Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e...Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.展开更多
A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse...A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.展开更多
This is the second paper of a series where we introduce a control volume based finite element method （CVFEM） to simulate multiphase flow in porous media. This is a fully conservative method able to deal with unstruc...This is the second paper of a series where we introduce a control volume based finite element method （CVFEM） to simulate multiphase flow in porous media. This is a fully conservative method able to deal with unstructured grids which can be used for representing any complexity of reservoir geometry and its geological objects in an accurate and efficient manner. In order to deal with the inherent heterogeneity of the reservoirs, all operations related to discretization are performed at the element level in a manner similar to classical finite element method （FEM）. Moreover, the proposed method can effectively reduce the so-called grid orientation effects. In the first paper of this series, we presented this method and its application for incompressible and immiscible two-phase flow simulation in homogeneous and heterogeneous porous media. In this paper, we evaluate the capability of the method in the solution of highly nonlinear and coupled partial differential equations by simulating hydrocarbon reservoirs using the black-oil model. Furthermore, the effect of grid orientation is investigated by simulating a benchmark waterflooding problem. The numerical results show that the formulation presented here is efficient and accurate for solving the bubble point and three-phase coning problems.展开更多
Immersed tunnel is an important part of the Hong Kong–Zhuhai–Macao Bridge(HZMB) project. In immersed tunnel floating, translation which includes straight and transverse movements is the main working mode. To decide ...Immersed tunnel is an important part of the Hong Kong–Zhuhai–Macao Bridge(HZMB) project. In immersed tunnel floating, translation which includes straight and transverse movements is the main working mode. To decide the magnitude and direction of the towing force for each tug, a particle swarm-based translation control method is presented for non-power immersed tunnel element. A sort of linear weighted logarithmic function is exploited to avoid weak subgoals. In simulation, the particle swarm-based control method is evaluated and compared with traditional empirical method in the case of the HZMB project. Simulation results show that the presented method delivers performance improvement in terms of the enhanced surplus towing force.展开更多
Feedforward control is the core to control function in the cooling process of hot strip. One of the most important tasks in feedforward control is to determine the arrival time of the strip at various locations on the...Feedforward control is the core to control function in the cooling process of hot strip. One of the most important tasks in feedforward control is to determine the arrival time of the strip at various locations on the runout table for effective control. Based on the principles of element tracking and tracking strategies for variable rolling speed and constant rolling speed, a simple diagonal tracking method for an existing hot strip mill was proposed and tested. The test results show that the proposed strategies are effective for improving tracking control.展开更多
This paper, probing into heavy metal control in domestic rubbish by source screening and nutrient element analysis, revealed the feasibility of source control of heavy metals and the suitability of rubbish as turfgras...This paper, probing into heavy metal control in domestic rubbish by source screening and nutrient element analysis, revealed the feasibility of source control of heavy metals and the suitability of rubbish as turfgrass medium. Heavy metals in domestic rubbish were controlled by source screening before composting. The study consisted of a control with garden soil. The contents of main mineral elements and heavy metals in rubbish compost and control were determined by the method of ICP-AES. The results showed that heavy metal concentrations in rubbish were lower than those in garden soil, and little difference occurred between rubbish and garden soil in main mineral element concentrations. Based on this, it was concluded that rubbish compost was favorable for using as turfgrass medium and heavy metal control in rubbish by source screening was effective.展开更多
Presents the general formula derived with a smart beam structure bonded with piezoelectric material using the piezoelectricity theory, elastic mechanism and Hamilton principle for electromechanically coupled piezoelec...Presents the general formula derived with a smart beam structure bonded with piezoelectric material using the piezoelectricity theory, elastic mechanism and Hamilton principle for electromechanically coupled piezoelectric finite element and dynamic equations, the second order dynamic model built, and the expression of state space, and the analysis of conventional speed and position feedback and the design of optimum feedback controller for output, the finite element models built for a piezoelectric cantilever beam, and the feedback controller designed eventually, and concludes with simulation results that the vibration suppression obtained is very satisfactory and the algorithms proposed are very useful.展开更多
The efficacy of shape control is the core of this technology and the main basis of automatic shape control system model designing. This passage constructs the three-dimensional elastic deformation model of CVCplus rol...The efficacy of shape control is the core of this technology and the main basis of automatic shape control system model designing. This passage constructs the three-dimensional elastic deformation model of CVCplus roll system in 2250 mm hot rolling mill. Comparing and analyzing different influence of working factors on control characteristic, the shape control characteristic of CVCplus roll system in its whole work time is studied, and the cause is analyzed and the difference of the roll gap curve and crown adjustable area in early and latter work time is compared. The outcome has crucial meaning in both theory and production.展开更多
A model for evaluating the controller workload was presented based on matter-element analysis, particularly from a mansystem engineering perspective. On the basis of a questionnaire survey, 18 kinds of indexes which i...A model for evaluating the controller workload was presented based on matter-element analysis, particularly from a mansystem engineering perspective. On the basis of a questionnaire survey, 18 kinds of indexes which influence the controller workload were determined. By establishing the classical field and node field of the controller workload, the correlation function of the controller workload grade was obtained; then the correlation degree and estimated grade of controller workload were given. A case study verifies the feasibility of the proposed evaluation method.展开更多
Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method...Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L<sup>2</sup> (Γ) and L<sup>∞</sup> (Γ) norm. For state and adjoint state, optimal convergence order in the L<sup>2</sup> (Ω) and H<sup>1</sup> (Ω) can also be obtained.展开更多
In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and &l...In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and <em>L</em>1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.展开更多
The authors firstly introduce deformation control of deep excavation pit indetail, and then put forward new conceptions such as: effective coefficient of excavation pit,effective area, ineffective area and critical li...The authors firstly introduce deformation control of deep excavation pit indetail, and then put forward new conceptions such as: effective coefficient of excavation pit,effective area, ineffective area and critical line, and also put forward the referential criteria ofdeformation control. The System of Optimization Design with Deformation Control of Deep ExcavationPit and Numerical Simulation with Finite Element Method (SDCDEFEM) is also briefly introduced.Factors influencing deformation of excavation pit are analyzed by the system. The measured andsimulated data of maximum deformations (settlement, displacement and upheaval) and their positionsare analyzed and discussed. The statistic formula estimating maximum deformations and theirpositions was gained, and economical-effective measures of deformation control were brought forward.展开更多
In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretizati...In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L<sup>2</sup> and H<sup>1</sup> norm are derived. The theoretical findings are illustrated by the numerical experiments.展开更多
Based on knowledge of meteorology, pastoral meteorology and medical meteorology, the paper discusses relationship between various meteorological elements and animal husbandry production or animal disease prevention an...Based on knowledge of meteorology, pastoral meteorology and medical meteorology, the paper discusses relationship between various meteorological elements and animal husbandry production or animal disease prevention and control.展开更多
This paper presents the optimal control variational principle for Perzyna modelwhich is one of the main constitutive relation of viscoplasticity in dynamics. And itcould also be transformed to solve the parametric qua...This paper presents the optimal control variational principle for Perzyna modelwhich is one of the main constitutive relation of viscoplasticity in dynamics. And itcould also be transformed to solve the parametric quadratic programming problem.The FEM form of this problem and its implementation have also been discussed in thepaper.展开更多
Presents the design scheme developed for design of software for Integrated Passive and Active Vibration Control(IPAVC) and the coding of a prototyne system, and the selection of the famous finite element program MSC/N...Presents the design scheme developed for design of software for Integrated Passive and Active Vibration Control(IPAVC) and the coding of a prototyne system, and the selection of the famous finite element program MSC/NASTRAN as an important module of software to deal with large and complicated structures and systems with an example to demonstrate the prototype system.展开更多
Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data ...Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data for the detection of DHIs, new methods have been investigated. Marine controlled source electromagnet (MCSEM) or Sea bed logging (SBL) is new method for the detection of deep target hydrocarbon reservoir. Sea bed logging has also the potential to reduce the risks of DHIs in deep sea environment. Modelling of real sea environment helps to reduce the further risks before drilling the oil wells. 3D electromagnetic (EM) modelling of seabed logging requires more accurate methods for the detection of hydrocarbon reservoir. Finite element method (FEM) is chosen for the modelling of seabed logging to get more precise EM response from hydrocarbon reservoir below 4000 m from seabed. FEM allows to investigate the total electric and magnetic fields instead of scattered electric and magnetic fields, which shows accurate and precise resistivity contrast below the seabed. From the modelling results, It was investigated that Hz field shows higher magni- tude with 342% than the Ex field. It was observed that 0.125 Hz frequency can be able to show better resistivity contrast of Hz field (31.30%) and Ex field (16.49%) at target depth of 1000 m below seafloor for our proposed model. Hz and Ex field delineation was found to decrease as target depth increased from 1000 m to 4000 m. At the target depth of 4000 m, no field delineation response was seen from the current electromagnetic (EM) antenna used by the industry. New EM antenna has been used to see the EM response for deep target hydrocarbon detection. It was investigated that novel EM antenna shows better delineation at 4000 m target depth for Ex and Hz field up to 10.3% and 15.1% respectively. Novel EM antenna also shows better Hz phase response (128.4%) than the Ex phase response (38.3%) at the target depth of 4000 m below the seafloor.展开更多
In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and ...In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.展开更多
Pebble bed reactors use cycling scheme of spherical fuel elements relying on fuel elements cycling system (FECS). The structure and control logic of FECS are very complex. Each control link has strict requirements on ...Pebble bed reactors use cycling scheme of spherical fuel elements relying on fuel elements cycling system (FECS). The structure and control logic of FECS are very complex. Each control link has strict requirements on time and sequence. This increases the difficulties of description and analysis. In this paper, timed places control Petri nets (TPCPN) is applied for the modeling of FECS. On this basis the simulation of two important processes, namely uploading fuel elements into the core for the first time and emptying the core is finished by simulation software Arena. The results show that as TPCPN is able to describe different kinds of logic relationship and has time properties and control properties, it’s very suitable for the modeling and analysis of FECS.展开更多
基金Iranian Offshore Oil Company (IOOC) for financial support of this work
文摘Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.
基金supported by the Innovation Foundation of BUAA for PhD Graduates (No.YWF-12-RBYJ-024)the National Natural Science Foundation of China (No.11002008)National Basic Research Program of China (No.2009CB723906)
文摘A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.
基金Iranian Offshore OilCompany (IOOC) for financial support of this work
文摘This is the second paper of a series where we introduce a control volume based finite element method （CVFEM） to simulate multiphase flow in porous media. This is a fully conservative method able to deal with unstructured grids which can be used for representing any complexity of reservoir geometry and its geological objects in an accurate and efficient manner. In order to deal with the inherent heterogeneity of the reservoirs, all operations related to discretization are performed at the element level in a manner similar to classical finite element method （FEM）. Moreover, the proposed method can effectively reduce the so-called grid orientation effects. In the first paper of this series, we presented this method and its application for incompressible and immiscible two-phase flow simulation in homogeneous and heterogeneous porous media. In this paper, we evaluate the capability of the method in the solution of highly nonlinear and coupled partial differential equations by simulating hydrocarbon reservoirs using the black-oil model. Furthermore, the effect of grid orientation is investigated by simulating a benchmark waterflooding problem. The numerical results show that the formulation presented here is efficient and accurate for solving the bubble point and three-phase coning problems.
基金financially supported by the Ministry of Education of Humanities and Social Science Project(Grant Nos.15YJC630145 and 15YJC630059)the Natural Science Foundation of Shanghai Science and Technology Committee(Grant No.15ZR1420200)
文摘Immersed tunnel is an important part of the Hong Kong–Zhuhai–Macao Bridge(HZMB) project. In immersed tunnel floating, translation which includes straight and transverse movements is the main working mode. To decide the magnitude and direction of the towing force for each tug, a particle swarm-based translation control method is presented for non-power immersed tunnel element. A sort of linear weighted logarithmic function is exploited to avoid weak subgoals. In simulation, the particle swarm-based control method is evaluated and compared with traditional empirical method in the case of the HZMB project. Simulation results show that the presented method delivers performance improvement in terms of the enhanced surplus towing force.
文摘Feedforward control is the core to control function in the cooling process of hot strip. One of the most important tasks in feedforward control is to determine the arrival time of the strip at various locations on the runout table for effective control. Based on the principles of element tracking and tracking strategies for variable rolling speed and constant rolling speed, a simple diagonal tracking method for an existing hot strip mill was proposed and tested. The test results show that the proposed strategies are effective for improving tracking control.
基金NationalNaturalScienceFoundation (59878033)Tianjin Science and Technology Developm entProgram (043100611).
文摘This paper, probing into heavy metal control in domestic rubbish by source screening and nutrient element analysis, revealed the feasibility of source control of heavy metals and the suitability of rubbish as turfgrass medium. Heavy metals in domestic rubbish were controlled by source screening before composting. The study consisted of a control with garden soil. The contents of main mineral elements and heavy metals in rubbish compost and control were determined by the method of ICP-AES. The results showed that heavy metal concentrations in rubbish were lower than those in garden soil, and little difference occurred between rubbish and garden soil in main mineral element concentrations. Based on this, it was concluded that rubbish compost was favorable for using as turfgrass medium and heavy metal control in rubbish by source screening was effective.
文摘Presents the general formula derived with a smart beam structure bonded with piezoelectric material using the piezoelectricity theory, elastic mechanism and Hamilton principle for electromechanically coupled piezoelectric finite element and dynamic equations, the second order dynamic model built, and the expression of state space, and the analysis of conventional speed and position feedback and the design of optimum feedback controller for output, the finite element models built for a piezoelectric cantilever beam, and the feedback controller designed eventually, and concludes with simulation results that the vibration suppression obtained is very satisfactory and the algorithms proposed are very useful.
文摘The efficacy of shape control is the core of this technology and the main basis of automatic shape control system model designing. This passage constructs the three-dimensional elastic deformation model of CVCplus roll system in 2250 mm hot rolling mill. Comparing and analyzing different influence of working factors on control characteristic, the shape control characteristic of CVCplus roll system in its whole work time is studied, and the cause is analyzed and the difference of the roll gap curve and crown adjustable area in early and latter work time is compared. The outcome has crucial meaning in both theory and production.
基金The National Natural Science Foundation of China (60742117)
文摘A model for evaluating the controller workload was presented based on matter-element analysis, particularly from a mansystem engineering perspective. On the basis of a questionnaire survey, 18 kinds of indexes which influence the controller workload were determined. By establishing the classical field and node field of the controller workload, the correlation function of the controller workload grade was obtained; then the correlation degree and estimated grade of controller workload were given. A case study verifies the feasibility of the proposed evaluation method.
文摘Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L<sup>2</sup> (Γ) and L<sup>∞</sup> (Γ) norm. For state and adjoint state, optimal convergence order in the L<sup>2</sup> (Ω) and H<sup>1</sup> (Ω) can also be obtained.
文摘In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and <em>L</em>1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.
文摘The authors firstly introduce deformation control of deep excavation pit indetail, and then put forward new conceptions such as: effective coefficient of excavation pit,effective area, ineffective area and critical line, and also put forward the referential criteria ofdeformation control. The System of Optimization Design with Deformation Control of Deep ExcavationPit and Numerical Simulation with Finite Element Method (SDCDEFEM) is also briefly introduced.Factors influencing deformation of excavation pit are analyzed by the system. The measured andsimulated data of maximum deformations (settlement, displacement and upheaval) and their positionsare analyzed and discussed. The statistic formula estimating maximum deformations and theirpositions was gained, and economical-effective measures of deformation control were brought forward.
文摘In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L<sup>2</sup> and H<sup>1</sup> norm are derived. The theoretical findings are illustrated by the numerical experiments.
文摘Based on knowledge of meteorology, pastoral meteorology and medical meteorology, the paper discusses relationship between various meteorological elements and animal husbandry production or animal disease prevention and control.
文摘This paper presents the optimal control variational principle for Perzyna modelwhich is one of the main constitutive relation of viscoplasticity in dynamics. And itcould also be transformed to solve the parametric quadratic programming problem.The FEM form of this problem and its implementation have also been discussed in thepaper.
文摘Presents the design scheme developed for design of software for Integrated Passive and Active Vibration Control(IPAVC) and the coding of a prototyne system, and the selection of the famous finite element program MSC/NASTRAN as an important module of software to deal with large and complicated structures and systems with an example to demonstrate the prototype system.
文摘Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data for the detection of DHIs, new methods have been investigated. Marine controlled source electromagnet (MCSEM) or Sea bed logging (SBL) is new method for the detection of deep target hydrocarbon reservoir. Sea bed logging has also the potential to reduce the risks of DHIs in deep sea environment. Modelling of real sea environment helps to reduce the further risks before drilling the oil wells. 3D electromagnetic (EM) modelling of seabed logging requires more accurate methods for the detection of hydrocarbon reservoir. Finite element method (FEM) is chosen for the modelling of seabed logging to get more precise EM response from hydrocarbon reservoir below 4000 m from seabed. FEM allows to investigate the total electric and magnetic fields instead of scattered electric and magnetic fields, which shows accurate and precise resistivity contrast below the seabed. From the modelling results, It was investigated that Hz field shows higher magni- tude with 342% than the Ex field. It was observed that 0.125 Hz frequency can be able to show better resistivity contrast of Hz field (31.30%) and Ex field (16.49%) at target depth of 1000 m below seafloor for our proposed model. Hz and Ex field delineation was found to decrease as target depth increased from 1000 m to 4000 m. At the target depth of 4000 m, no field delineation response was seen from the current electromagnetic (EM) antenna used by the industry. New EM antenna has been used to see the EM response for deep target hydrocarbon detection. It was investigated that novel EM antenna shows better delineation at 4000 m target depth for Ex and Hz field up to 10.3% and 15.1% respectively. Novel EM antenna also shows better Hz phase response (128.4%) than the Ex phase response (38.3%) at the target depth of 4000 m below the seafloor.
文摘In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.
文摘Pebble bed reactors use cycling scheme of spherical fuel elements relying on fuel elements cycling system (FECS). The structure and control logic of FECS are very complex. Each control link has strict requirements on time and sequence. This increases the difficulties of description and analysis. In this paper, timed places control Petri nets (TPCPN) is applied for the modeling of FECS. On this basis the simulation of two important processes, namely uploading fuel elements into the core for the first time and emptying the core is finished by simulation software Arena. The results show that as TPCPN is able to describe different kinds of logic relationship and has time properties and control properties, it’s very suitable for the modeling and analysis of FECS.
