Sliding lines S1 and S2 are the constant acceleration segments
that are responsible for limiting the maximum forward and
reverse acceleration of the drive, whereas S3 is responsible
for bringing the system (xl, xl) to the origin of the phase
plane (Fig. 12(b)). The prescribed dynamic of xl in S3 is
a first-order response with l/c being the time constant of
the error response, whereas the dynamics with S1 or S2 is a
ramp. Upon step changes in xl , the system trajectory (x 1, X 1)
in the state plane is not robust until it hits one of the sliding
lines. Once hitting occurs, the system will enter sliding mode
(if sufficient controller gains are used) and slide along the
prescribed trajectories towards the origin of the phase plane.
It may be noticed that the trajectories (Sl, S2, and S3) do not
depend on the system parameters (a, 6). Hence, parameterinsensitive
control can be obtained with SLMC.