A kind of generalized proportional-integral(GPI) observer for descriptor linear systems is introduced. We first propose two complete parametric solutions to generalized Sylvester matrix equation corresponding to the left eigenvector matrices in the case of Jordan form. Then a parametric design approach for the observer is presented. The proposed method provides all parametric expression of the gain matrices and the corresponding finite left eigenvector matrix and guarantees the regularity and impulse-freeness of the expanded error system. Two numerical examples are given to explain the design procedure and illustrate the effectiveness of the proposed method.

The most commonly quenching process for carburizing gears is the oil-quenching (OQ) and salt-quenching (SQ), and finite analysis and comparison of OQ and SQ on the carburizing gear ring were performed. Wherein, the accurate simulation of gear carburization was obtained by the alloying element coefficient for diffusion coefficient and experiment validation. The heat transfer coefficients measured by the inverse heat transfer method was used to the temperature simulation, and the gear distortion mechanism was analyzed by the simulated results. By the comparison of OQ, SQ had higher cooling capacity in the high temperature region and slow cooling rate in the temperature range where martensite transformation occurs. The martensite transformation was more sufficient, and the compressive stress of the tooth was greater in the SQ. The tooth showed a drum-shaped and slight saddle-shaped distortion in the OQ and SQ, respectively. The simulated distortion results have good consistency with the measured results, and the SQ distortion was more uniform and stable based on the measured results.

Through partially replacing Y element, Ce was added into near-equiatomic AlNiY medium-entropy amorphous alloy (denoted as MEAA) ribbons by the melt spinning process in this study. The differences of microstructure, thermal stability, hardness and corrosion resistance of Al33.3Ni33.3Y33.4-xCex (x = 0, 2, 5, 8, 13) alloy ribbons were investigated by X-ray diffraction (XRD), scanning electron microscope (SEM), differential scanning calorimeter (DSC) and Vickers-type hardness tester. The anti-corrosion performance in 3.5 wt.% NaCl solution of alloy ribbons was investigated elaborately through the general potentiodynamic polarization curves (Tafel) and electrochemical impedance spectroscopy (EIS). Results suggested that all ribbon samples could remain amorphous structure and the hardness are all above 510 HV0.1. With the increase of Ce content, the thermal stability begins to be gradually lower. However, according to the analysis of crystallization kinetics, all types of MEAA ribbons presents the relatively prominent thermal stability compared with traditional Al-based amorphous alloys. The corrosion current density raises firstly, then shows a decreasing trend, and has a slight increase at last. Therefore, appropriate content of Ce element can improve the corrosion protection performance of alloy ribbons and the 5 at.% Ce MEAA ribbons exhibited the excellent corrosion resistance in this study.