Variable fractional order sliding mode control for seismic vibration suppression of building structure

Abstract

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.

Investigation on the tunable bi-stable clustered energy conversion inspired dynamic vibration absorbers: A theoretical study

“…Combining the advantages of passive and semi-active vibration control strategies, the passive vibration absorbers with adjustable parameters are the desired alternatives for vibration suppression and energy transfer. Dynamic vibration absorbers (DVAs) have been extensively exploited to protect sorts of civil or mechanical structures in order to mitigate vibration yielded by seismic excitations (Wang et al, 2021; Wani and Tantray, 2021; Lu et al, 2018), flow induced vibrations (FIV) (Wang et al, 2020; Muthalif et al, 2021; Zhou et al, 2021; Wang et al, 2020), unbalanced rotating machinery (Heng et al, 2009; Lei et al, 2013), dynamic vibration caused from vehicle traffic (Xie et al, 2012; Guclu and Metin, 2009; Liu et al, 2011), vibrations caused by thermal alternating loads (Cao et al, 2020; Peng et al, 2018), and other causes. A classic DVA is always composed of a single degree-of-freedom (SDOF) mass-spring-damper system, which is only effective when its natural frequency matches or approaches the natural frequency of the main structure.…”

Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

“…29,30 The existence results of the solution and stability are studied by Jiang et al 31 for the variable fractional order differential equation, and they also researched the finite time stability and control for a class of uncertain variable fractional order nonlinear systems by using a sliding mode controller. 32 The problems of robust seismic control for building structures and uncertain ones are studied by using two different sliding mode controllers, 33,34 respectively. Luo et al 35 concerned the Ulam-Hyers stability results for a novel nonlinear nabla Caputo fractional variable order difference system.…”