zbMATH — the first resource for mathematics

A sliding-mode based smooth adaptive robust controller for friction compensation. (English) Zbl 0913.93038
The paper presents a new sliding-mode approach for tracking control of a servo-system with stick-slip friction and uncertain parameters, which employs a smooth adaptive robust controller. The construction of the mathematical model for the DC motor takes into consideration the following contribution to the friction force: (i) viscous friction (term linear in the velocity), (ii) Coulomb friction (term linear in the parameter), (iii) exponential friction (nonlinear term), (iv) position-dependent friction (nonlinear term). The proposed controller consists of three parts (a feedforward component, a linear PD feedback and a robust compensator) and operates in a sliding mode. The feedforward compensator is updated according to an adaptive algorithm which ensures total compensation for the forces of type (i), (ii), and partial compensation for the forces of type (iii), (iv). The robust compensator achieves the compensation for the uncertainties due to inexact cancellation of the terms corresponding to the forces of type (iii), (iv) and relies on an adaptive algorithm able to learn the upper-bounding function on-line. Lyapunov’s direct method has been used to prove the global asymptotic stability of the closed-loop system. To illustrate the proposed control method, numerical simulations were performed for a DC motor with both uncertain parameters and stick-slip friction, showing that stick-slip friction can be effectively compensated and the desired trajectory can be followed precisely.

93C40 Adaptive control/observation systems
93D21 Adaptive or robust stabilization
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
93C10 Nonlinear systems in control theory
93B12 Variable structure systems
Full Text: DOI