is to design an integrated control and communication strategy that enforces the desired closed-loop stability and performance for the plant while minimizing network utilization and communication costs. The idea is to reduce the exchange of information between the local control systems as much as possible without sacrificing stability of the individual units and the overall plant. To this end, dynamic models of the interconnected units are embedded in the local control system of each unit to provide it with an estimate of the evolution of its neighbors when measurements are not transmitted through the network. The use of a model to recreate the interactions of a given unit with one of its neighbors allows the sensor suite of the neighboring unit to send its data in a discrete fashion since the model can provide an approximation of the unit's dynamics. The state of each model is then updated using the actual state of the corresponding unit provided by its sensors at discrete time instances to compensate for model uncertainty. By formulating the networked closed-loop plant as a hybrid system, an explicit characterization of the maximum allowable update period (i.e., minimum cross communication frequency) between each control system and the sensors of its neighboring units is obtained in terms of the degree of mismatch between the dynamics of the units and the models used to describe them. The developed control strategy is illustrated using a network of interconnected chemical reactors with recycle.
... Recent work on multiple reactor configurations with cubic autocatalytic reactions has demonstrated a rich spectrum of static and dynamic behavior [2]. The topography of interconnected CSTR networks has been shown to drastically affect the steady state bifurcation structure of the system [2], [3]. Spatial inhomogeneity of the network can be increased by increasing the number of reactors in the network as well as manipulating the interconnection flow rates of the network. ...
Controlling reactors in distributed manufacturing processes producing different grades of a product requires intelligent reconfiguration strategies. Agent-based approaches are ideal for such cases, since they can provide flexible, robust, and emergent solutions during dynamically changing process conditions. A hierarchical, agent-based system with local and global control agents is developed to control networks of interconnected chemical reactors. This paper proposes a multi- layered, multiagent framework based on a decentralized approach for the supervision of grade transitions in autocatalytic reactor networks. The values for the manipulated variables are chosen to give the least disturbance to the system. The case studies show that the approach is successful in controlling the reactor network and being able to keep the desired grade even after the need of shutting down some of the reactors.
... So-called hybrid control systems combine process dynamics and discrete control elements through the use of multiple linear models at different operating points [16,1]. An alternative approach is based on a hierarchical agent-based system with local and global control structures [21]. ...
Control of spatially distributed systems is a challenging problem because of their complex nature, nonlinearity, and generally high order. The lack of accurate and computationally efficient model-based techniques for large, spatially distributed systems leads to challenges in controlling the system. Agent-based control structures provide a powerful tool to manage distributed systems by utilizing (organizing) local and global information obtained from the system. A hierarchical, agent-based system with local and global controller agents is developed to control networks of interconnected chemical reactors (CSTRs). The global controller agent dynamically updates local controller agent’s objectives as the reactor network conditions change. One challenge posed is control of the spatial distribution of autocatalytic species in a network of reactors hosting multiple species. The multi-agent control system is able to intelligently manipulate the network flow rates such that the desired spatial distribution of species is achieved. Furthermore, the robustness and flexibility of the agent-based control system is illustrated through examples of disturbance rejection and scalability with respect to the size of the network.
... Multi-agent frameworks were originally restricted to the field of computer science where typical applications are of discrete nature such as puzzle solving, planning, and combinatorial arrangement. More recently, control engineers realized that such frameworks can be extended to operate dynamic systems, specially complex distributed systems such as petrochemical plants and transportation networks [19,22,23]. The operation of such complex, spatiallydistributed dynamic systems is a formidable challenge to control engineering, to a great extent due to the intrinsic complexity, sheer size, and nonlinearities. ...
The operation of large dynamic systems such as urban traffic networks remains a challenge in control engineering to a great extent due to their sheer size, intrinsic complexity, and nonlinear behavior. Recently, control engineers have looked for unconventional means for modeling and control of complex dynamic systems, in particular the technology of multi-agent systems whose appeal stems from their composite nature, flexibility, and scalability. This paper contributes to this evolving technology by proposing a framework for multi-agent control of linear dynamic systems, which decomposes a centralized model predictive control problem into a network of coupled, but small sub-problems that are solved by the distributed agents. Theoretical results ensure convergence of the distributed iterations to a globally optimal solution. The framework is applied to the signaling split control of traffic networks. Experiments conducted with simulation software indicate that the multi-agent framework attains performance comparable to conventional control. The main advantages of the multi-agent framework are its graceful extension and localized reconfiguration, which require adjustments only in the control strategies of the agents in the vicinity.
There are three main simulation paradigms. They are as follows: discrete-event modeling, system dynamics and agent-based modeling. In this set, the agent-based paradigm is the one geared towards economic and social system modelling, and, thus, called ‘the right mathematics for the social sciences’. When it was decided to explore communications in an economic system, it has become evident that the most suitable technology for economic system model engineering is the agent-based technology, whose concepts and software toolkits have been developed greatly during several past decades. This paper discusses the process of toolkit choice for communication model engineering, reveals some problems that can be solved with this model and delivers some specific results which were obtained via simulations. Some interesting phenomena were revealed while experimenting with this model.
In this paper, we propose a novel homogenous multi-agent optimization (HMAO) framework for optimal design of large scale process system engineering problems. The platform is validated using a benchmark problems and a computer-aided molecular design (CAMD) problem. The molecular design problem is a solvent selection problem and it is formulated as a mixed integer nonlinear programming (MINLP) in which solute distribution coefficient of a candidate solvent is maximized subject to structural feasibility, thermodynamic property and process constraints. The model simultaneously determines the optimal decisions that include the size and the functional groups of the candidate solvents. In developing the HMAO framework, multiple efficient ant colony optimization (EACO) algorithms are considered as distinct algorithmic agents. We illustrate this approach through a real world case study of the optimal design of solvent for extraction of acetic acid from waste process stream using liquid-liquid extraction. The UNIFAC model based on the infinite dilution activity coefficient is used to estimate the mixture properties. The results show that quality of the objective function and the computational efficiencies are improved by a factor ranged from 1.475 to 4.137. The new solvents proposed in this work are with much better targeted thermodynamic properties compared to the solvents proposed so far in previous studies.
There is a trend in the process industries towards the use of multiple small reconfigurable production units rather than a single large unit to increase production, product range and operation flexibility. Monitoring, supervision and control of these processes is difficult because traditional methods typically do not handle well the increased heterogeneity, nonlinearity and complexity. In this work, statistical multiblock process monitoring techniques and an agent- based diagnosis and control methodology are integrated. The performance of this combined monitoring-diagnosis-control system is illustrated with a case study using a network of spatially distributed reactors.
A comprehensive investigation of wastewater treatment operation is provided through utilization of a validated dynamic model, historical data from a real plant, and bifurcation theory. Bifurcation analysis was carried out with wastewater flow rate, stormwater flow rate, airflow rate, water temperature, and influent ammonia concentration as the free parameters. A two-parameter continuation using airflow rate and water temperature simultaneously was also performed. Results indicate an overall robustness of the plant toward disturbances, which comes at the cost of excessive energy usage. Even then, transients caused by those disturbances are inevitable and can cause violations of regulatory permits on effluent ammonia and dissolved oxygen concentrations. Another important finding is the excessive air usage in aeration tanks, which can be cut by 50% on average without affecting the effluent quality.
Spatially distributed systems hosting autocatalytic species are an excellent test bed as a complex network because of their non-linear structure and ability to display a rich spectrum of behavior. The network system is designed to produce a robust, autocatalytic host species. It so happens that an invasion in the form of another autocatalytic species with higher reproduction rates disrupts normal operation. When an invading species gains foothold in the system, the concentration of the host species decreases and thereby the network elicits different behavioral patterns. The complex network is supervised and tested under an agent based architectural framework which employs a hierarchical structure for agents distributed in different layers. The generic agent structure is comprised of a variety of agents designed for monitoring and control purposes. To combat infection, multi-agent strategies are employed to explore alternatives and intelligently control the network. This choice is ideal because agent based approaches are flexible, robust and can adapt to changing conditions.
In the study, a challenge is posed to investigate a 25 reactor grid network with unequal volumes attacked by a temporary disturbance of an invading cubic autocatalytic species in inflow. The analysis shows that after the disturbance is removed, the network displays interesting patterns. Depending on the magnitude of invasion, growth and death rates of the invading species, case studies demonstrate that undesirable species can disappear from the environment, coexist with the host, flush out the host species or propagate through the network as a disturbance. Elimination of the invader or disturbance rejection can be achieved by using alternative mechanisms, namely, flushing out the invading species, starving the invading species to death or adding an external entity or antibiotic to kill the undesired species.
Owing to the complex nature of the system, an agent based strategy provides a generic detection and control scheme for detection and control of invading species. With the invading species being an immeasurable quantity, there is a need to device a specialized invasion detector agent which controls based on system knowledge. As a knowledge building exercise, sans invasion, a large number of case studies were simulated using feed flow rate, interaction flow rate and resource concentration in the feed as free parameters. The data organize themselves into a manifold which relate the consumption of resource and the production of host autocatalytic species. A control ellipse is constructed using statistical tools to encapsulate normal operating data. For data points within the control ellipse, the gradient in concentration for host species and resource is often negative. A rule based strategy is used to build agents to raise alarms when invasion occurs. What happens is, invasion originates at a specific location in a network, the concentration gradients follow dynamic trajectory and finally settle down at a steady state. Rules are designed to capture invasion patterns at an early stage based on projecting the invasion data onto the control ellipse and estimating the changes in the gradients in concentration of resource and host species. Performance of the system was tested for different operating conditions. Depending on the degree of invasion in the system, agent based control is employed using a variety of manipulated variables.
Multi-agent systems provide a powerful platform for supervision and control of distributed and complex processes. This work focuses on controlling the product grade distribution in RAFT polymerization reactor networks for smooth transition between different product grades or maintaining the targeted product grade despite various disturbances using an agent based approach. The control algorithm is designed for control of the complete molecular weight distribution. The use of a distributed reactor network allows for flexibility in targeting almost any shape for the overall molecular weight distribution.
RAFT polymerization is one of the most popular living polymerization methods. Compared to the other living polymerization methods a wider range of monomers can be used for RAFT Polymerization with more flexible operating conditions. This system is studied in a network of interconnected continuous stirred tank reactors (CSTRs). Individual reactors produce polymer chains with different molecular weight distributions contributing to the overall molecular weight distribution of the network.
A number of centralized and decentralized agent-based control structures have been developed for controlling the distribution of autocatalytic species in CSTR networks [1, 2, 3, 4, 5]. These distributed structures consist of multiple layers of agents where in one layer, local controller agents work on the local objectives in parallel using local information in that region of the network together with heuristics. On the other hand, agents in higher layers coordinate local controller agents in order to achieve the global objective.
A similar agent-based structure is implemented to control the molecular weight distribution in RAFT polymerization in CSTR networks. Molecular weight distribution is one of the most important properties that characterize the application properties of polymeric materials which makes it a critical control issue. In this work two control problems will be studied. The first problem is to maintain the overall molecular weight distribution of the RAFT polymerization system in the CSTR network that is subject to a number of disturbances and the second one is to drive the system from one molecular weight distribution to another.
The overall distribution obtained for the network results from the blend of the individual reactor's distributions taking into account the material flow between the reactors. One can change the individual reactors' molecular weight distributions to control the overall network distribution. KR Method [6, 7, 8] is used for solving the corresponding population balance equations for obtaining the individual and overall molecular weight distributions. As a result, the distribution is represented by a number of pivot points that are used as the basis for controlling the system. A global agent will track the current overall molecular weight distribution and compare it with the desired one. In the case of a difference between the current and targeted distribution, local controller agents will calculate their individual contributions to the error at each pivot point and shift their reactor's molecular weight distribution to minimize the error, in accordance with their local objectives. The local controller agents have access to a number of manipulated variables such as the inlet monomer concentration, inlet initiator concentration, RAFT agent concentration and interconnection flow rates between reactors. Using local information available and heuristics, local controller agents decide on which manipulated variables to adjust to reach their local objectives.
The state equations of the individual CSTR's that are obtained by applying KR Method are solved by a DAE solver available in MATLAB. The agent based control framework is developed in REPAST Symphony which is an agent development platform based on Java. The connection between the control system and the process simulator is achieved by JMatLink library.
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[8] S. Kumar, D. Ramkrishna, On the Solution of Population Balance Equations by Discretization-I. A Fixed Pivot Technique, Chem. Eng. Sci. 1997, 52, 4659.
Fault-Tolerant Process Control focuses on the development of general, yet practical, methods for the design of advanced fault-tolerant control systems; these ensure an efficient fault detection and a timely response to enhance fault recovery, prevent faults from propagating or developing into total failures, and reduce the risk of safety hazards. To this end, methods are presented for the design of advanced fault-tolerant control systems for chemical processes which explicitly deal with actuator/controller failures and sensor faults and data losses. Specifically, the book puts forward: A framework for detection, isolation and diagnosis of actuator and sensor faults for nonlinear systems; Controller reconfiguration and safe-parking-based fault-handling methodologies; Integrated-data- and model-based fault-detection and isolation and fault-tolerant control methods; Methods for handling sensor faults and data losses; and Methods for monitoring the performance of low-level PID loops. The methodologies proposed employ nonlinear systems analysis, Lyapunov techniques, optimization, statistical methods and hybrid systems theory and are predicated upon the idea of integrating fault-detection, local feedback control, and supervisory control. The applicability and performance of the methods are demonstrated through a number of chemical process examples. Fault-Tolerant Process Control is a valuable resource for academic researchers, industrial practitioners as well as graduate students pursuing research in this area.
This paper presents a quasi-decentralized networked control methodology for the robust stabilization of process networks whose constituent subsystems communicate over a shared resource-constrained communication medium and are subject to time-varying external disturbances. The objective is to stabilize the plant and attenuate the influence of the disturbances while keeping the communication to a minimum in order to reduce the unnecessary utilization of network resources. Both state- and output-feedback control problems are considered. Initially, a local robust feedback controller is synthesized for each unit to account for the effect of the disturbances. Then, the exchange of information between the distributed control systems is reduced by embedding, within each control system, a set of dynamic models that provide forecasts of the evolution of the plant states when measurements are not transmitted through the shared network, and updating the state of each model when communication is re-established at discrete time instances. By analyzing the resulting combined discrete-continuous closed-loop system, a necessary and sufficient condition for robust stability of the networked closed-loop plant is obtained. The stability condition can be used to explicitly characterize the interplay between the update period, the degree of plant–model mismatch, the selection of the controller design parameters, the size of the disturbances, and the size of the achievable degree of disturbance attenuation. Finally, the implementation of the robust networked control structure is demonstrated through an application to a chemical plant example.
Critical mechanical devices (CMDs) such as high-pressure air compressors (HPACs) are these kinds of devices which are independently distributed, working in cluster, high-power-cost, big-volume and very crucial to industrial production. To make CMDs exhibit with characteristics of autonomy, interaction, collaboration, robustness, etc., this paper employs an agent-based approach to design CMD controllers. HPACs, the typical CMDs, are selected as one case study. The process flows of HPACs, concepts of agent and agent-based control technologies are described. The architecture of HPAC agent, including agent shell and agent kernel, is discussed and modeled. HPAC agent language system-HPACAL is constructed for communication. with assuring HPAC agents to efficiently realize the common control goal, TWTC Algorithm, a total-working-time-based collaboration algorithm for HPAC agents, is brought up and developed. HPAC agents controllers have been successfully applied and checked in LSBIS Project. This agent-based approach can be universally used to design the controllers of other CMDs, e.g., big dehumidifiers and diesel generators.
It is highly desirable to have a statistical process monitoring (SPM) system that detects the abnormalities in process operations quickly with as few missed and false alarms as possible while the process operates under various operating conditions. An agent-based combined monitoring and fault detection framework is proposed in this study. In this framework, different SPM techniques compete with and complement each other to enhance detection speed and accuracy. SPM techniques from literature such as principal component analysis (PCA), multiblock PCA (MBPCA), and dynamic PCA (DPCA) techniques are implemented in this agent-based process supervision system. An agent performance assessment and agent management layer provides dynamic adaptation of the supervision system and improves the performance of SPM. The statistical information coming from each of the statistical techniques is summarized through a consensus mechanism. The performance of the agent-based consensus mechanism using different consensus criteria is tested for system disturbances of various magnitudes. The effectiveness of the proposed agent-based framework with different consensus criteria is evaluated based on fault detection times and missed alarm rates and the adaptation of the supervision system is illustrated.
A quasi-decentralized state estimation and control architecture for plants with limited state measurements and distributed, interconnected units that exchange information over a shared communication network is developed in this work. The objective is to stabilize the plant while minimizing unnecessary network resource utilization and communication costs. The networked control architecture is composed of a family of local control systems that transmit their data in a discrete (on/off) fashion over the network. Each control system includes a state observer that generates estimates of the local state variables from the measured outputs. The estimates are used to implement the local feedback control law and are also shared over the network with the control systems of the interconnected units to account for the interactions between the units. To reduce the exchange of information over the network as much as possible without sacrificing stability, dynamic models of the interconnected units are embedded in the local control system of each unit to provide it with an estimate of the evolution of its neighbors when data are not transmitted through the network. The state of each model is then updated using the state estimate generated by the observer of the corresponding unit and transmitted over the network when communication is re-established. An explicit characterization of the maximum allowable update period (i.e., minimum cross communication frequency between the distributed control systems) needed to enforce the desired stability and performance properties is obtained in terms of the plant−model mismatch, controller, and observer design parameters. The design and implementation of the developed architecture are illustrated using a chemical plant example and compared with other possible networked control strategies. The comparison reveals that the lack of full state measurements imposes limitations on the maximum allowable update period, even if the models used to recreate the plant units’ dynamics are accurate. It is also shown that the quasi-decentralized control architecture is more robust than a centralized networked control structure, with respect to communication suspension.
Systems with high steady-state multiplicity and rich dynamic behavior are difficult to investigate using conventional reductionist methods. A network of more than five reactors hosting cubic autocatalytic reactions may potentially have more than 102 steady states and many distinct dynamic regimes, all for the same parameter set. This paper discusses how the static complexity of such systems can be measured to give a holistic picture. To achieve this, stochastic simulations were performed to statistically determine the bifurcation structure of the system, and the gathered information is summarized using a measure akin to fractal dimension. With this measure, the growth of static complexity is investigated as a function of the network size.
An adaptive hierarchical framework for process supervision and fault-tolerant control with agent-based systems is presented. The framework consists of modules for fault detection and diagnosis (FDD), system identification and distributed control, and a hierarchical structure for performance-based agent adaptation. Multivariate continuous process monitoring methodologies and several fault discrimination and classification techniques are implemented in the FDD modules to be used by multiple agents. In the process supervision layer, the continuous intramodular communication between FDD and control modules communicates the existence of an abnormality in the process, type of the abnormality, and affected process sections to the distributed model predictive control agents. In the agent management layer, the performances of all FDD and control agents are evaluated under specific process conditions. Performance-based consensus criteria are used to prioritize the best-performing agents in consensus decision making in every level of process supervision and fault-tolerant control. The collective performance of the supervision system is improved via performance-based consensus decision making and adaptation. The effectiveness of the proposed adaptive agent-based framework for fault-tolerant control is illustrated using a simulated continuous stirred-tank reactor network. Copyright © 2011 John Wiley & Sons, Ltd.
This paper presents a model-based networked control approach for managing Distributed Energy Resources (DERs) over communication networks. As a model system, we consider a solid oxide fuel cell (SOFC) plant that com-municates with the central controller over a bandwidth-constrained communication network that is shared by several other DERs. The objective is to regulate the power output of the fuel cell while keeping the communication requirements with the controller to a minimum in order to reduce network utilization and minimize the susceptibility of the SOFC plant to possible communication disruptions in the network. Initially, an observer-based output feedback controller is designed to regulate the power output of the SOFC plant at a desired set-point by manipulating the inlet fuel flow rate. Network utilization is then reduced by minimizing the rate of transfer of information between the fuel cell and the supervisor without sacrificing stability or performance. To this end, a dynamic model of the fuel cell is embedded in the supervisor to approximate the dynamics of the fuel cell when measurements are not transmitted by the sensors, and the state of the model is updated using the observer-generated state estimate that is provided by the SOFC plant sensors at discrete time instances. An explicit characterization of the maximum allowable transfer time between the sensor suite of the fuel cell and the controller (i.e., the minimum allowable communication rate) is obtained in terms of model uncertainty and the choice of the control law. The characterization accounts for both stability and performance considerations. Finally, numerical simulations that demonstrate the implementation of the control architecture and its disturbance handling capabilities are presented.
Control of spatially distributed systems is a challenging problem because of their complex nature, nonlinearity, and generally high order. Agent-based control structures provide a powerful tool for managing distributed systems by utilizing local and global information obtained from the system. A hierarchical, agent-based system with local and global control agents is developed to control networks of interconnected chemical reactors hosting multiple autocatalytic species. The global controller agent dynamically updates the objective of local control agents as the reactor network conditions change. The case illustrated in this paper is to change the dominant species in one CSTR by modifying feed and interconnection flow rates with the constraint of shortest path possible, which causes the least amount of changes in the whole network. The agent-based system and the reactor networks are implemented using the agent-based system development framework RePast
This paper develops a quasi-decentralized control framework for plants with distributed, interconnected units that exchange information over a shared communication network. In this architecture, each unit in the plant has a local control system that communicates with the plant supervisor – and with other local control systems – through a shared communication medium. The objective is to design an integrated control and communication strategy that ensures the desired closed-loop stability and performance for the plant while minimizing network utilization and communication costs. The idea is to reduce the exchange of information between the local control systems as much as possible without sacrificing stability of the individual units and the overall plant. To this end, dynamic models of the interconnected units are embedded in the local control system of each unit to provide it with an estimate of the evolution of its neighbors when measurements are not transmitted through the network. The use of a model to recreate the interactions of a given unit with one of its neighbors allows the sensor suite of the neighboring unit to send its data in a discrete fashion since the model can provide an approximation of the unit’s dynamics. The state of each model is then updated using the actual state of the corresponding unit provided by its sensors at discrete time instances to compensate for model uncertainty. By formulating the networked closed-loop plant as a hybrid system, an explicit characterization of the maximum allowable update period (i.e., minimum cross communication frequency) between each control system and the sensors of its neighboring units is obtained in terms of the degree of mismatch between the dynamics of the units and the models used to describe them. The developed control strategy is illustrated using a network of interconnected chemical reactors with recycle.
The agents and multiagent systems technology is ac- tivelyresearchedbytheacademiaandindustrialcommunity.How- ever, the technology is particularly popular in the manufacturing domain, while the applications in other domains of industrial con- trol are scarce. This survey focuses exclusively on the technology applications in the automation of continuous industrial processes, as the differences in the technology adoption between the process automation and manufacturing are significant. A large part of the literature on the subject is reviewed. The analysis of the literature is provided from several points of view, the main trends of research are described, including the shift of the researchers' interest from the agent-based supervisory control to the low-level agent-based control algorithms. Conclusions are provided regarding the lack of the technology support on the part of control instrumentation ven- dors; probable directions of the development are indicated, which turn out to be especially promising in the domain of biotechnolog- ical processes.
Supervision of distributed manufacturing processes producing different grades of a product requires intelligent reconfiguration strategies during grade transition phases to minimize off-spec production. Agent-based approaches are ideal for such problems and they provide flexible, robust, and emergent solutions during dynamically changing process conditions. Three different multi-layered, multi-agent frameworks are proposed for the supervision of grade transitions in autocatalytic reactor networks. The first framework is the centralized framework and it is useful for small-scale grade transitions where only a small region of the network needs to be reconfigured. Alternatively, the other two frameworks use a decentralized approach. The first decentralized framework implements genetic algorithms and the second one uses self-organizing heuristics and auctions for large-scale grade transitions. The case studies demonstrate that as the complexity of the reconfiguration problem increases, decentralized solutions perform more efficiently.
In this paper, the design and implementation of an agent-based framework to safeguard an auto-catalytic reactor network against external disturbances is discussed. The autocatalytic reactor network producing a robust, host species is attacked by an unmeasured, un-sustained disturbance of a non-robust invading species. The invading species adversely affects host species and manifests different behavioural responses depending on its magnitude and location of injection. The agent framework is employed to detect and counteract the invasion. The agent architecture consists of the physical layer and multiple invasion detection and local operator agents. Based on the operation state of the process, the detection agent raise a variety of flags (for example, “normal operation”, “severe invasion” etc.), whereas the operator agents take control actions based on the flags raised by the detection agent. The agent knowledge in the form of rule-based heuristics designed based on process knowledge gained through simulation under open-loop. The agent knowledge base consists of several parameters which affect their behaviours. Here, we propose a methodology to optimize the parameters critical to agent design. With this method, the agent system evolves in its structure, which facilitates more accurate responses.
The paradigm of cubic autocatalytic replicators with decay in coupled isothermal continuous stirred tank reactors is selected as a model to study complex behavior in population dynamics of sexually reproducing species in a heterogenous environment. It is shown that, even a setup with single species in two coupled environments may have regions in parameter space that result in chaotic behavior, hence segregation in the environment causes complexity in the system dynamics. Furthermore, partitioning is found to lead to emergence phenomena exemplified by steady states not obtainable in the equivalent homogeneous system. These phenomena are illustrated through case studies involving single or multiple species. Results show that the coupled environments can host species, that would not survive should the coupling be removed.
Scientific research and practice in multiagent systems focuses on
constructing computational frameworks, principles, and models for how
both small and large societies of intelligent, semiautonomous agents can
interact effectively to achieve their goals. This article provides a
personal view of the key application areas for cooperative multiagent
systems, the major intellectual problems in building such systems, the
underlying principles governing their design, and the major directions
and challenges for future developments in this field
This article has sought to justify precisely why agent-oriented approaches are well suited to developing complex software systems in general and control systems in particular. These general points are then made concrete by showing how they apply in two very different agent-based control systems--Iber- 26 drola's electricity transportation management system and DaimlerChrysler's manufacturing line control system. In making these arguments, proponents of other software engineering paradigms can claim that the key concepts of agent-oriented computing can be reproduced using their technique. This is undoubt- edly true. Agent-oriented systems are, after all, computer programs, and all programs have the same set of computable functions. However, this misses the point. The value of a paradigm is the mindset and the techniques it provides to software engineers. In this respect, agent-oriented concepts and techniques are both well suited to developing complex, distributed systems and an extension of those currently available in other paradigms
The dynamic behavior of the continuous stirred tank reactor is analysed and classified for a variable reactor residence time. Although earlier work, treating the bifurcation to limit cycles and steady states with changing Damköhler number, yields a complete description of the problem, the evolution of multiple steady states and limit cycles is much more bizarre as the reactor residence time varies. In addition, it is the reactor residence time which is most easily varied experimentally so that the present results are more readily compared with experiment. Plots are given to show the influence of system parameters on the reactor behavior.
Multiplicity, stability and dynamics for autocatalytic reactions of the type A⋯ → rR + ⋯ with overall rate expression rA = kCAmCRn in a continuous stirred tank reactor (CSTR) are studied. Exact multiplicity criteria are defined in the parameter space. Stability analysis shows that no periodic oscillation is possible for the system. When multiplicity occurs, some minimum of R present initially in the reactor is required in order for the high steady state to be achieved. Loci of transient extreme for product are also investigated. Multiplicity and uniqueness criteria are further compared with reported experimental data in literature.
The types of dynamic behavior possible for a single first order reaction carried out in a stirred tank reaction are classified according to values of the parameters and plots in parameter space used to define the various possibilites. Analytic criteria are developed which predict the existence and stability character of limit cycles as a function of the system parameters. The types of dynamic behavior predicted are illustrated by numerical computation of the temperature and concentration trajectories. Several kinds of new jump phenomena for this problem are observed and explained in terms of the parameter space plots. The theory and analysis methods can be easily generalized to other types of reaction systems.
In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for systems of nonlinear algebraic equations. KINSOL was first developed as a sequential solver, on a design that permitted extending it to a parallel version with fairly minimal additions. Both PVODE and KINSOL are being used within a parallel version of the tokamak edge plasma model UEDGE. KINSOL is also being applied in the ParFlow groundwater flow model to solve a nonlinear pressure equation.
The recent contention that isothermal systems in a continuously stirred tank reactor can exhibit only extinction (ΔG is positive) as the flow rate is increased (the residence time reduced) and only ignition (ΔG is negative) as the flow rate is decreased is shown not to be correct. The simple, autocatalytic sequence A + 2B → 3B, rate = k1ab2, for which the catalyst B is not indefinitely stable, but undergoes a first-order removal of decay B → inert, rate = k2b, may also have ignition accompanying an increase in the flow rate and extinction accompanying a decrease. This gives rise to S-shaped curves, Z-shaped curves, and also to closed curves in the dependence of the extent of conversion on residence time or flow rate. Under these circumstances, the sign of the free energy change accompanying the observed behavior is determined by the kinetics: the behavior is not determined by the sign of ΔG.
The static and dynamic behavior of the autocatalytic reaction R + 2P → 3P with decay P → D is studied in networks of coupled continuous stirred tank reactors (CSTRs). Numerical bifurcation studies of the system are performed, resulting in rich steady-state bifurcation structures with multiple steady states and isolas. The heterogeneity of the networks is influenced by the number of reactors as well as the network topology. It is shown that the number of steady states of the network increases with heterogeneity, thereby allowing those autocatalytic species to exist in the network that would normally not exist in the homogeneous environment of a single CSTR. Spatial patterns of stable steady states are evident in reactor networks. Dynamic simulation studies are performed to illustrate the transition from one stable state configuration to another or from stable steady states to periodic regimes.
Two types of nonlinear feedback control schemes are introduced and analyzed for their capability of recovering the original state of an isothermal continuous-flow stirred tank reactor with one robust cubic autocatalytic species, perturbed by a temporary disturbance of an invading cubic autocatalytic species in the inflow. The control objectives are to eliminate the invading species from the system and to restore the original state of the host species. The extent of applicability of the control design to different nonrobust invading species is studied, when the controller is tuned for a specific invader. Moreover, a time-delay feature is suggested in one of the control schemes developed to achieve the control objectives in systems with poor detection of invading species.
The competition of two species for a common resource is illustrated using the paradigm of autocatalytic replicators inhabiting a continuous stirred tank reactor (CSTR) environment that is continuously fed with the resource. In most cases presented, one species is robust (appears in reactor feed) while the other is not. The introduction of the second (invading) species into the CSTR via an unsustained disturbance has a strong effect on the steady-state and dynamic behavior of the first (host) species. New steady states are added to the bifurcation diagram that show that the invading species can coexist in the system with the host species when its growth and death characteristics are similar to those of the latter. The population levels of the host species are greatly reduced in these cases as a result of the considerable decrease in resource concentration at steady state. Open-loop strategies for the elimination of the invading species are developed and discussed. These strategies involve the manipulation of the reactor residence time to destabilize the states of coexistence.
The purpose of this paper is to consider the well agitated continuous reactor from the standpoint of stability of the steady state. It has been shown in the past that chemical-reaction systems may be unstable in the sense that on slight perturbation they tend to move to a more stable state or that they are stable in their steady states, small perturbations being self-correcting so that the system possesses autoregulation. In this paper methods of developing criteria for the quantitative determination of stability or instability or presented and applied to some simple problems. In order that the effect of large perturbations on the system may be determined, complete solutions of the rigorous equations are obtained on the analogue computer (R.E.A.C.). A complete plot of reaction paths in the concentration-temperature plane may be obtained in this manner. Because of the nonlinearity of the system one cannot predict with certainty what steady state will be approached after a given large perturbation, multiple steady states being assumed possible. From the phase plot of reaction paths the regions in the plane which lead to certain steady states are delineated. Also it is shown that the natural behavior of a reactor is not to approach an unstable state. So far as the reactor is concenrned, the unstable state does not exist. The stability of the system is important to the engineer, as control will be easy or difficult and product quality will be satisfactory or not depending upon the relative stability of the steady state. An unstable state would require more elaborate control than a stable state.
The question of the multiplicity of the steady states of a chemical reactor was one of the concerns in the pioneering work of Bilous and Amundson. Their diagrams showed quite clearly the geometry of the situation, and this kind of analysis sufficed for many years. It remained for Balakotaiah and Luss, using the methods of singularity theory, to give a comprehensive treatment of the question. After a brief survey, we take up the case of consecutive first-order reactions and show that up to seven steady states are possible.
Agent-based computer systems are surprisingly effective at solving complex problems. Built by combining autonomous computer routines, or agents, with low-bandwidth communication capabilities, these systems typically perform significantly better than the individual routines operating alone. One source of this improvement lies in the cooperative collaboration among the individual agents that compose the system. This work proposes a modular framework for implementing agent-based systems for engineering design. Using a variety of different algorithmic agents, the key ideas are highlighted by identifying multiple identical global optima for a non-convex optimization problem with numerous local minima. The results show that inter- and intra-agent collaboration have a significant impact on system performance. Further, the system can be parallelized with little or no penalty. By observing and analyzing the interactions among individual agents, we gain insights that will aid in the development and management of a conceptual design system for truly hard and large problems.
Autocatalytic reactions are often complicated, and analyses of their behaviour in open systems can seem too particular to permit useful generalisation. We study here the simplest of circumstances (uniform temperatures and concentrations in the isothermal CSTR) and the simplest of reaction schemes: (i) quadratic autocatalysis (A + B→2B); and (ii) cubic autocatalysis (A + 2B→3B). The catalyst B may be stable or have a finite lifetime (B→ inert products). Allowing for this finite lifetime adds another dimension to the interest.The phenomena encountered include multistability, hysteresis, critical extinctions, critical ignitions, and anomalous relaxation times (though infinite values do not arise). Patterns of stationary states as function of residence time can show isolas and mushrooms. All these aspects yield to simple algebraic analysis. The presence of the catalyst B in the inflow can make qualitative differences of a kind parallelled by an additional, non-catalytic reaction of the same stoichiometry (e.g. A→B). Invoking the reversibility of the reactions neither increases nor diminishes their variety, and thermodynamic considerations have little to do with the many different patterns of reactivity displayed.The local stability of the various stationary states has also been characterized. Quadratic autocatalysis shows limited variety (stable node, stable focus); cubic autocatalysis generates all the kinds of stationary state possible in a two-variable system. Again all the algebra is straightforward if not always simple. Sustained oscillatory behavior (limit cycles) also occur.All these remarks relate to isothermal systems, but there are the most striking parallels between isothermal autocatalysis and the exothermic, first-order reaction in the CSTR. Behaviour with an autocatalyst of complete stability corresponds to perfect heat insulation (adiabatic operation) in the non-isothermal, exothermic system.
The prototype, cubic autocatalytic reaction (A + 2B → 3B) forms the basis for the simplest homogeneous system to display “exotic” behaviour. Even under well-stirred, isothermal, open conditions (CSTR) we may find multistability, hysteresis, extinction, ignition and anomalous relaxation times. Allowing for the finite lifetime of the catalyst (B→inert products) adds another dimension. The dependence of the stationary-states on residence-time now yields isolas or mushrooms. Sustained oscillations (stable limit cycles) are also possible. The onset of oscillation corresponds to a change in the character of the stationary-state (from stable focus to unstable focus) and the conditions for this change can be evaluated analytically. The period of the oscillations and their amplitudes increase as the residence time is lengthened. A total of nine different phase-portraits in the a–b plane has been found.The isothermal system is less complex than the exothermic, first-order reaction in a CSTR, but there are strong analogies between the two.
Static and dynamic properties of multiple cubic autocatalytic reactions in an isothermal continuous stirred tank reactor are investigated. It is shown that in the bifurcation diagram of the system should an n-interaction isola exist, it is to reside in the intersection of all possible (n−1)-interaction isolas of the n species constituting the n-interaction. Next, it is discussed that once the ratio of reproduction to death rates for a species is fixed, then the size of its single species isola is fixed, in logarithmic residence time. Furthermore, it is found that any interaction isola in the bifurcation diagram is unstable, whereas single species isolas will have ranges of stable steady states. Finally, these findings and some dynamic properties of the system are demonstrated in case studies.
This work proposes a methodology for coordinating feedback controller synthesis and actuator configuration switching in control of spatially-distributed processes, described by highly dissipative partial differential equations (PDEs) with actuator constraints. Under the assumption that the eigenspectrum of the spatial differential operator can be partitioned into a finite slow set and an infinite stable fast complement, Galerkin's method is initially used to derive a finite-dimensional system (set of ordinary differential equations (ODEs) in time) that captures the dominant dynamics of the PDE system. Using this ODE system, a stabilizing nonlinear feedback controller is designed, for a given actuator configuration, and an explicit characterization of the corresponding stability region is obtained in terms of the size of actuator constraints and the spatial locations of the actuators. Switching laws are then derived, on the basis of the stability regions, to orchestrate the transition between multiple, spatially-distributed control actuator configurations, in a way that respects actuator constraints, accommodates multiple (possibly conflicting) control objectives and guarantees closed-loop stability. Precise conditions that guarantee stability of the constrained closed-loop PDE system under switching are provided, and the proposed approach is successfully applied to the problem of constrained, fault-tolerant stabilization of unstable steady-states of a representative diffusion-reaction process and a non-isothermal tubular reactor with recycle.
Agent-based computing represents an exciting new synthesis both for Artificial Intelligence (AI) and, more generally, Computer Science. It has the potential to significantly improve the theory and the practice of modeling, designing, and implementing computer systems. Yet, to date, there has been little systematic analysis of what makes the agent-based approach such an appealing and powerful computational model. Moreover, even less effort has been devoted to discussing the inherent disadvantages that stem from adopting an agent-oriented view. Here both sets of issues are explored. The standpoint of this analysis is the role of agent-based software in solving complex, real-world problems. In particular, it will be argued that the development of robust and scalable software systems requires autonomous agents that can complete their objectives while situated in a dynamic and uncertain environment, that can engage in rich, high-level social interactions, and that can operate within flexible organisational structures.
A model of a reaction system consisting of two parallel, isothermal autocatalytic reactions in a CSTR has been examined. It is shown that self-sustained chaotic behavior can occur in this system. The region of chaos is entered and exited according to period-doubling and halving sequences, with both sets of bifurcations giving rise to Feigenbaum's number. Power spectral density calculations show that the nature of the chaotic behavior depends quite strongly on the parameter values. From a calculation of the Lyapunov exponents it is found that the Lyapunov dimension of the strange attractor is only slightly greater than that of a two-periodic torus.
Particle swarm optimization is employed here to evaluate the parametric regions where different dynamic phenomena (periodic oscillations, double-period oscillations, chaos) can be expected in dynamic models. The proposed algorithm comprises two fundamental steps: the rough evaluation of regions where the desired solutions can be found and solution refining. The refining step allows the search for unstable solutions that may coexist with the other stable attractors. No preliminary bifurcation analysis is required. Simulations performed for distinct dynamic models show that the proposed algorithm is indeed able to locate different dynamic phenomena in the parameter space and that the algorithm may be of help for those interested in increasing the speed of more traditional dynamic bifurcation analysis.
This article reviews the principles of agent-based computing and discusses its relevance for control. Applications to power generation and manufacturing are also discussed.
The integration of a supervisory knowledge-based system (KBS) with a multivariable control system is examined to provide robust multivariable control of a chemical reaction process. The supervisory KBS is capable of monitoring the process to detect system faults as well as assessing control system performance. If a control system performance deficiency is detected, the KBS formulates and implements the necessary corrective controller tuning. This adaptive capability reduces the conservatism of the robust control system. The underlying mechanisms are discussed and the re-tuning ability of the KBS is illustrated by using rigorous simulations of a chemical reaction process.< >
A numerical algorithm for continuation of stationary solutions to nonlinear evolution problems representable in the form u t = F (uxx ; ux ; u; x; ff); 0 ! x ! 1; f 0 (ux ; u; ff) = 0; x = 0; f 1 (ux ; u; ff) = 0; x = 1; is described as implemented in content. Here F : R n ThetaR n ThetaR n ThetaR m ! R n and f 0;1 : R n ThetaR n ThetaR m ! R n are sufficiently smooth nonlinear functions. The algorithm is based on the second-order finite-difference approximation with an adaptive non-uniform mesh selection. Special methods for efficient solution of linear systems appearing in the continuation are presented. Several examples are given. AMS Subject Classification (1991): 35B32, 35B60, 35G30, 65N06, 65N50, 68N99 Keywords & Phrases: Numerical continuation, partial differential equations, nonlinear boundary-value problems, finite-difference approximation, interactive software. Note: This work has been partially supported by the Visitor Program of the Neder...
Static and dynamic behavior of autocatalytic replicators in heterogeneous reactor networks (paper 457f)
- E Tatara
- I Birol
- F Teymour
- A Cinar
Tatara, E., Birol, I., Teymour, F., & Cinar, A. (2003). Static and dynamic
behavior of autocatalytic replicators in heterogeneous reactor networks
(paper 457f). AIChE Annual Meeting, San Francisco, CA, November
16-21.