A general approach to dynamic gain adaptation of sliding mode control for robotic arms with parameter uncertainty

Facing parameter uncertainty is inevitable in control systems. Sliding mode control (SMC) is robust to uncertainty. To lead the system’s states towards a sliding surface and keep them there, the control input is required and it must include an additional discontinuous part. This part has a gain where its magnitude defines as the rate of this action. Setting the gain more than enough produces undesirable effects such as extra pressure and chattering on actuators. Hence, computing the precise gain is essential based on the sliding condition. In this paper, a general approach was introduced to specify adaptive gains of the SMC, regarding the sliding condition for multi-input multi-output (MIMO) systems. Adaptation of control gains, results in control effort reduction and weakening of the chattering phenomenon. To minimize the chattering even more, inverse tangent was used instead of sign function in control law and the structure of adaptive gain with this change is presented. The proposed formulation was applied on a planar arm and 6R robot to show precision and control effort reduction of the adaptive gain of the sliding mode controller. A comparison between the proposed method and conventional SMC was carried out to confirm the statement; and at the end, the proposed method is conducted on 6R robot experimentally.