Abstract
In this paper, we investigate the combined effect of viscous damping and Coulomb friction on sampled-data mechanical systems. In these systems, instability can occur due the sampling of the applied discrete-time controller which is compensated by the two different physical dissipation effects. In order to investigate the interplay between these, we focus on how the stable domain of operation is extended by the dry friction compared to viscous damping. We also show that dry friction causes concave envelope vibrations in this extended region. The analytical results, presented in the form of stability charts, are verified by a detailed set of simulations at different representative control parameter values.
Highlights
Positioning is a basic task in automation, where the control system aims to drive a device into a desired position
From the engineering point of view, these simplifications can be good approximations in a lot of cases, but sometimes more details have to be considered to obtain a representative model. As it was demonstrated by simulations in [2], special vibrations occur with concave envelope when Coulomb friction compensates for the possible instability caused by the sampling
Based on [5], in robotic systems the power losses that play important role in the dynamics consist of a viscous damping and a Coulomb friction terms in general
Summary
Positioning is a basic task in automation, where the control system aims to drive a device into a desired position. In reference [3], a passivity based approximation was used to determine the stability limit of a haptic application, while in reference [4], a closed form result was presented for the same stability limit by neglecting the harmonics due to sampling In these two papers, the only considered source of dissipation was Coulomb friction. The stability analysis of the corresponding discrete-time position controller is presented in Section 3 with comparing the effect of dry friction and viscous damping. The corresponding stable domain of control parameters is illustrated in the plane of dimensionless sampling time θand dimensionless proportional gain pin Fig. 1 It is noted, when the effect of viscous damping is neglected, the desired position xdis always unstable [4]. In the solid yellow region, the characteristic multipliers z1 ,2∈Cwith Im(z1,2) ≠ 0 and the system oscillates similar to an underdamped secondorder system
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