ADALINE based robust control in robotics: a Riemann-Liouville fractional differintegration based learning scheme

This paper presents an approach to improve the performance of intelligent sliding model control achieved by the use of a fundamental constituent of soft computing, named Adaptive Linear Element (ADALINE). The proposed scheme is based on the fractional calculus. A previously considered tuning scheme is revised according to the rules of fractional order differintegration. After a comparison with the integer order counterpart, it is seen that the control system with the proposed adaptation scheme provides (1) better tracking performance, (2) suppression of undesired drifts in parameter evolution and (3) a very high degree of robustness and insensitivity to disturbances. The claims are justified through some simulations utilizing the dynamic model of a two degrees of freedom (DOF) direct drive robot arm and overall, the contribution of the paper is to introduce the fractional order calculus into a robust and nonlinear control problem with some outperforming features that are absent when the integer order differintegration operators are adopted.

[1]  Mehmet Önder Efe.  A novel error critic for variable structure control with an ADALINE , 2002 .

[2]  I. Podlubny.  Fractional differential equations , 1998 .

[3]  Samir Ladaci,et al.  On Fractional Adaptive Control , 2006 .

[4]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[5]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[6]  Okyay Kaynak,et al.  A comparative study of soft-computing methodologies in identification of robotic manipulators , 2000, Robotics Auton. Syst..

[7]  Eliezer Colina-Morles,et al.  A sliding mode strategy for adaptive learning in Adalines , 1995 .

[8]  Karl Johan Åström,et al.  Adaptive Control (2 ed.) , 1995 .

[9]  D. Matignon.  Stability properties for generalized fractional differential systems , 1998 .

[10]  Y. Q. Chen,et al.  Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control , 2002 .

[11]  Okyay Kaynak,et al.  Sliding Mode Neuro-Adaptive Control of Electric Drives , 2007, IEEE Transactions on Industrial Electronics.

[12]  Shaher Momani,et al.  Lyapunov stability solutions of fractional integrodifferential equations , 2004, Int. J. Math. Math. Sci..

[13]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[14]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .