Handling stiction with variable structure control

Abstract

When the control system falls in a class obeying non-Lipschitzian (or "non-smooth") dynamics, the conventional nonlinear theory can not be readily applied. Among the common non-smooth nonlinearities are those which are discontinuous in the state variables. Existence of such inherent right hand side discontinuities may induce undesirable stiction while hardening the control task during reference tracking. In this work, we analyze the "stiction" phenomenon in depth using analogies from the sliding mode control theory and propose a multi layer variable structure reference tracking controller for a class of systems in their companion forms. Results for an interesting physical example is provided to clarify the concepts.

Model reference discrete-time sliding mode control of linear motor precision servo systems

“…These works focus mainly on handling the inherent discontinuity, characterised on a course level as Coulomb friction, via variable structure control. According to [5], the discontinuous friction induces a stiction manifold in the system state space, and this stiction manifold can only be shrunk or entirely eliminated by applying another discontinuous control in the same subspace of the friction. In practice, however, discontinuous control is hardly applicable due to the above mentioned chattering problem, which is especially problematic in systems that contain mechanical flexibility, since vibrational modes are likely to be intensively excited by the chattering.…”

“…However, the friction problem is not as simple as the problem of smooth exogenous disturbances and plant uncertainties. So far, only a few papers [4,5,14,15], which investigate the friction problems in SMC control systems, have been found. These works focus mainly on handling the inherent discontinuity, characterised on a course level as Coulomb friction, via variable structure control.…”

Design of a Pressure Control System With Dead Band and Time Delay

“…They range from friction compensation based on accurate determined models through robust control methods like the sliding mode e.g. [13], [14], [15] or adaptive algorithms to identifying the friction on-line e.g. [16], [17].…”