New fractional-order proportional integral derivative semi-active control composite magnetorheological damping system

Abstract

In this paper, semi-active control analysis and research on the vibration reduction system of vibratory roller with nonlinear stiffness and fractional damping are carried out. A two-degree-of-freedom semi-vehicle mathematical model with nonlinear stiffness and fractional damping is established, and the fractional calculus operator in the model is approximated by using the Oustaloup filter algorithm. The vibration characteristics of passive control, proportional integral derivative control, and fractional-order $\mathrm{P}{\mathrm{I}}^{\lambda }{\mathrm{D}}^{\mu }$ control on the vibration reduction system of the vibratory roller are simulated and analyzed. Results show that the vibration reduction effect of the first-stage vibration reduction device of the vibratory roller is evidently improved by using fractional-order $\mathrm{P}{\mathrm{I}}^{\lambda }{\mathrm{D}}^{\mu }$ controller. Compared with traditional passive control, the parameters are increased by about 40%, and the vibration intensity evaluation grade of the vibratory roller can be improved by about one level, which provides a new idea for the research of the vibration reduction system of the vibratory roller.