Vibration control of two-degree-of-freedom exponentially damped oscillators

Abstract

Vibration control of two-degree-of-freedom (2DOF) exponentially damped oscillators is considered. Firstly, the equations of motion for 2DOF exponentially damped oscillators are established by using the nonviscous damping models that depend on the past history of motion. Secondly, the equations of motion for 2DOF exponentially damped oscillators are transformed into state equations with six dimensions by using a set of internal variables. Thirdly, Sliding control design is proposed. Furthermore, this control method can also be used in the multi-degree-of-freedom (MDOF) exponentially damped oscillators. Finally, numerical simulations are provided to illustrate the above control designs.