A gain shaped sliding mode control scheme using filtering techniques with applications to multi-link robotic manipulators

A gain shaped sliding mode control scheme is proposed for tracking control tasks of multi-link robotic manipulators. In the new scheme, filtering techniques play the key role in acquiring equivalent control signals and shaping the switching control gain automatically. Once the system entering the sliding motion, two classes of low-pass filters are introduced to work concurrently for the purpose of acquiring equivalent control, reducing the switching gain effectively and in the sequel eliminating chattering. By virtue of equivalent control theory, one class of filters is designed to capture the "average" profile of the switching quantity which is in proportion to the desired control input. Meanwhile, another class of low-pass filters is added to scale down the gain of the switching control. The convergence property of the proposed control scheme is rigorously analyzed in time domain, and the frequency domain knowledge can be easily incorporated into the construction of the two classes of filters. Excellent tracking performance is achieved with the direct manipulation of switching control input using the filtering technology and with the integration of both time domain and frequency domain system knowledge in the controller design