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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. [ABSTRACT FROM AUTHOR]

Proportional-derivative (PD) and proportional-integral-derivative (PID) controllers are popular control algorithms in industrial applications, especially in structural vibration control. In this paper, the designs of two dampers, namely the horizontal actuator and torsional actuator, are combined for the lateral and torsional vibrations of the structure. The standard PD and PID controllers are utilized for active vibration control. The sufficient conditions for asymptotic stability of these controllers are validated by utilizing the Lyapunov stability theorem. An active vibration control system with two floors equipped with a horizontal actuator and a torsional actuator is installed to carry out the experimental analysis. The experimental results show that bidirectional active control has been achieved. [ABSTRACT FROM AUTHOR]