Sliding mode control for structures based on the frequency content of the earthquake loading

Abstract

A control algorithm for seismic protection of building structures based on the theory of variable structural control or sliding mode control is presented. The paper focus in the design of sliding surface. A method for determining the sliding surface by pole assignment algorithm where the poles of the system in the sliding surface are obtained on-line, based on the frequency content of the incoming earthquake signal applied to the structure, is proposed. The proposed algorithm consists of the following steps: (i) On-line FFT process is applied to the incoming part of the signal and its frequency content is recognized. (ii) A transformation of the frequency content to the complex plane is performed and the desired location of poles of the controlled structure on the sliding surface is estimated. (iii) Based on the estimated poles the sliding surface is obtained. (iv) Then, the control force which will drive the response trajectory into the estimated sliding surface and force it to stay there all the subsequent time is obtained using Lyapunov stability theory. The above steps are repeated continuously for the entire duration of the incoming earthquake. The potential applications and the effectiveness of the improved control algorithm are demonstrated by numerical examples. The simulation results indicate that the response of a structure is reduced significantly compared to the response of the uncontrolled structure, while the required control demand is achievable.