Stable Discrete-Time Impedances for Haptic Systems With Vibration Modes and Delay

A Practically Linear Relation Between Time Delay and the Optimal Settling Time of a Haptic Device

“…Note that the investigated approach is valid only if the influence of other effects does not compromise the optimal performance of a haptic device. In certain cases, especially if the total time delay is small and the theoretical regions become large, the stability and the performance of the haptic system may be limited due to other factors including the nonlinear effect of sensor quantization [5], [12] or the mechanical flexibility of a haptic device [7]. Future research will tackle such interferences and will investigate other performance criteria as well as the human perception in the optimal points.…”

“…These authors performed two analyses: an analytical continuous-time analysis that approximates the discrete-time effects by a delay, and a numerical simulation of a hybrid haptic system that contains discreteand continuous-time elements. This pioneering work motivated further extensive research from other researchers to investigate stability [3]- [7] or passivity as a tool for obtaining stability [8]- [12].…”

“…This positive effect also appears for greater delay factors, even to a (6) as dashed lines, and the effect of physical stiffness γ and physical damping δ up to their realistic limits as small markers below the respective curves. The lower plot shows the relative approximation error ρ as defined in (7) for γ = 0 and δ = 0.…”

Sliding mode control design for haptic system with vibration mode

“…Further, the elastic deformation are generated in the haptic device between the user and driving motor which result change in output and referred as vibration mode in literature [Ciaurriz et al, 2014;Dang et al, 2012]. This vibration mode is included into the system which makes system nonlinear, as shown in Fig.…”