Sliding Mode Control (SMC) is a powerful approach to solve the tracking problem for dynamic systems with uncertainties. However, the traditional SMCs introduce actuator Chattering phenomenon which performs a desirable behavior in many physical systems such as servo control and robotic systems, particularly, when the zero steady state error is required. Many methods have been proposed to eliminate Chattering from SMCs which use a finite DC gain controller.Although these methods provide a free Chattering control but they only deal with the steady state error and are not able to reject input disturbances. This paper presents a fuzzy combined control (FCC) using appropriate PID and SMCs which presents infinite DC gain. The proposed FCC is a free Chattering control which guarantees a zero steady state error and rejects the disturbances. The stability of the closed loop system with the proposed FCC is also proved using Lyapunov stability theorem. The proposed FCC is applied to a two degree of freedom robot manipulator to illustrate effectiveness of the proposed scheme.

Control of biped walking robots based on designated smooth and stable trajectories is a challenging problem that is the focus of this article. Because of highly nonlinear dynamics of biped robots, minor uncertainties in systems parameters may drastically affect the system performance, leading to a Chattering phenomenon. To tackle this, a new Sliding Mode Control (SMC) approach is proposed privileging a Chattering elimination method based on Fuzzy logic to regulate the switching gain. To this end, first a desired trajectory for the lower body will be designed to alleviate the impacts due to contact with the ground. This is obtained by fitting proper polynomials at appropriate break points.Then, the upper body motion is planned based on the Zero Moment Point (ZMP) criterion to provide a stable motion for the biped robot. Next, dynamics equations will be obtained for both single support phase (SSP) and double support phase (DSP). Finally, the SMC approach is applied for both the SSP and the DSP, while a new Chattering elimination method using Fuzzy logic will be proposed based on regulating a constant switching gain. Obtained simulation results show that the performance of the system is properly accurate in terms of the tracking errors even in the presence of considerable uncertainties and exerted disturbances. Furthermore, the new proposed method substantially reduces Chattering effects and avoids the instability of the biped robot due to this phenomenon, resulting in stable smooth motion control of this complicated system.

In this paper, a Chattering-free sliding-mode control is mainly proposed in a second-order discrete-time system. For achieving this purpose, firstly, a suitable control law would be derived by using the discrete-time Lyapunov stability theory and the sliding-mode concept. Then the input constraint is taken into account as a saturation function in the proposed control law. In order to guarantee the closed-loop system stability, a sufficient stability condition would be addressed in the presence of unstructured uncertainties. Hence the states of the discrete-time system are moved to a predefined sliding surface in a finite sampling time. Then the system states are asymptotically converged to the origin through the sliding line. The suggested SMC is successfully applied in two discrete-time systems (i. e. regulation and tracking problems). The effectiveness of the proposed method will be verified via numerical examples.