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226 Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics

Table 14.1 Comparison for tracking y = 0.5sin(t)
d
2
Controller IAE (rad) ITAE (rad/s) ISDE (rad )
PID 0.0287 0.1267 0.0087
SMC 0.0257 0.0653 0.0070
NTSMC 0.0295 0.0696 0.0092
NTSMFC 0.0178 0.0569 0.0036

14.5 CONCLUSION
In this chapter, a non-singular terminal sliding mode funnel control
(NTSMFC) is proposed to achieve a prescribed tracking performance for
uncertain servo systems with unknown input saturation. The non-smooth
saturation is reformulated as an affine form by defining a smooth function.
A new funnel variable is proposed and incorporated into control design
such that the tracking error will be forced to retain the prescribed bound.
An NN is used to approximate the unknown lumped non-linearities in
a NTSMFC designs. With the proposed control, no prior knowledge of
system dynamics and the input saturation bound is required, and the closed-
loop system stability is proved. Comparative simulations are provided to
show the efficacy of the proposed control method.

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