  This paper presents an integration of nonlinear disturbance observer within
proxy-based sliding mode control (IDO-PSMC) approach for Pneumatic Muscle
Actuators (PMAs). Due to the nonlinearities, uncertainties, hysteresis, and
time-varying characteristics of the PMA, the model parameters are difficult to
be identified accurately, which results in unmeasurable uncertainties and
disturbances of the system. To solve this problem, a novel design of
proxy-based sliding mode controller (PSMC) combined with a nonlinear
disturbance observer (DO) is used for the tracking control of the PMA. Our
approach combines both the merits of the PSMC and the DO so that it is
effective in both reducing the ``chattering" phenomenon and improving the
system robustness. A constrained Firefly Algorithm is used to search for the
optimal control parameters. Based on the Lyapunov theorem, the states of the
PMA are shown to be globally uniformly ultimately bounded. Extensive
experiments were conducted to verify the superior performance of our approach,
in multiple tracking scenarios.
