Low-Speed Voltage-Input Tracking Control of a DC-Motor Numerically Modelled by a Dynamical System with Stick-Slip Friction

Abstract

Stick-slip vibrations appear during relative motion between contacting surfaces of miscellaneous frictional pairs. They depend on the viscous force, Coulomb force or other velocity-dependent forces. These effects appear in almost all mechanical systems, for instance, in positioning systems like servomechanisms, impulse encoders and stepper motors which operate at, or about zero velocity of relative motion between shafts and sliding bearings. This paper presents numerical modelling of a DC-motor as a dynamical system with stick-slip effect which appears while direction of rotation of its rotor crosses zero velocity speed. These investigations are aimed on some future applications of the control technique serving for explanation of bifurcation phenomena existing in such kind of discontinuous systems. Putting emphasis on nonlinear effects we apply the well-known, but a bit extended sliding-surface method allowing for compensation of frictional effects. A limit cycle on a phase plane as well as time-histories of control inputs and system outputs were obtained using numerical simulations performed in Simulink.