Sliding mode control of linear structures and a Duffing system using active tendons

Abstract

In this paper, the sliding mode control (SMC) method, one of the most efficient algorithms in the mitigation of excessive vibrations, was designed to reduce the dynamic responses of dynamical systems. Direct implementation of the switching-type control law in the proposed algorithm leads to a highly undesirable characteristic of the SMC called chattering and thereafter carries on by unwanted dynamics in the practical implementation of the SMC method. Thereafter, the control law is smoothed by replacing its chattering-generating part with a saturation function. The resultant method is called the chattering-free SMC. In this study, to examine the validity of the proposed method, a linear multi-degree-of-freedom building structure and a non-linear single-degree-of-freedom Duffing system were simulated under external excitations. The linear system was equipped with the active tendon mechanism to mitigate seismic-induced excitations on the floors. The first bifurcation length of the Duffing system was obtained by approximate methods to illustrate the instability. Thereafter, the system was modelled using Caughy's linearisation method and controlled under a harmonic excitation. The results of the numerical simulation indicate the satisfactory performance of the chattering-free SMC method in reducing the dynamic responses of both systems to an acceptable level while removing the chattering and the bifurcation phenomenon.