Fractional order actuation systems: Theoretical foundation and application in feedback control of mechanical systems

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

“…Boulham et al [25] constructed an L 1 adaptive controller to control FO systems with uncertainties and external disturbances. For more advances about FO control theory and application, one can refer to literatures [26][27][28]. Significantly, research demonstrates that fractional calculus has high potential to improve control performance since designers have more flexibility in selecting parameters of FO controllers in comparison with IO controllers [20][21][22][23][24][25][26][27][28].…”

“…For further analysis, equation(27) can be rewritten in the state space form as = system (28) is a Hamilton system whose Hamilton function is ( ) lead to the following homoclinic orbits…”

Output feedback robust H∞ control for uncertain descriptor fractional order systems with 0 < α < 1

“…More and more researchers pay attention to FOS since dynamic behaviors of most FOS are described more precisely than integer order systems. Therefore, FOS have been widely applied to power systems in Tzounas and Dassios (2020), electrical circuit systems in Kaczorek (2019), mechanical systems in Homaeinezhad and Shahhosseini (2020), and other fields. Fruitful achievements on FOS have been reported in (Zhang et al (2020), Farges et al (2010), Li et al (2009), Zhang et al (2021), and Lu et al (2021)).…”

Algorithm for the torque sensorless worm gearbox servo application based on kinetic motion/friction realization

“…6 They can also be discussed dynamically, but more sophisticated tools must be selected for the efficient treatment of materials with fractional-order dynamics. [7][8][9] Despite the widespread applications of worm gearboxes in industry, the researches conducted on the dynamical analysis of such systems are not properly advanced and cannot provide a foundation for adequate employment of worm gearboxes in precise servo applications. This point is briefly discussed by Yeh and Wu 10 and is mainly concerned with analyzing the worm gearbox, both kinetically and kinematically, which is amongst the very few valid approaches in accurate modeling of the motion of worm gearbox systems.…”