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Robust sliding-mode control for a gantry crane system subject to external disturbance

NONLINEAR DYNAMICS 2024年第6期112卷 4169-4182页

作者： Zhang, Jiayang Wu, Wei Huang, Xin Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China

This paper devotes to proposing a sliding-mode controller to reject external disturbance and stabilize the gantry crane system which formulated by the partial differential equations (PDEs). The control objectives are transporting trolley hanging with a payload to the specified place while eliminating the oscillation and rejecting the external disturbance in transportation. By applying the operator semigroup theory, it can be proved that proposed controller is well-posed to the gantry crane system. Furthermore, asymptotic stability has been proved through the application of the extended Krasovskii-LaSalles' invariance principle. Ultimately, numerical simulations are given to illustrate the advance of proposed control scheme and an experiment is conducted to display the feasibility of proposed sliding-mode controller.

关键词： Gantry crane system Partial differential equations Sliding-mode controller Operator semigroup distributed parameters system

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The chemostat reactor: A stability analysis and model predictive control

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JOURNAL OF PROCESS CONTROL 2024年 138卷

作者： Cassol, Guilherme Ozorio Koch, Charles Robert Dubljevic, Stevan Univ Alberta Chem & Mat Engn Dept Edmonton AB T6G 2V4 Canada Univ Alberta Mech Engn Dept Edmonton AB T6G 2V4 Canada

This contribution develops the model predictive control for an unstable chemostat reactor. Initially, we analyze the system's model - a nonlinear first -order hyperbolic partial integro-differential equation (PIDE) - and carry the model linearization around an unstable operating condition. Employing the structure -preserving Cayley- Tustin transformation, we obtain a discrete -time model representation of the continuous model. Subsequently, we solve the operator Ricatti equations in the discrete -time setting to derive a full state feedback controller that stabilizes the closed -loop and design a Luenberger observer for state reconstruction given the system output measures. Finally, we formulate a dual -mode MPC ensuring constraint satisfaction and optimality, integrating the gain -based unconstrained full -state feedback optimal control obtained from the Ricatti equation. This dual -mode strategy describes an optimization problem where the predictive controller acts only if constraints become active within the control horizon. Simulation studies validate the controller performance, where the MPC only takes action if the constraints are predicted to be active within the control horizon while also guaranteeing closed -loop stabilization under only output feedback. This type of controller can be easily implemented with other control strategies and significantly decreases the computational costs of solving the optimal control problems when compared to other MPC approaches.

关键词： Dual-mode model predictive control distributed parameters system Chemostat reactor Population balance

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A Numerical-Analytical Model of Heat Transfer for a Variable Rate Flow 21

A Numerical-Analytical Model of Heat Transfer for a Variable...

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21st International Conference on Complex systems - Control and Modeling Problems (CSCMP)

作者： Danilushkin, Ivan Samara State Tech Univ Samara Russia

ISBN: (纸本)9781728167008

The heat exchange process between the medium and a constant rate flow for a certain class of problems is described with adequate accuracy by a one-dimensional first-order hyperbolic partial differential equation. Such an equation has an exact solution that can be represented as a block diagram with typical transfer functions. When formulating a problem with a time-varying rate flow, there is no exact solution to the hyperbolic equation. The paper considers an approach where a numerical model of a heat exchange process between the medium and a time-varying rate flow is based on an exact solution of the heat exchange problem between the medium and the constant rate flow. In terms of the structural theory of distributed systems, the transfer function of an object with distributed parameters is obtained, the structural representation of which includes a dead time element with constant time delay. As the main element of the numerical model of heat exchange with a variable flow rate, a block of simulation of a variable transport delay is used. The signal from the block input passes on to the output with a time delay. Its duration is determined as the ratio between the length of the heat exchange section and an integral of the flow rate. The paper proposes a numerical-analytical model of the heat exchange process when the exterior temperature is the same along the length of the heat exchange section and varies arbitrarily with the time. The developed model is compared with the exact solution for the special case of a step variation of the flow rate. The results of computer simulation are given. The proposed approach simplifies the model block diagram with a moderate decrease in the accuracy of transient process modeling. In addition, the behavior of the model in statics fully conforms to the analytical solution for a constant flow rate.

关键词： numerical-analytical model variable-speed flow heat transfer hyperbolic equation distributed parameters system

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Decentralized estimation of forest fire spread using reactive and cognitive mobile sensors

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NATURAL COMPUTING 2018年第3期17卷 537-551页

作者： Schlotterbeck, Guillaume Raievsky, Clement Lefevre, Laurent Univ Grenoble Alpes LCIS F-26000 Valence France

This paper presents a study of the ability to build an observer for a complex system using a decentralized multi-agent system for the coordination of mobile sensors. The environment is modeled using a CA model representing forest fire spread. The initial distribution for the different species in the vegetation is generated using a Perlin algorithm. Implementation is realized on GPGPU. A coherence measure for the observation error is defined. The observation itself is realized with mobile sensors and a decentralized coordination of the trajectories. We analyze the balance between individual and collective behaviours of agents which is required to achieve the best performance with respect to the chosen coherence measure. Two kinds of agent' behaviour are studied: reactive and cognitive.

关键词： Mobile sensors Multi agent systems State estimation distributed parameters system Forest fire spread Cellular automata Reactive/cognitive agents

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A Numerical-Analytical Model of Heat Transfer for a Variable Rate Flow

A Numerical-Analytical Model of Heat Transfer for a Variable...

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International Conference on Complex systems: Control and Modeling Problems (CSCMP)

作者： Ivan Danilushkin Samara State Technical University Samara Russian Federation

ISBN: (纸本)9781728167015

关键词： Numerical-analytical model Variable-speed flow Heat transfer Hyperbolic equation distributed parameters system Heat transfer Heat exchange Flow rates TRANSFER FUNCTIONS hyperbolic equations Transport delay Computer Simulation Constant Time Delay EXACT SOLUTIONS structural theory

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Flocculant Dosage Optimizing in Water Treatment based on Nonlinear Mathematical Model

Flocculant Dosage Optimizing in Water Treatment based on Non...

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International Conference on Environmental Science and Information Application Technology (ESIAT 2009)

作者： Guo Yufeng Ma Jun Zhai Xuedong Fan Yi Harbin Inst Technol Sch Elect Engn & Automat Harbin 150006 Peoples R China Harbin Inst Technol Sch Municipal & Environm Engn Harbin 150006 Peoples R China Harbin Inst Technol Sch Energy Sci & Technol Harbin 150006 Peoples R China

ISBN: (纸本)9780769536828

The artificial mathematical model of feed water treatment is investigated by the method of mechanism and modeling of distributed parameter system;it includes the basic processes of feed water treatment, i.e. coagulation, flocculation and sedimentation. This model can give the dynamic response of relationship between coagulant dosage and water turbidity after flocculation and sedimentation. The influence of water plant design parameters on water treatment effect can be analyzed from the simulation results of the model. Through the model at last, we had done an analog computation to the dynamic influence of sudden changes of inlet water turbidity on the outlet water turbidity after flocculation and sedimentation, and the simulation results are very close to the real experiment datum in water-plant. This model can be used for the process control of feed water treatment and offers a good simulation and analysis platform to the nonlinear control of water treatment.

关键词： Feed water treatment Dosage automatic control nonlinear mathematic model distributed parameters system

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Flocculant Dosage Optimizing in Water Treatment based on Nonlinear Mathematical Model

Flocculant Dosage Optimizing in Water Treatment based on Non...

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2009 International Conference on Environmental Science and Information Application Technology

作者： GUO Yufeng,School of Electrical Engineering and Automation Harbin Institute of Technology Harbin,China MA Jun School of Municipal and Environmental Engineering Harbin Institute of Technology Harbin,China ZHAI Xuedong School of Municipal and Environmental Engineering Harbin Institute of Technology Harbin,China FAN Yi School of Energy Science and Technology Harbin Institute of Technology Harbin,China

The artificial mathematical model of feed water treatment is investigated by the method of mechanism and modeling of distributed parameter system;it includes the basic processes of feed water treatment,***,flocculation and *** model can give the dynamic response of relationship between coagulant dosage and water turbidity after flocculation and *** influence of water plant design parameters on water treatment effect can be analyzed from the simulation results of the *** the model at last,we had done an analog computation to the dynamic influence of sudden changes of inlet water turbidity on the outlet water turbidity after flocculation and sedimentation,and the simulation results are very close to the real experiment datum in *** model can be used for the process control of feed water treatment and offers a good simulation and analysis platform to the nonlinear control of water treatment.

关键词： Feed water treatment Dosage automatic control nonlinear mathematic model distributed parameters system

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Explicit integral operator feedback for local stabilization of nonlinear thermal convection loop PDEs

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systemS & CONTROL LETTERS 2006年第8期55卷 624-632页

作者： Vazquez, R Krstic, M Univ Calif San Diego Dept Mech & Aerosp Engn San Diego CA 92093 USA Univ Calif San Diego Fac Mech & Aerosp Engn San Diego CA 92093 USA

A state feedback boundary control law that stabilizes fluid flow in a 2D thermal convection loop is presented. The fluid is enclosed between two cylinders, heated from above and cooled from below, which makes its motion unstable for a large enough Rayleigh number. The actuation is at the boundary through rotation (direct velocity actuation) and heat flux (heating or cooling) of the outer boundary. The design is a new approach for this kind of a coupled PDE problem, based on a combination of singular perturbation theory and the backstepping method for infinite dimensional linear systems. Stability is proved by Lyapunov method. Though only a linearized version of the plant is considered in the design, an extensive closed loop simulation study of the nonlinear PDE model shows that the result holds for reasonably large initial conditions. A highly accurate approximation to the control law is found in closed form. (c) 2006 Elsevier B.V. All rights reserved.

关键词： distributed parameters system flow control singularly perturbed systems partial differential equations Lyapunov analysis

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FAST AND SLOW GENERATION OF A MULTILEVEL CONTROL FOR THE WOOD DRYING PROCESS

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Drying Technology 2000年第8期18卷 1709-1735页

作者： S. Tarasiewicz. F. Ding. T. Kudra, Z. Mrozek

ABSTRACTABSTRACTThe dynamic characteristics of the wood drying process were represented by an actuator network and an internal model. These two subsystems are composed of a set of ordinary differential, partial differential and algebraic equations with adjusting operating functions. The formulation of the operating functions is based on interaction between air and the lumber board in a semi-industrial drying kiln. Using this internal model, it was possible to establish a state observer, a state predictor, and a reference model for which the boundary conditions were generated by the actuator network. Simulation results were obtained with a C++ software package. In order to implement the optimization techniques to the wood drying process, the two-level control structure was proposed and tested for a minimum drying time as a performance criterion. Numerical results confirm that the internal model and its operating functions were properly chosen.

关键词： actuator network distributed parameters system Euclidean norm fast and slow subsystems internal model mobile control volume operating functions variable structure system

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Front motion and convective heat flux determination in a phase change process

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Inverse problems in engineering 1996年第1期4卷 53-91页

作者： Y. Jarny J. P. Humeau S. Pé neau Laboratoire d’Automatique de Nantes (URA 823) Ecole Centrale de Nantes 1 rue de la noë Nantes cedex 03 44072 FRANCE Laboratoire d’Automatique de Nantes (URA 823) Ecole Centrale de Nantes 1 rue de la noë Nantes cedex 03 44072 FRANCE Laboratoire de Thermocinétique de Nantes (URA 869) ISITEM La Chantrerie Nantes cedex 03 44072 France

This paper deals with modelling of phase change phenomena with convection in the fluid in a pure phase change material. This model is related to several industrial applications as ablation, solidification, melting, iron casting. Temperature in the solid region is governed by a parabolic equation. The front between solid and fluid is a free boundary. Heat transfers on this free-boundary are modellized by a Stefan condition. The convection phenomena are taken into account in this condition by adding a source term which is the convective heat flux through the free boundary. This problem is called single phase Stefan problem with convection. By using the Duvaut's transform the problem is formulated as a parabolic variational inequality. Direct measurement of a front position and measurement of heat flux value on a free boundary are very difficult to perform. Here, the front motion and the value of the convective heat flux through this front are determined by optimal control of the variational inequality right hand side and by using temperature measurements in the phase change material. The optimal control is calculated by minimizing a criterion which characterizes the difference between calculated temperatures and temperature measurements.

关键词： Inverse Stefan problem variational inequality optimal contol phase change process distributed parameters system

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