This work may be viewed as a contribution to the study of control of the dynamics of physical systems in which the potential have a catastrophic single well ?6 configuration. We demonstrated that The mathematical model of various non-linear structures (inverted pendulum, articulated beam, elastic beam fixed at its base and free at the top) is that of a particle moving in a catastrophic single well ?6 potential. control by sandwich and the one using piezoelectric absorber are investigated. The range of coupling or control parameters that can produce an e?ective control (reduction of amplitude, avoidance of unbounded motion and horseshoes chaos) are determined. Emphasis is laid on the e?ects of time-delay between the detection of the structure''s motion and the restoring action of the control device. Numerical simulation has been done to con?rm and complement the analytical prediction.