Discrete-time sliding mode for building structure bidirectional active vibration control

Abstract

In terms of vibrations along bidirectional earthquake forces, several problems are faced when modelling and controlling the structure of a building, such as lateral-torsional vibration, uncertainties surrounding the rigidity and the difficulty of estimating damping forces. In this paper, we use a fuzzy logic model to identify and compensate the uncertainty which does not require an exact model of the building structure. To attenuate bidirectional vibration, a novel discrete-time sliding mode control is proposed. This sliding mode control has time-varying gain and is combined with fuzzy sliding mode control in order to reduce the chattering of the sliding mode control. We prove that the closed-loop system is uniformly stable using Lyapunov stability analysis. We compare our fuzzy sliding mode control with the traditional controllers: proportional–integral–derivative and sliding mode control. Experimental results show significant vibration attenuation with our fuzzy sliding mode control and horizontal-torsional actuators. The proposed control system is the most efficient at mitigating bidirectional and torsional vibrations.

Overlapping Decentralized Guaranteed Cost Control Method for Discrete-Time Systems of Building Structures with Uncertain Parameters under Earthquake Action

“…erefore, it is particularly necessary to study the structural vibration control of discrete-time systems. Paul et al [8] proposed a novel discretetime sliding mode control in order to attenuate the bidirectional vibrations of building structures, comparing the fuzzy sliding mode control with conventional controllers, which was found to be the most effective in mitigating bidirectional and torsional vibrations. Kemerli et al [9] proposed the design and implementation of the discretetime sliding mode controller with a hybrid control strategy according to Gao's reaching law and variable rate reaching law and conducted simulated experiments with a 5-story building under seismic excitation; the results show that better results were achieved in terms of controller energy consumption and structural response compared to Gao's controller.…”

A backstepping control design for ATMD systems of building structure against earthquake excitations in the presence of parametric uncertainty

“…Owing to the mentioned simple working principle, TMD and ATMD have been used very effectively in numerous applications, including reducing wind response from tall buildings to reducing vibration in an aircraft. [2][3][4] To increase the effectiveness of TMD systems, a controllable actuator is added to the spring and damper system by considering the fact that active control has undeniable advantages over passive control as reducing unwanted vibration much faster and requiring a smaller control mass. Various studies 5,6 have shown that semi-active TMDs (STMDs), another method frequently used in the literature, are effective in reducing the vibrations of linear and nonlinear structures.…”

“…The working principle of these systems is based on the simple idea of transferring the kinetic energy of the vibrating structure to a properly tuned and specially designed single degree of freedom oscillator. Owing to the mentioned simple working principle, TMD and ATMD have been used very effectively in numerous applications, including reducing wind response from tall buildings to reducing vibration in an aircraft 2–4 . To increase the effectiveness of TMD systems, a controllable actuator is added to the spring and damper system by considering the fact that active control has undeniable advantages over passive control as reducing unwanted vibration much faster and requiring a smaller control mass.…”

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

“…In recent years, sliding mode control (SMC) has received extensive attention, and many scholars have applied it to suppress the vibration of structures. Based on the fuzzy SMC method, a time varying gain discrete sliding mode control (TVDSMC) method is proposed in Paul et al (2019) for the vibration suppression of the building structure under a bi-directional seismic action. Josué and Gerardo (2016) combined the multi-positive position feedback with sliding mode to control the vibration responses of a three-story building-like structure, and this method can simultaneously attenuate the three vibration modes of the system.…”