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Although most real building structure controllers are in the form of proportional-derivative/proportional-integral-derivative (PD/PID), there have been few published theory results of PD/PID on structural vibration control. In order to minimize the regulation error, a PD/PID control needs relatively large derivative and integral gains. These deteriorate the transient performances of the vibration control. In this paper, a natural combination of industrial PD/PID control with fuzzy compensation is proposed. The main contribution of this paper is that the stability of the fuzzy PD/PID control is proven with standard weight training algorithms. These conditions give explicit selection methods for the gains of the PD/PID control. Experimental studies on a two-story building prototype with the controllers are addressed. The experimental results validate our theoretical analysis. [ABSTRACT FROM AUTHOR]