Interconnected Tanks Research Articles

Performance Evaluation of Fractional Proportional–Integral–Derivative Controllers Tuned by Heuristic Algorithms for Nonlinear Interconnected Tanks

This article presents an in-depth analysis of three advanced strategies to tune fractional PID (FOPID) controllers for a nonlinear system of interconnected tanks, simulated using MATLAB. The study focuses on evaluating the performance characteristics of system responses controlled by FOPID controllers tuned through three heuristic algorithms: Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Flower Pollination Algorithm (FPA). Each algorithm aims to minimize its respective cost function using various performance metrics. The nonlinear model was linearized around an equilibrium point using Taylor Series expansion and Laplace transforms to facilitate control. The FPA algorithm performed better with the lowest Integral Square Error (ISE) criterion value (297.83) and faster convergence in constant values and fractional orders. This comprehensive evaluation underscores the importance of selecting the appropriate tuning strategy and performance index, demonstrating that the FPA provides the most efficient and robust tuning for FOPID controllers in nonlinear systems. The results highlight the efficacy of meta-heuristic algorithms in optimizing complex control systems, providing valuable insights for future research and practical applications, thereby contributing to the advancement of control systems engineering.

Improving precision and robustness in level control of coupled tank systems: A tree seed optimization and [formula omitted]-analysis approach

Background:Efficient control of liquid levels in interconnected tank systems is a fundamental challenge in various industries, including chemical processes, wastewater treatment, and manufacturing. The traditional approach to achieving precise control has relied on Proportional–Integral–Derivative (PID) controllers, whose performance largely depends on tuned parameters. However, tuning PID controllers for complex and nonlinear systems like coupled tanks remains a challenging task. In recent years, nature-inspired optimization algorithms have gained prominence in control system design. The tree seed optimization (TSO), inspired by the dispersion of tree seeds in search of optimal growth conditions, has shown promise in solving complex optimization problems. This study seeks to explore the application of TSO in tuning PID controllers for coupled tank systems. Methodology:This research employs the TSO to optimize PID controller parameters for enhanced liquid-level control in coupled tank systems. The optimization process involves integrating performance metrics and closed-loop gain constraints to achieve optimal control of coupled tank systems. The imposed constraints aim to ensure robustness and system stability in the face of uncertainties and disturbances. Besides, μ analysis quantifies the robustness of the system by assessing its ability to tolerate uncertainties. Findings:Simulation studies conducted in this research verify the efficacy of the proposed TSO-based approach for tuning PID controllers in coupled tank systems. Compared with various methods, the TSO consistently yields better control performance, reduces settling time, and minimizes overshoot. The robustness of the optimized controllers is also evaluated, showing the ability to handle varying operating conditions effectively.

Advanced tree‐seed optimization based fractional‐order PID controller design for simplified decoupled industrial tank systems

AbstractControlling coupled tank systems is challenging due to interactions between tanks, nonlinear dynamics, time delays, uncertainties, and cross‐coupling effects. The design of effective control strategies to address these complexities while ensuring stability and robust performance is difficult. Hence, this study focuses on presenting an innovative approach to enhance level control in coupled tank systems by employing a fractional‐order proportional‐integral‐derivative (FOPID) controller. The FOPID controller is designed by imposing constraints on the performance metric and closed‐loop gain. Besides, the defined optimization problem is solved by employing a tree seed algorithm. Further, the stability is analyzed graphically using the singular value analysis. The inherent complexities of coupled tank systems are effectively addressed by designing decouplers. The unique characteristics of the tree seed algorithm to navigate complex solution spaces and its effective handling of constraints offer a robust optimization framework. The validity and efficiency of the proposed method are analyzed in a range of simulation experiments conducted on distinct interconnected tank systems. Besides, the stability is verified graphically. The analysis highlights the effectiveness of the control law in handling uncertainties and disturbances. Besides, the proposed method reduces the settling time to around . Through a systematic integration of optimization and comprehensive stability analysis, the study provides a holistic solution for optimizing level control in coupled tank systems.

A distributed MPC approach — Local agents decide network convergence

In an earlier work, the Limited Communication-Distributed Model Predictive Control (LC-DMPC) scheme for controlling networks with dynamically coupled and locally constrained linear systems is presented. The scheme has an iterative and cooperative structure in which the systemwide optimum point is achieved by the distributed controllers requiring only coupled agents to cooperate. For assessing the network convergence, it is essential to possess complete information pertaining to all subsystems which has to be available to a central monitor. The current work endeavors to investigate this challenging point by distributing the network convergence within the local agents. With the new version of the algorithm, the convergence of the network is now guaranteed through the dissipativity of the local information exchange dynamics in the iteration domain. This is accomplished by introducing a set of free design variables into the distributed problems which are utilized by the agents to fulfill a simple local LMI problem employing local information only. Despite that the new approach is eliminating the necessity for a centralized observer, it may result in suboptimal local solutions. This is because the convergence of the information sharing loop between the coupled subsystems is insured by the small gain theorem. The new algorithm exhibits enhanced modularity due to the novel introduced convergence condition, implying that any updates to a subsystem physicals or design parameters do not require corresponding updates to neighboring subsystems or the network. The presented concepts are demonstrated by simulating a network of eight interconnected tanks.

TRANSIENT ANALYSIS OF LIQUID-HYDROGEN TRANSFER IN CRYOGENIC STORAGE TANKS

Efficient transfer of liquid hydrogen is critical for a myriad of processes in terrestrial and extraterrestrial applications. The objective of this study is to model and quantify the amount of liquid parahydrogen vaporized during a discharging/charging process in a cryogenic storage system. The effects that are included include geometrical effects (storage tank volume), two-phase compressible flow, choking/unchoking, and wall-fluid heat transfer. A brief description of other physical boil-off mechanisms is also presented. This study provides a foundation for applicationspecific optimization. The storage system studied comprises two interconnected tanks whose transfer line has a variation in the flow area. This simulates current liquid-hydrogen storage and transportation systems. The model tracks the temperature- and pressure-time histories of liquid hydrogen as it flows between storage tanks, in both the choked and unchoked flow regimes. The transfer of liquid is induced solely by the pressure differential that exists between the two storage tanks. An iterative technique helps account for choking, which is likely to exist at the throat in two-phase flow. Cases of zero and infinite tank-wall thermal mass are also discussed. By analyzing the behavior of fundamental variables during the transient transfer of liquid hydrogen, boil-off losses may be minimized if the variables with the greatest effect on boil-off losses are controlled.

Identification of the regularities of the thermohydraulic processes of the cooling system of an experimental device based on a mathematical model

The article is devoted to the study of a nitrogen supply system for cooling an experimental device designed for testing in a pulsed reactor with a graphite moderator. To analyze emergency situations caused by disruption of the nitrogen supply system in the cooling paths of the fuel assembly cover and the experimental device power housing, a mathematical model has been developed to describe thermodynamic processes in a system of interconnected tanks that simulate individual sections of the experimental device hydrodynamic cooling system in a pulsed graphite reactor and implemented in the mathematical interactive package for engineering calculations in MATLAB/Simulink. To study the normal operation of the system and analyze possible emergencies, the cooling system of the experimental device was presented in the form of groups of interconnected sections of the hydrodynamic system-tanks, with specified volumes and hydraulic resistances of pipelines connecting these tanks. Verification of the model, calculations of the experimental device cooling system normal operation mode, calculations of emergency situations caused by a violation of the nitrogen supply system normal operation in the cooling paths of the fuel assembly cover were carried out, in particular, it was found that for the cooling system of the experimental device WF-2, the breakdown of the gearbox P-12 can cause depressurization of the fuel assembly cover and an increase in pressure in the power housing, the opening of the safety valve prevents exceeding the pressure limit in the housing, the device maintains integrity even in emergency situations, without being subjected to destruction of the power elements of the structure at a pressure of up to 8 MPa

Observer Design for Detection of Attack Patterns in Cyber-Physical Systems

This article focuses on the design of a Luenberger structure observer with residual generation for the detection of different attack schemes (Denial of Service (DoS) and False Data Injection (FDI)) targeting the sensors and actuators of a discrete cyber-physical system. To simulate a more realistic attack signal, Markovian distribution logic is used to simulate the behavior of the signals. To demonstrate the effectiveness of the proposed scheme, a system of three interconnected tanks is used.

Fractional Transformation-Based Decentralized Robust Control of a Coupled-Tank System for Industrial Applications

Petrochemical and dairy industries, waste management, and paper manufacturing fall under the category of process industries where flow and liquid control are essential. Even when liquids are mixed or chemically treated in interconnected tanks, the fluid and flow should constantly be observed and controlled, especially when dealing with nonlinearity and imperfect plant models. In this study, we propose a nonlinear dynamic multiple-input multiple-output (MIMO) plant model. This model is then transformed through linearization, a technique frequently utilized in the analysis and modeling of fractional processes, and decoupling for decentralized fixed-structure H-infinity robust control design. Simulation tests based on MATLAB and SIMULINK are subsequently executed. Numerous assessments are conducted to evaluate tracking performance, external disturbance rejection, and plant parameter fluctuations to gauge the effectiveness of the proposed model. The objective of this work is to provide a framework that anticipates potential outcomes, paving the way for implementing a reliable controller synthesis for MIMO-connected tanks in real-world scenarios.

A Comprehensive Overview on Performance of Cascaded Three Tank Level System using Neural Network Predictive Controller

A Neural Network Predictive Controller (NNPC) is a deep learning-based controller (DLC) that uses artificial neural networks (ANN) to predict the future behavior of a system and accordingly control its outputs. In this paper, an NNPC was used to predict the level of the three cascaded tank and then adjust the inputs as flow rate to maintain the desired level in the tank. A three-tank level system is a system consisting of three interconnected tanks used to store liquids. To achieve the desired level, the NNPC first collects data on system behavior, including inputs and outputs, and uses this data to train the neural network. The trained network was then used to make predictions about the future level of each tank and to generate control signals to adjust the inputs as needed. NNPC also incorporates feedback from the system to continuously refine its predictions and improve its control performance over time. The mean squared error (MSE) of different backpropagation training algorithms available in MATLAB deep learning toolbox were evaluated and presented. Based on the MSE and best validation, Levenberg Marquardt algorithm were used in NNPC controller for further step response tracking. Different performance metrics were evaluated and presented.

Deep Reinforcement Learning Agent for Negotiation in Multi-Agent Cooperative Distributed Predictive Control

This paper proposes a novel solution for using deep neural networks with reinforcement learning as a valid option in negotiating distributed hierarchical controller agents. The proposed method is implemented in the upper layer of a hierarchical control architecture composed at its lowest levels by distributed control based on local models and negotiation processes with fuzzy logic. The advantage of the proposal is that it does not require the use of models in the negotiation, and it facilitates the minimization of any dynamic behavior index and the specification of constraints. Specifically, it uses a reinforcement learning policy gradient algorithm to achieve a consensus among the agents. The algorithm is successfully applied to a level system composed of eight interconnected tanks that are quite difficult to control due to their non-linear nature and the high interaction among their subsystems.

Negotiation agent based on Deep reinforcement learning for multi-agent cooperative distributed predictive control

In this work, deep neural network trained by the model-free reinforcement learning method is proposed as a negotiation agent in multi-agent distributive model predictive control. The negotiation agent is implemented in the upper layer of a hierarchical control architecture based on distributed model predictive controller with pairwise negotiation fuzzy logic. The proposed is data-driven in order to achieve the minimization of any dynamic behavior index and the specification of constraints. Specifically, the deep neural network provides consensus coefficients to address the final control action applied by each agent. The proposed is successfully applied to a hydraulic system composed of eight interconnected tanks that are very difficult to control due to non-linearities nature and high interaction between its subsystems.

Multistage optimization of a petroleum production system with material balance model

In this paper, we propose a mathematical formulation for the optimal management over time of an oil production network as a multistage optimization problem. The proposed model differs from common practice where the reservoir of the oil production network is approximated by decline curves or by black-box simulators. We model the reservoir as a controlled (non-linear) dynamical system by using material balance equations, under the standard assumptions that the fluids follow a black-oil model and that the reservoir has a tank-like behavior. The state of the dynamical system has five dimensions: the total volume of respectively oil, gas, and water in the reservoir; the total pore volume; and the reservoir pressure. We use a dynamic programming algorithm to numerically solve the multistage optimization problem on two specific instances of the general optimization problem where the state dimension can be reduced from dimension five to dimension one or two. More precisely, the first numerical application consists in optimizing the production of a dry gas reservoir which is subdivided in two tanks and which leads to a two-dimensional state (one dimension per tank), whereas the second numerical application tackles an oil reservoir with water injection which leads to a two-dimensional state. The two applications illustrate that our approach handles interconnected tanks (in the dry gas case) and that our approach allows optimization beyond first recovery of oil (in the oil with water injection case). We also provide numerical and theoretical comparisons with decline curves in the dry gas application.

Reproducible low-cost flexible quadruple-tank process experimental setup for control educators, practitioners, and researchers

The major hurdle in accessing laboratory experimentation is the cost of acquiring experimental scientific equipment, which is unbearable for many institutions. This paper aims to provide the community of control educators, practitioners, and researchers with an open-source low-cost experimental setup and dedicated interface, which is flexible and very easily reproducible. The proposed apparatus is a setup of four interconnected tanks. The setup is representative of real-life industrial processes and it can be adjusted to allow for several configurations for flexibility. A user-friendly dedicated MATLAB/Simulink interface with a personal computer is developed. It supports a seamless shift between a numeric simulation of the quadruple-tank process dynamics and the interface with the physical experimental plant. The CAD models, technical drawings, wiring schematics, PCB design, interface, assembly tutorials, and several examples are provided in an open-source repository. The parts are inexpensive, readily obtained, and fast to assemble. Each setup costs under 650€ and takes roughly 4 h to assemble. In this paper, several application examples are presented, not only for educational purposes, but also for the validation of a state-of-the-art decentralized control method.

Discrete-time distributed Kalman filter design for networks of interconnected systems with linear time-varying dynamics

This paper addresses the problem of designing distributed state estimation solutions for a network of interconnected systems modelled by linear time-varying (LTV) dynamics in a discrete-time framework. The problem is formulated as a classical optimal estimation problem, for the global system, subject to a given sparsity constraint on the filter gain, which reflects the distributed nature of the network. Two methods are presented, both of them able to compute a sequence of well-performing stabilising gains. Moreover, both methods are validated by resorting to simulations of: (i) a randomly generated synthetic LTV system; and (ii) a large-scale nonlinear network of interconnected tanks. One of the proposed methods relies on a computationally efficient solution, thus it is computed very rapidly. The other achieves better performance, but it is computationally more expensive and requires that a window of the future dynamics of the system is known. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well-performing gains that stabilise the estimation error dynamics. Both algorithms are scalable, being adequate for implementation in large-scale networks.

Detection and Isolation of DoS and Integrity Cyber Attacks in Cyber-Physical Systems with a Neural Network-Based Architecture

New applications of industrial automation request great flexibility in the systems, supported by the increase in the interconnection between its components, allowing access to all the information of the system and its reconfiguration based on the changes that occur during its operations, with the purpose of reaching optimum points of operation. These aspects promote the Smart Factory paradigm, integrating physical and digital systems to create smarts products and processes capable of transforming conventional value chains, forming the Cyber-Physical Systems (CPSs). This flexibility opens a large gap that affects the security of control systems since the new communication links can be used by people to generate attacks that produce risk in these applications. This is a recent problem in the control systems, which originally were centralized and later were implemented as interconnected systems through isolated networks. To protect these systems, strategies that have presented acceptable results in other environments, such as office environments, have been chosen. However, the characteristics of these applications are not the same, and the results achieved are not as expected. This problem has motivated several efforts in order to contribute from different approaches to increase the security of control systems. Based on the above, this work proposes an architecture based on artificial neural networks for detection and isolation of cyber attacks Denial of Service (DoS) and integrity in CPS. Simulation results of two test benches, the Secure Water Treatment (SWaT) dataset, and a tanks system, show the effectiveness of the proposal. Regarding the SWaT dataset, the scores obtained from the recall and F1 score metrics was 0.95 and was higher than other reported works, while, in terms of precision and accuracy, it obtained a score of 0.95 which is close to other proposed methods. With respect to the interconnected tank system, scores of 0.96,0.83,0.81, and 0.83 were obtained for the accuracy, precision, F1 score, and recall metrics, respectively. The high true negatives rate in both cases is noteworthy. In general terms, the proposal has a high effectiveness in detecting and locating the proposed attacks.

Discrete‐time decentralized linear quadratic control for linear time‐varying systems

AbstractThis article addresses the problem of designing a decentralized control solution for a network of agents modeled by linear time‐varying (LTV) dynamics, in a discrete‐time framework. A general scheme is proposed, in which the problem is formulated as a classical linear quadratic regulator problem, for the global system, subject to a given sparsity constraint on the gain, which reflects the decentralized nature of the network. A method able to compute a sequence of well‐performing stabilizing regulator gains is presented and validated resorting to simulations of two randomly generated LTV systems, one stable and the other unstable. Moreover, a tracking solution is developed, building on the solution to the regulator problem. Both methods rely on a closed‐form solution, thus they can be computed very rapidly. Similarly to the centralized solution, both the presented methods require that a window of the future system dynamics is known. Both methods are validated resorting to simulations of: (i) a nonlinear network of four interconnected tanks; and (ii) a large‐scale nonlinear network of interconnected tanks. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well‐performing gains that track the desired output. Finally, both algorithms are scalable, being adequate for implementation in large‐scale networks.

Estimation and Fault Detection on Hydraulic System with Adaptive-Scaling Kalman and Consensus Filtering

The area of fault detection is becoming more interesting since there have been many unique designs to detect or even compensate the faults, either from sensor or actuator. This paper applies the hydraulic system with interconnected tanks by implementing a leakage on one of the three tanks. The mathematical model along with the details of stability properties are highly discussed in this paper by imposing the Lyapunov and boundedness stability. The theory of fault detection with certain threshold after the occurrence of the fault corresponding to the state estimation error is mathematically presented ended by simulation. Moreover, the system compares the effectiveness of the proposed observer using Luenberger observer, adaptive-scaling Kalman and consensus filtering. The results for some different initial condition guarantee the detection of the fault for some time $t_d > t_f$

Application of Tanks-in-Series Model to Characterize Non-Ideal Flow Regimes in Continuous Casting Tundish

This study describes a new tanks-in-series model for analyzing non-ideal flow regimes in a single-strand tundish. The tundish was divided into two interconnected tanks, namely an inlet tank and an outlet tank. A water model experiment was carried out to separately measure the residence-time distribution (RTD) of the two tanks. Drift beads were adopted in the water model experiment to simulate the non-metallic inclusions in molten steel. Dead volume fraction was evaluated by analyzing measured RTD curves. The ratio between mixed flow volume and plug flow volume was proposed as a new criterion to evaluate the inclusion removal. In the inlet tank, a higher mixed flow fraction was preferred to effectively release turbulent kinetic energy and enhance inclusion collision growth. In the outlet tank, a higher plug flow fraction was preferred to facilitate inclusion removal by flotation. The optimal positions of the weir were recommended based on the RTD analysis and the inclusion removal from the results of water model experiments. A theoretical equation was derived based on the tanks-in-series model, providing a good fitting function to analyze the experimental data. The confirmation test was performed by applying computational fluid dynamics simulations of liquid steel flow in the real tundish.

Fault-Tolerant Control for Three-Tank System in Case of Sensor Faults

This research paper would be devoted to the application of a fault-tolerant control (FTC) for a benchmark system composed of three interconnected tanks in case of sensor faults. The control scheme includes two blocks: fault detection and isolation (FDI) block and a control law reconfiguration block. The strategy of the FDI method is based on a bank of high gain observers; each of them is constructed to estimate the system state vector. Thus, the diagnostic signal-residuals are generated by the comparison of measured and estimated outputs and the faulty sensor is isolated. The reconfiguration block performs an update of the controller parameters according to the operating mode. The application of this method to a pilot plant demonstrates that the hydrographic system maintains quite performances after sensor faults occurrence.

Distributed controller design and performance optimization for discrete‐time linear systems

SummaryThis article addresses the problem of distributed controller design for linear discrete‐time systems. The problem is posed using the classical framework of state feedback gain optimization over an infinite‐horizon quadratic cost, with an additional sparsity constraint on the gain matrix to model the distributed nature of the controller. An equivalent formulation is derived that consists in the optimization of the steady‐state solution of a matrix difference equation, and two algorithms for distributed gain computation are proposed based on it. The first method consists in a step‐by‐step optimization of said difference matrix equation, and allows for fast computation of stabilizing state feedback gains. The second algorithm optimizes the same matrix equation over a finite time window to approximate asymptotic behavior and thus minimize the infinite‐horizon quadratic cost. To assess the performance of the proposed solutions, simulation results are presented for the problem of distributed control of a quadruple‐tank process, as well as a version of that problem scaled up to 40 interconnected tanks.