Fractional Order Periodic Adaptive Learning Compensation for State-Dependent Periodic Disturbance

• Published in: IEEE transactions on control systems technology Vol. 20; no. 2; pp. 465 - 472
• Main Authors: YING LUO, QUAN CHEN, Yang, AHN, Hyo-Sung, GUO PI, You
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Adaptive systems; Applied sciences; Asymptotic properties; Asymptotic stability; Calculus; Compensation; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Disturbances; Exact sciences and technology; Fractional calculus; fractional order control; Friction; Learning; Mathematical analysis; Optimization; periodic adaptive learning compensation (PALC); Real time systems; Servomotors; Stability analysis; state-dependent periodic disturbance (SDPD); Trajectories; Trajectory; Input output; Input signal; fractional order control; Periodicity; Control synthesis; Minimization; Output signal; Experimental study; Adaptive control; Adaptive method; Fractional calculus; state-dependent periodic disturbance (SDPD); Fractional derivative; Asymptotic stability; State dependence; Intelligent control; periodic adaptive learning compensation (PALC)
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2011.2117426

In this brief, a fractional order periodic adaptive learning compensation (FO-PALC) method is devised for the general state-dependent periodic disturbance minimization on the position and velocity servo platform. In the first trajectory period of the proposed FO-PALC scheme, a fractional order adaptive compensator is designed which can guarantee the boundedness of the system state, input and output signals. From the second repetitive trajectory period and onward, one period previously stored information along the state axis is used in the current adaptation law. Asymptotical stability proof of the system with the proposed FO-PALC is presented. Experimental validation is demonstrated to show the benefits from using fractional calculus in periodic adaptive learning compensation for the state-dependent periodic disturbance.