Reaching law based sliding mode control for a frame structure under seismic load

Implementation of efficient vibration control schemes for seismically excited structures is becoming more and more important in recent years. In this study, the influence of different control schemes on the dynamic performance of a frame structure excited by El Centro wave, with an emphasis on reaching law based control strategies, is examined. Reaching law refers to the reachable problem and criteria for the sliding state of a control system. Three reaching laws are designed to present different sliding mode control strategies by incorporating a state space model that describes structural dynamic characteristics of a frame structure. Both intact and damaged structures are studied by using the aforementioned control strategies. The influence of different structural damage extents, control locations and reaching law based control methods are further investigated. The results show that the structure can be well controlled using the sliding mode strategy when the induced structural damage extent does not exceed the standard percentage for considering the structure was damaged, which is 20% reduction in structure stiffness, as reported in the literature. The control effectiveness is more satisfactory if the control location is the same as the direction of external excitation. Furthermore, to study the chattering phenomenon of the sliding mode control method, approximation and detail components extracted from the phase plots of the sliding mode control system are compared via wavelet transform at different scales. The results show that for the same type of control law, the system behaves with similar chattering phenomenon.