Constant fractional order vibration control strategy has been one of research hotspots in recent decades. However, the variable fractional order control method is seldom concerned up to now. In this article, a novel variable fractional order sliding mode control (VOSMC) method is proposed to suppress the responses of building structure caused by seismic excitations, including El Centro, Hachinohe, Northridge, and Kobe earthquakes. Based on the proposed variable fractional order sliding mode surface, the control law of VOSMC is presented. The global asymptotic stability of the control system is analyzed and proved by utilizing variable fractional order Lyapunov stability theorem. Besides, the corresponding constant fractional order sliding mode control (COSMC) method is also given. The control effects of VOSMC and COSMC methods are discussed by four performance indices. Finally, the utilizability and reasonability of the proposed control method is verified by using two examples (include two-story and five-story shear buildings). Compared with the COSMC method, the proposed variable fractional order controller not only has a lesser control output, but also has a higher utilization of the output, which is conducive to energy saving.
Alkali-resistant glass fiber reinforced concrete (AR-GFRC) has greatly improved in terms of tensile strength, toughness, durability, and reduction of cracking, which has been proven by testing. However, the constitutive relationship of fiber reinforced concrete under complicated stress represents a complex theoretical problem. In order to investigate the microscopic damage evolution and failure mechanism of AR-GFRC, the meso-statistical damage theory, microcontinuum theory, and composite material theory were considered, and uniaxial tensile tests of two types of AR-GFRC were conducted. A new damage variable expression of the AR-GFRC was proposed, and the stress-strain curve was redefined by considering the residual strength based on experimental fitting parameters and statistical parameters. A Weibull distribution was assumed and a statistical damage constitutive model was developed of the deformation process of the AR-GFRC while considering the residual strength effect; detailed calculation methods to determine the mechanical and statistical parameters of the concrete were developed. The validation results show that the theoretical stress-strain curve of the constitutive model is in good agreement with the experimental curve and the trend is consistent.
The robust control for uncertain variable fractional order time‐varying delayed differential systems with nonlinear perturbations are concerned in this article. Firstly, by introducing a novel form of the control law which is inspired by the sliding mode design, a new state feedback controller is built. Besides, a specific and comprehensive Lyapunov–Krasovskii function is adopted to deduce the sufficient conditions for the stability and robust stabilization of the system by using some linear matrix inequalities. In addition, the controller gain matrix can also be derived from the point of stability. Finally, two comparison examples are presented to demonstrate the effectiveness of the proposed control technique. The simulation results show that this method can make the state variables converge to the steady ones more quickly and stably.
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