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Some remarks on the convergence analysis of adaptive controllers for robot manipulators
Author(s) -
Maliotis G. N.,
Dawson D. M.,
Lewis F. L.
Publication year - 1990
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480040609
Subject(s) - control theory (sociology) , adaptive control , convergence (economics) , controller (irrigation) , lyapunov function , rate of convergence , stability (learning theory) , upper and lower bounds , lyapunov stability , mathematics , reference model , robot , computer science , control (management) , nonlinear system , artificial intelligence , computer network , mathematical analysis , channel (broadcasting) , physics , software engineering , quantum mechanics , machine learning , agronomy , economics , biology , economic growth
The objective of this paper is to explore several robust adaptive control schemes for a class of partially known robot systems described by the equation M(q)q̈ + F(q, q̇)q̇ + G(q) = f (t) where f (t) is the control input. First we take advantage of any known system dynamics to simplify the adaptive control problem for the unknown portion of the dynamics. Then a model‐reference adaptive control based on the Lyapunov stability criterion is designed for the remaining unknown portion of the plant. Using the Lyapunov approach, under a slowly time‐varying assumption we derive a magnitude bound and a maximum achievable convergence rate for the error. The magnitude bound as well as the convergence rate are functions of the reference model degree of stability α (‐ α is the maximum real part of model poles). We show that there is an optimal location for the reference model poles that is independent of the robot dynamics. This value of α is well defined, and if the feedback gains are further increased, making the model more stable, the performance of the adaptive system is degraded . It is also shown that the gains in the adaptive portion of the algorithm may be made as high as desired in order to make the actual performance approach the maximum achievable convergence rate. The effect of these adaptive gains does depend on the unknown dynamics. Simulation results will demonstrate the improved performance of the adaptive controller and the detrimental effects of high gains on the system performance. Next the slowly time‐varying assumption is relaxed to obtain more realistic bounds on the error. Formulation into a more structured system also allows us to derive a control law that does not require accelerations.