Model predictive control (MPC), that can consider system constraints, is one of the most advanced control technology used nowadays. In power systems, MPC is applied in a way that an optimal control sequence is given every step by an online MPC controller. The main drawback is that the control law cannot be evaluated before the MPC controller is put into service. Therefore, system operators may not validate its performances in advance. To overcome this drawback, the explicit MPC (EMPC) method is introduced and applied to obtain an explicit control law. In addition, another major contribution is that an improved partition algorithm of EMPC is studied which enables the EMPC method to be extended to a system of large number of state variables and more constraints. A simple single generator single load case is used to illustrate the whole procedure of EMPC and then the EMPC is applied to an actual isolated power system for frequency control. Simulation results show that the explicit control law of EMPC is able to restore system frequency to its nominal value under large disturbance. Moreover, the physical meaning of the explicit control law given by EMPC can be clearly explained for the studied system.

Modified basalt microfiber-reinforced polyurethane elastomer composites were prepared by a semi-prepolymer method with two different silane coupling agents (KH550 and KH560) in this study. Infrared spectroscopy was used to quantify the degree of microphase separation and analyze the formation of hydrogen bonding in polyurethane. The interfacial surface and the morphology of fibers and composites from tensile fracture were examined by a scanning electron microscope. Further measurements were performed on an electronic universal testing machine for characterizing the mechanical properties of composites. Moreover, the loss factor and transmission loss of composite materials were obtained from dynamic thermomechanical analysis and acoustic impedance tube, respectively. The suitable concentrations in the modification of basalt fibers were established at 1% for KH550 and 1.5% for KH560. The best overall performance was obtained in KH550-BMF/PUE group, as the properties increased by 31% in tensile strength, 37% in elongation at break, and 21% in acoustic insulation.

Polyurethane microcellular elastomers (PUME) are good at impact protection and energy absorption, and belong to rate sensitive- and strain history-dependent materials. In this study, PUME with different densities of 800 kg/m³, 600 kg/m³ and 400 kg/m³ were prepared, then the compressive responses of PUME in the strain rate range of 0.001 s⁻¹ to 3400 s⁻¹ were systemically investigated. By studying the energy absorption and efficiency diagram of PUME, the compressive properties of materials with different densities under compressive impact load were described, which showed that PUME with a density of 600 kg/m³ had better performance. A visco–hyperelasticity–air constitutive model was established to describe the large deformation response of PUME at high strain rates. The model included three components: hyperelastic part, viscoelastic part and gas pressure part. Quasi-static and dynamic compression tests were used to determine the constitutive relations of seven parameters. The samples with a density of 600 kg/m³ at different strain rates were fitted by MATLAB software, and the constitutive model parameters were obtained. The comparison between the constitutive equation and the experimental results showed that there was a good consistency. The constitutive model can provide data support for simulation analysis and application of PUME as energy absorbing protective facilities.