# Practical Adaptive Sliding-Mode Control Approach for Precise Tracking of Robot Manipulators
###### Abstract
In other words, given that these control approaches are addressed by the continuous function, i.e., saturation function, they can avoid a major concern in the practical implementation of the conventional SMC. However, the boundary-layer SMC approaches still have the limitation that they require information about the upper bound on the uncertain terms. The SMC approaches with low-pass filter [12; 13] have been developed as another countermeasure against the chattering. Their switching gains depend on the system state that can be obtained while employing the low-pass filter. Therefore, these control approaches do not invite any complexity in the control design for avoiding the chattering. However, it may be hard to achieve the desired tracking performance because the overestimated switching gains are consistently required for suppressing the upper bound in the presence of significantly large disturbances. Conventional adaptive sliding-mode control (ASMC) approaches [14; 15; 16] have been designed to alleviate the above-mentioned problems while using time-varying switching gains with the adaptive laws. An ASMC approach [14] has been based on the Lyapunov theory, which is further addressed by input coefficient matrices and unknown system. Although its switching gains are monotonically increased to suppress the maximum uncertainty bound, they are never decreased due to its control structure. For this reason, it may cause the chattering on the sliding surface, which may result in the system instability. To solve this problem, an ASMC approach [15] has been introduced by using an adaptive law that can adjust the switching gains appropriately according to the magnitude of the sliding variable. However, this control approach has been limited to the control in the single-input single-output system. Its property is not able to eliminate the dynamic coupling effects in the joints of the robot manipulators. Since then, an ASMC approach [16] has overcome such a monotonic nature of the switching gains in the multi-input multi-output system. However, if this control approach requires the large switching gains for achieving fast convergence rate, it may cause the high-frequencydynamics because of the switching gains in the slow adaptation rate. As such, there is a need for effective ASMC approaches with powerful switching gains. An ASMC approach [17] has been first developed to be operated in the powerful switching gains, which aims at achieving fast adaptation rate at any time as the switching gains increase or decrease. Although it offers favorable tracking performance, the switching gains may be sensitive to the parameter setting for adjusting the adaptation rate near the sliding manifold. After that, another ASMC approach [18] with auxiliary parameters has been employed to alleviate the sensitivity in relation to the parameter setting. Unfortunately, it requires a time-consuming task because of a huge amount of tuning parameters. It may cause a result that the control performance is influenced by the local switching gains, not the global switching gains. An ASMC approach [19] has been introduced to avoid these problems in the literature, which is based on the existing ASMC approach [17] for integrating the advantages derived from the fast adaptation rate. Then, its adaptive law is composed of a combination sliding variable and exponential function so that the control input fluctuation does not occur near the sliding manifold. Given that the number of parameters can be also reduced when compared to an ASMC approach [18], it offers the potential for application to real systems. However, the adaptation rate of the switching gains is not directly influenced to the magnitude of the sliding variable while staying in the vicinity of the sliding manifold, and therefore this control approach may provide unstable switching gains temporarily because of the improper and insufficient adaptation rate.