In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-lo...In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-loop reference trajectory and the actual process.In the upper layer,the variant time scale based control vector parametric methods(VTS-CVP) was used for dynamic optimization of transition reference trajectory,while nonlinear model predictive controller(NMPC) based on closed-loop subspace and piece-wise linear(SSARX-PWL) model in the lower layer was tracking to the reference trajectory from the upper layer for overcoming high-frequency disturbances.Besides,mechanism about trajectory deviation detection and optimal trajectory updating online were introduced to ensure a smooth transition for the entire process.The proposed method was validated with the real data from an industrial double-loop propylene polymerization reaction process with developed dynamic mechanism mathematical model.展开更多
It is well known that for non-linear Hamiltonian systems there exist ordered regions with quasi-periodic orbits and regions with chaotic orbits. Usually, these regions are distributed in the phase space in very compli...It is well known that for non-linear Hamiltonian systems there exist ordered regions with quasi-periodic orbits and regions with chaotic orbits. Usually, these regions are distributed in the phase space in very complicated ways, which often makes it very difficult to distinguish between them, especially when we are dealing with many degrees of freedom. Recently, a new, very fast and easy to compute indicator of the chaotic or ordered nature of orbits has been introduced by Zotos (2012), the so-called "Fast Norm Vector Indicator (FNV1)". Using the double pendulum system, in the paper we present a detailed numerical study comporting the advantages and the drawbacks of the FNVI to those of the Smaller Alignment Index (SALI), a reliable indicator of chaos and order in Hamiltonian systems. Our effort was focused both on the traditional behavior of the FNVI for regular and fully developed chaos but on the "sticky" orbits and on the quantitative criterion proposed by Zotos, too.展开更多
This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of ent...This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem (CRTBP) are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator (OFLI). The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.展开更多
The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit...The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.展开更多
基金Supported by the Electronic Information Industry Development Foundation of China(20140806)the National Natural Science Foundation of China(61374121,61134007)
文摘In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-loop reference trajectory and the actual process.In the upper layer,the variant time scale based control vector parametric methods(VTS-CVP) was used for dynamic optimization of transition reference trajectory,while nonlinear model predictive controller(NMPC) based on closed-loop subspace and piece-wise linear(SSARX-PWL) model in the lower layer was tracking to the reference trajectory from the upper layer for overcoming high-frequency disturbances.Besides,mechanism about trajectory deviation detection and optimal trajectory updating online were introduced to ensure a smooth transition for the entire process.The proposed method was validated with the real data from an industrial double-loop propylene polymerization reaction process with developed dynamic mechanism mathematical model.
文摘It is well known that for non-linear Hamiltonian systems there exist ordered regions with quasi-periodic orbits and regions with chaotic orbits. Usually, these regions are distributed in the phase space in very complicated ways, which often makes it very difficult to distinguish between them, especially when we are dealing with many degrees of freedom. Recently, a new, very fast and easy to compute indicator of the chaotic or ordered nature of orbits has been introduced by Zotos (2012), the so-called "Fast Norm Vector Indicator (FNV1)". Using the double pendulum system, in the paper we present a detailed numerical study comporting the advantages and the drawbacks of the FNVI to those of the Smaller Alignment Index (SALI), a reliable indicator of chaos and order in Hamiltonian systems. Our effort was focused both on the traditional behavior of the FNVI for regular and fully developed chaos but on the "sticky" orbits and on the quantitative criterion proposed by Zotos, too.
基金supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11525208)the National Natural Science Foundation of China(Grant No.11572166)
文摘This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem (CRTBP) are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator (OFLI). The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10832004 and 11072122)
文摘The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.