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In order to enhance the convergence rate of NTSM (3), a new FNTSM is designed as
The FNTSM (6) is a switching sliding surface which transfers the system dynamic from a LSM (q = l) toa NTSM (l < q < 2) (Figure 1; e.
Here, a simple example is given to compare the NTSM (3) and the FNTSM (6),
Considering system (7), the control input was taken as the NTSM controller form of [14]
Note that the FNTSM became equivalent to the NTSM within the region [absolute value of [x.
Most of the NTSM controllers were designed for system (1) with a known y (or with an uncertain item).
Generally, the NTSM control design contains the sliding surface and the reaching law.
2]) in the existing NTSM controllers, for example, the controller (8).
In the studies of adaptive NTSM control [22, 23], the switching gain was directly adjusted by the adaptive technique.
In this section, a double sliding surfaces control scheme is designed to combine the NTSM control with the adaptive technique.
Although the proposed NTSM controller (11) in Theorem 2 can be used to design [u.
In this section, the designed robust and adaptive NTSM controllers were tested for the tracking control of a variable-length pendulum [25] (Figure 3) formulated as