Stability Analysis of a 1 DOF Haptic Interface Using the Routh–Hurwitz Criterion

Stability Boundary and Transparency for Haptic Rendering

“…17). The critical virtual stiffness of the device has been calculated by means of the relay experiment described in (Barbé et al, 2006;Gil et al, 2004;Åström & Hägglund, 1995), with and without time delay. In this experiment a relay feedback-an on-off controller-makes the system oscillate around a reference position.…”

Stability Boundary and Design Criteria for Haptic Rendering of Virtual Walls

“…Adams and B. Hannaford, 1999;Gil et al, 2004). As the haptic device has to be stable for all possible configurations, the stability analysis was performed for this worst-case scenario without a human operator:…”

“…the time needed for the force calculation of complex virtual scenarios. Yet, in most publications about this topic this delay is usually omitted (Gil et al, 2004), (Colgate and Brown, 1994) or assumed to be one sampling period T (Salcudean and Vlaar, 1997). In the following both of these cases are analyzed.…”

“…Recently, Gil et al (Gil et al, 2004) computed the exact stability boundary for virtual damping and stiffness for their haptic interface. Furthermore, they showed that a human operator tends to stabilize the system, i.e.…”

Stability of sampled‐data, delayed haptic interaction under passive or active operator

“…Another approach to the stability analysis of a similar HVE system was provided by Gil et al In a series of papers [5,8], using the Routh-Hurwitz criterion, the closed-loop stability problem of the 1-DOF, HVE system was addressed directly. The environment was modeled as a virtual spring and damper in mechanical parallel and the stability condition for a delayed HVE system, which delay t d can be the sum of several effects (computations, communications, etc), the stability condition was found to be…”