haptic control of hydraulic machinery using proportional valves

example, a two-port network can be used to describe the impedance of a system as
seen by each side and the relationships between the corresponding force and velocity
signals. One system attribute that can be specifically analyzed using two-port
networks is system transparency. Transparency is a visual parallel used by haptic
researchers to describe how well a system can relay the force and motions of the opposite
side of the network. Just as transparent glass allows a human to see objects
on the other side, a transparent teleoperator allows a human to experience the same
motion and forces acting on the remote end effector.
A simple mathematical explanation for transparency can be given by looking
at two-port network parameters that describe a system. A two-port network can
describe the relationship between teleoperator’s inputs and outputs. The subscripts
h stands for hand or human and the subscript e stands for end-effector, environment
or exogenous force. The variables V and F are velocity and force respectively. Z in is
the impedance of the input haptic interface and Z out is the impedance of the remote
manipulator.
⎡
⎤
⎢
⎣ h 11 h 12 ⎥
⎦ =
h 21 h 22
⎡ ⎤
⎢
⎣ F h ⎥
⎦ =
−V e
⎡
⎢
⎣
Z in
⎡
⎢
⎣ h 11 h 12
h 21
⎤⎡
⎤
⎥⎢
⎦⎣ V h ⎥
⎦ (2.1)
h 22 F e
Force Scale
V elocity Scale
1
Z out
⎤
⎥
⎦ (2.2)
The system is “Perfectly Transparent” if and only if the following holds:
⎡ ⎤
⎢
⎣ F h ⎥
−V e
⎦ =
⎡
⎢
⎣ 0 1
−1 0
⎤⎡
⎤
⎥⎢
⎦⎣ V h ⎥
⎦ (2.3)
F e
It has also been shown that a perfectly transparent teleoperator is impossible to
achieve without limitations on bandwidth because a perfectly transparent system by
definition is marginally stable [79]. However, transparency is still an ideal for which
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