In the paper we consider the parameter identification problem of distributed parameter systems as solving nonlinear operator equations. Thus, a rapid converqent iterative method for identifying distributedparameters ...
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In the paper we consider the parameter identification problem of distributed parameter systems as solving nonlinear operator equations. Thus, a rapid converqent iterative method for identifying distributedparameters in distributed parameter systems is presented. And we prove the method has a 3rd-order convergent speed when there exists a unique bounded solution to the identification problem and that this method with regularization also is convergent under the assumption of no unique solution. A computational example to identify the permeability k(x, y) in the permeation equation is presented to illustrate the validity of the method.
This work addresses the boundary control problem for prescribed-time stabilisation of a parabolic reaction-diffusion system (PRDS) with time delay via the backstepping-based approach and Razumikhin method. The inverti...
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This work addresses the boundary control problem for prescribed-time stabilisation of a parabolic reaction-diffusion system (PRDS) with time delay via the backstepping-based approach and Razumikhin method. The invertible Volterra transformation is used to convert the PRDS into a suitable prescribed-time stable PRDS with time-dependent coefficient, which is related to time-dependent kernel function. The obtained kernel partial differential equations are proven to be well-posed using the successive approximation. The boundary controller is designed by solving the kernel equations to guarantee the prescribed-time stabilisation of the delayed PRDS. Finally, two numerical examples are given to testify the feasibility of the proposed methodology.
The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued mea...
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The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function.
A digital control system for a rotary cement kiln has been developed and implemented on computer. The controller design is based on process identification results, obtained during open loop operation. Optimal kiln ope...
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A digital control system for a rotary cement kiln has been developed and implemented on computer. The controller design is based on process identification results, obtained during open loop operation. Optimal kiln operation requires a very performant control system. The process control needs to ensure stable behaviour of the kiln in front of numerous and random system perturbations as well as to guide the process in optimal productivity conditions. Hierarchical and auto-adaptive control algorithms have been developed to adapt the controller the best to the production requirements. Actually, industrial application of the control system shows to work and is very well adapted to the nature of the process. Resulting improvements are very satisfying, mainly the remarkable energy consumption reductions.
Abstract A control strategy is proposed to control the internal fluid temperature at the outlet of a co-current heat exchanger by manipulating the inlet external fluid temperature. The dynamic model of the heat exchan...
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Abstract A control strategy is proposed to control the internal fluid temperature at the outlet of a co-current heat exchanger by manipulating the inlet external fluid temperature. The dynamic model of the heat exchanger is given by two partial differential equations. Based on nonlinear geometric control, a state-feedback law that ensures a desired performance of a measured output defined as spatial average temperature of the internal fluid is derived. Then, in order to control the outlet internal fluid temperature, a control strategy is proposed where an external controller is introduced to provide the set point of the considered measured output by taking as input the error between the outlet internal fluid temperature and its desired set point. The validity of the proposed control design and strategy is examined in simulation by considering the tracking and perturbation rejection problems.
The temperature distribution in the fluid in a floated gyroscope is described by a Dirichlet-Neumann’s mixed boundary value problem of 2nd order linear elliptic equations. Using the Lions’ function space optimizatio...
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The temperature distribution in the fluid in a floated gyroscope is described by a Dirichlet-Neumann’s mixed boundary value problem of 2nd order linear elliptic equations. Using the Lions’ function space optimization method, we estimate the float surface temperature by means of measuring the temperature on the part of the gyroscope hull. It is proved that the above problem is identifiable when the unknown float temperature (the parameter) varies in some admissible set.
Efficient monitoring and control of a plug flow reactor system requires knowledge of temporal variations of spatial profiles of concentrations. However, estimating the state profiles in spatial domain requires discret...
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Efficient monitoring and control of a plug flow reactor system requires knowledge of temporal variations of spatial profiles of concentrations. However, estimating the state profiles in spatial domain requires discretization of the governing PDEs at a large number of spatial grid points, which results in high order DAE systems. Computational cost associated with solving these DAEs makes them unattractive candidates for development of advanced on-line monitoring and control schemes. In this work, a novel method for reconstructing spatial profiles of state variables is proposed, which exploits the fact that orthogonal collocation based discretization of PDEs employs time-dependent interpolation polynomials as approximate solutions. A reduced-order approximation of PDE system is developed using Lagrange interpolation polynomials and further used to develop a reduced dimensional extended Kalman filter (EKF). States estimated using the reduced-order EKF, in combination with Lagrange polynomials, are used to construct estimates of spatial profiles of state variables. The proposed approach facilitates handling of measurements available from sensors placed at arbitrary spatial locations other than the collocation points. The performance of proposed reduced-order observer is evaluated via simulation studies performed on a benchmark counter-current plug flow reactor system. Analysis of the simulation results reveals that the proposed approach is capable of generating state profile estimates that are comparable to profile estimates obtained using a high dimensional observer with a significant reduction in the computational cost.
In this project we investigate the active control of transverse vibrations of an elastic beam using active control strategies. The system is excited by a mass moving with constant velocity across a beam. The aims are ...
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In this project we investigate the active control of transverse vibrations of an elastic beam using active control strategies. The system is excited by a mass moving with constant velocity across a beam. The aims are to minimize the transverse deflections under the moving mass and the total maximum deflection of the beam. The finite element approach and modal analysis for modeling is used. We apply two different control strategies to reach the aims. The first one is an optimal discrete time control which allows to implement both aims. The second one is an adaptive control strategy with a simple model to minimize the deflection under the moving mass. Numerical and experimental results are compared. Applying optimal control a reduction of the deflection under the moving mass of more than 98% with respect to the uncontrolled system is possible. Taking into account the total maximum deflection an optimum can be found where both deflections are reduced by more than 88%. The reduction of the deflection under the moving mass applying adaptive control is smaller than that using the optimal discrete time control.
Pressure swing adsorption (PSA) plants consist of several fixed-bed adsorbers and are operated as cyclic multi-step processes. PSA processes are used for the separation and purification of gas mixtures. Based on a rig...
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Pressure swing adsorption (PSA) plants consist of several fixed-bed adsorbers and are operated as cyclic multi-step processes. PSA processes are used for the separation and purification of gas mixtures. Based on a rigorous distributedparameter model of the considered 2-bed PSA plant, a process control scheme is derived which is composed of a nonlinear feedforward control and a linear feedback control. For the design of the feedforward control, a numerical approach for the inversion of the rigorous plant model is presented. The designed trajectory control scheme is evaluated by use of the PSA plant simulation model
The power factor of the nuclear reactor is an important characteristic index of the nuclear reactor. By means of diffusion approximation relating to neutron flux, the problem is reduced to the optimal control problem ...
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The power factor of the nuclear reactor is an important characteristic index of the nuclear reactor. By means of diffusion approximation relating to neutron flux, the problem is reduced to the optimal control problem of the distributed parameter system. First we prove the continuity of both the solution of neutron diffusion equation and the solution of perturbation equation. Then we deduce necessary conditions of the optimal control by means of Dubovitskii-Milyutin theorem. This condition is a system of coupled diffusion.
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