Contents I. Introduction
Mechatronic arms inherently have nonlinear properties. With regard to such a nonlinear system, various controllers have been developed. In recent years, the variable structure control (VSC) methodology has been widely used for controlling a class of nonlinear systems. However, fundamental problems still exist in the control of complex systems using sliding mode controllers, e.g., control chattering phenomenon and sensitivity to parameter uncertainties or noise disturbances in the reaching phase (RP). High gain feedback control was investigated to reduce the tracking error and reaching time [1], but it could cause unmodeled dynamics and chattering in a physical system. Furthermore, the transient and steady-state responses are equally important, especially, for applications involving robotic arm motion. A smooth and robust control methodology is desired. Chattering in the response would not be tolerable as the arm would seen to be vibrating/swaying or unstable. This will cause us to ponder to whether sliding mode control is the best candidate. Recently, an integral controller [2] and an integral switching surfaces [3] that combines with a sliding-mode controller were designed for achieving zero steady-state error under disturbances and plant uncertainties. In [4], a learning VSC approach was proposed for a general class of multi-input–multi-output (MIMO) systems, where VSC part was used to stabilize the system, and learning control part to completely nullify the effects of the matched uncertainties on tracking error almost everywhere. In practice, the inevitable switching nonidealities incur the chattering phenomenon. Replacing the signum function with a continuous function eliminates chattering, but degrades perfect tracking. VSC with time-varying sliding surface can effectively eliminate the RP and reduce chattering effects [5], [6] where the sliding-mode control combined with the fuzzy logic tuning scheme [5] and that with a bang-bang time optimal control algorithm with robustness [6]. The merit of the method can be used to accelerate the RP and reduce the influence of uncertainties and disturbances. Another VSC design method with chattering-free was introduced in [7] using two-phase variable structure controller, in [8] via high-order sliding-mode technique, in [9] via an arbitrary-order sliding controller for nonlinear uncertain systems, in [10] via a state-dependent boundary layer design, and in [11] via a switching on the derivative of control. Unlike the conventional sliding-mode controller which obeys the VSC principle by adopting a switching control term, the authors in [7] used a unified continuously varying term instead of taking the distance of the system's state from the sliding surface into account. The feature is that the sliding surface is moved toward a predetermined one via rotation and/or shift by changing the magnitude of the slope and intercept of the surface in phase plane. Before long, a sliding mode control with a moving sliding surface was proposed in [12]. The sliding surface can rotate or shift in phase plane in such a way that the tracking performance can be improved. Also the concept of terminal sliding mode or fast terminal sliding mode, which can have fast (finite time) transient convergence both at a distance from and at a close range of the equilibrium was mentioned in [1], [13], and [14]. However, the total tracking time of the tracking trajectory based on conventional sliding mode control (SMC) scheme has never been shown in the literature.
