The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and n...The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.展开更多
EDF R＆D is developing a new calculation scheme based on the transport-Simplified Pn （SPn） approach. The lattice code used is the deterministic code APOLLO2, developed at CEA. The core code is the code COCAGNE, deve...EDF R＆D is developing a new calculation scheme based on the transport-Simplified Pn （SPn） approach. The lattice code used is the deterministic code APOLLO2, developed at CEA. The core code is the code COCAGNE, developed at EDF R＆D. The latter can take advantage of a microscopic depletion solver expected to improve the treatment of spectral history effects. However, the direct use of the microscopic depletion solver is computationally very intensive because very small evolution steps （typically 100 MWd/t） are needed to reach a good accuracy, which is not always compatible with industrial applications. In order to reduce the calculation time associated with the use of the microscopic depletion solver, a predictor-corrector scheme has been implemented within COCAGNE. It enables the use of larger evolution steps, up to 1000 MWd/t. Tests show that the predictor-corrector procedure gives fairly accurate results while significantly reducing the calculation time.展开更多
基金Shanghai Science and Technology Devel-opm ent Funds ( No.0 1160 70 3 3)
文摘The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.
文摘EDF R＆D is developing a new calculation scheme based on the transport-Simplified Pn （SPn） approach. The lattice code used is the deterministic code APOLLO2, developed at CEA. The core code is the code COCAGNE, developed at EDF R＆D. The latter can take advantage of a microscopic depletion solver expected to improve the treatment of spectral history effects. However, the direct use of the microscopic depletion solver is computationally very intensive because very small evolution steps （typically 100 MWd/t） are needed to reach a good accuracy, which is not always compatible with industrial applications. In order to reduce the calculation time associated with the use of the microscopic depletion solver, a predictor-corrector scheme has been implemented within COCAGNE. It enables the use of larger evolution steps, up to 1000 MWd/t. Tests show that the predictor-corrector procedure gives fairly accurate results while significantly reducing the calculation time.
