Stability of a linear oscillator with damping force of the fractional-order derivative

摘要: It begins with the study of damping representation a linear vibration system single degree freedom (SDOF), from view point fractional calculus. By using idea stability switch, it shows that term involving fractional-order derivative an order between 0 and 2 always acts as force, so unique equilibrium is asymptotically stable. Further, based on switch again, paper proposes scheme for determining stable gain region under control. unlike classical velocity feedback which can adjust force only, not only but also elastic restoring in addition, PDα control either enlarge or narrow region. For dynamic systems described by integer-order derivatives, asymptotical guaranteed if all characteristic roots stay open left half-plane, while within sector complex plane. Analysis proposed method, works effectively analysis dynamical derivatives.