Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

作者：Zhang Youan; Yuan Jian^*; Liu Jingmao; Shi Bao

来源：Journal of Vibration and Acoustics-Transactions of the ASME, 2017, 139(1): 011014.

DOI：10.1115/1.4034843

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin-Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

• 出版日期2017-2
• 单位中国人民解放军海军航空工程学院