Set-theoretic approach to uncertain dynamical systems using convex polytopes

A set-theoretic approach to uncertain dynamical systems by using convex polytopes is treated. In some points, this approach is superior to the one using ellipsoids, though it also has some disadvantages. First, some fundamental operations are discussed, such as addition, intersection, and the linear transformation of convex polytopes. The results are applied to the analysis of reachable sets for discrete-time linear dynamical systems and also to the state estimation.     

Maintenance policies in markovian deterioration models of parallel unit systems

Markovian deterioration models of parallel unit systems are dealt with. Units of a system are supposed to be of different types, and a state of the system is represented by a vector whose component corresponds to the state of each unit. Therefore all the states of the system are only partially ordered, while they are totally ordered in ordinary markovian deterioration models. It is proved under some conditions that the optimal maintenance policy is a partial control limit policy, which is a generalization of the well-known control limit policy in the ordinary case. An algorithm improving the successive approximation method is proposed for obtaining the optimal policy. A typical case of the model is also discussed.     

Unscented Kalman Filtering for Self‐Sensing Magnetic Levitation against Magnetic Saturation

This paper investigates the magnetic saturation problem of self‐sensing electromagnetic levitation system and presents a novel self‐sensing scheme. The proposed approach employs a demodulation technique. By superimposing a high‐frequency voltage, the resulting electromagnet coil currents have ripples that can be used for gap sensing. This paper shows that the gap length is not uniquely estimated when using only the relation between the ripple, the control currents, and the gap. The constraint conditions are to be determined to solve the problem. The proposed approach utilizes the dynamical motion model of the electromagnetic levitation system to uniquely identify the gap. Introducing the system behavior dynamics, the gap can be exactly estimated. To incorporate the system model with the gap sensing algorithm, a nonlinear filtering methodology is employed. The proposed estimator is demonstrated by the experiments. The results show that it is possible to address magnetic saturation with the proposed gap sensing scheme. The estimator has a good accuracy in a wider gap range compared to the conventional methods.     

Nonstoichiometric Hexagonal Close-Packed Uranium Sesquinitride

When uranium metal is nitrified in 1 atm N₂, the well-known uranium sesquinitride with the bcc structure is obtained as a single phase at 1150° to 1175°C and below. A single phase of another sesquinitride with the hep structure is formed at 1330° to 1350°C. Between these temperatures, a kinetically stable mixture of sesquinitrides is obtained. Both sesquinitrides are nonstoichiometric; the bcc sesquinitride is UN_1.66–1.56 and the hep one UN_1.44–1.45 Above 1350°C, the sesquinitride decomposes into the mononitride. The transformation between the bcc and hep phases is not allotropic; a change in stoichiometry accompanies the transformation. For the sesquinitrides and the mononitride, the interplanar spacings and relative intensities of the X-ray reflection lines are reported and the lattice constants are presented. For the bcc sesquinitride, an approximate linear relation between stoichiometry and lattice constant is illustrated.