  This paper proposes a new stability analysis for the Reaction Torque Observer
(RTOb) based robust force control systems in the discrete-time domain. The
robust force controller is implemented by employing a Disturbance Observer
(DOb) to suppress disturbances, such as friction and hysteresis, in an
inner-loop and another disturbance observer, viz RTOb, to estimate contact
forces without using a force sensor. Since the RTOb-based robust force
controllers are always implemented using computers and/or microcontrollers,
this paper proposes a stability analysis in the discrete-time domain. It is
shown that the bandwidth of the DOb is limited not only by the noise of
velocity measurement but also by the waterbed effect. It is also shown that the
stability of the robust force controller may significantly deteriorate when the
design parameters of the RTOb are not properly tuned. For example, the robust
force controller may have a non-minimum phase zero(s) as the design parameter
of the identified inertia (torque coefficient) of the RTOb is increased
(decreased). This may lead to poor stability and performance in force control
applications. The proposed stability analysis conducted in the discrete-time
domain is verified by simulations and experiments.
