Improving existing 'reaching law' for better discrete control of seismically-excited building structures

In our opinion, the method in Refs. 7 (Zhao et al) and 8 (Cai et al), which propose a 'reaching law', is not yet quite effective. We now present what we believe is an improvement over it. In the full paper, we explain our novel 'composite reaching law' in some detail; in this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: the equation of discrete motion for a control system. In this topic, we discretize the equation of motion and obtain eq. (6) in the full paper. The second topic is: the design of discrete-time variable structure control. Its three subtopics are: the determination of discrete switching surface (subtopic 2.1), the design of composite reaching law (subtopic 2.2) and the design of saturated control law (subtopic 2.3). In subtopic 2. It we determine the discrete switching surface of the control system with an ideal quasi-sliding mode. In subtopic 2.2, we improve other reaching laws and propose the composite reaching law, as expressed by eq.(11) in the full paper. In subtopic 2.3, we design the saturated control law to be used when the control force needed according to eq.(11) exceeds the maximum control force of an actuator. Finally we use the model of a three-storey shear-type building structure to verify the effectiveness of the discrete variable structure control method. The results of numerical example analysis of the model, given in Figs. 1 and 2 and Table 1 in the full paper, show preliminarily that the control law can effectively reduce the peak value of seismic response of the building structure and the chattering effect of the control system; the reduction of chattering effect is considerably better than that achievable with the method of Refs. 7 and 8.