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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]

Proportional-derivative and proportional-integral-derivative (PD/PID) controllers are popular algorithms in structure vibration control. In order to maintain minimum regulation error, the PD/PID control require big proportional and derivative gains. The control performances are not satisfied because of the big uncertainties in the buildings. In this paper, type-2 fuzzy system is applied to compensate the unknown uncertainties, and is combined with the PD/PID control. We prove the stability of these fuzzy PD and PID controllers. The sufficient conditions can be used for choosing the gains of PD/PID. The theory results are verified by a two-storey building prototype. The experimental results validate our analysis. [ABSTRACT FROM PUBLISHER]