Page 262 - Mathematical Techniques of Fractional Order Systems

Design of Fractional Order Fuzzy Sliding Mode Controller Chapter | 9 251

To control the manipulator system by using classical SMC techniques,
several good works have been reported in the literature (Zhao et al., 2009;
Fallaha et al., 2011; Islam and Liu, 2011). Chattering was the common issue
in all these research works and to reduce it to a novel fuzzy SMC for robotic
manipulator was proposed in Chen et al. (2003) where the signum function
is replaced by the boundary layer. It was reported in this work that by
arranging the width of the boundary layer using FL technique, an effective
reduction in chattering was observed and at the same time a control feature
was also maintained. A hybrid structure of SMC with FL technique was also
proposed (Roopaei and Jahromi, 2009) to control a class of MIMO nonlinear
system in the presence of uncertainties and external disturbances. A series of
simulations justified the results that incorporating the FL with SMC reduced
the chattering and also the robustness of controller was increased. Extensive
works have been reported to this extent to reduce the chattering using FL
(Wu and Ham, 1996; Wai, 2007; Sadati and Ghadami, 2008).
Another important field of soft computing technique, ANN is also under-
pinned with SMC by different scientists and researchers to design the hybrid
controller to reduce the effect of chattering (Mu, 2010). It is well known that
ANN offers a model free approach to learn from the examples of unknown
dynamics. An ANN estimator is used to find the estimated error model (Munoz
and Sbarbaro, 2000) to compensate the SMC for reducing the set-point tracking
error of discrete nonlinear systems. In another research work performed by Niu
et al. (2003), ANN is used to estimate the lumped unmatched uncertainties
with time delay states of a dynamic system. A radial basis function neural net-
work (RBFNN) is used (Huang et al., 2003) for better tracking efficacy where
a lesser number of parameters has to learn and hence convergence speed is
increased. A model free approximator to estimate the adaptive SMC is used
which can deal with online learning parameters of matched and unmatched
uncertainties. A recurrent neural network (RNN) is used to design the adaptive
SMC (Karakasoglu and Sundareshan, 1995) to find the control solution for tra-
jectory tracking task of a robotic manipulator. An RNN with a special learning
algorithm for updating the parameters to be learnt is used by Fang et al. (1999).
In this work, RNN is constructed to estimate the equivalent control in order to
reduce the chattering. It has been shown by authors that incorporation of RNN
with SMC enhances convergence due to its feedback mechanism.
Although, the addition of fractional order calculus in SMC control tech-
nique improves the overall robustness, chattering in the controller output
may increase. To make a proper compromise between robustness and chat-
tering, simultaneous application of fractional order calculus and intelligent
techniques are reported. Nowadays, a hybrid structure of classical variable
order control schemes and intelligent techniques has been conveyed as a
recent trend. Several works are reported in this context which implement the
controller by SMC and FL. A novel parameter adjustment scheme was