Application of fractional calculus in iterative sliding mode synchronization control

In order to control joints of manipulators with high precision, a position tracking control strategy combining fractional calculus with iterative learning control and sliding mode control is proposed for the control of a single joint of manipulators. Considering the coupling between joints of manipulators, a fractional-order iterative sliding mode crosscoupling control strategy is proposed and the theoretical proof of its progressive stability is given. The paper takes a two-joint manipulator as the research object to verify the control strategy of a single-joint manipulator. The results show that the control strategy proposed in this paper makes the two-joint mechanical arm chatter less and the tracking more accurate. The synchronous control of the manipulator is verified by a three-joint manipulator. The results show that the angular displacement adjustment times of the threejoint manipulator are 0.11 s, 0.31 s and 0.24 s, respectively. 3.25 s > 5 s, 3.15 s of a PD cross-coupling control strategy; 2.85 s, 2.32 s, 4.22 s of a PD iterative cross-coupling control strategy; 0.14 s, 0.33 s, 0.28 s of a fractional-order sliding mode cross-coupling control strategy. The root mean square error of the position error of the designed control strategy is 6.47 × 10−6 rad, 3.69 × 10−4 rad, 6.91 × 10−3 rad, respectively. The root mean square error of the synchronization error is 3.96×10−4 rad, 1.36×10−3 rad, 7.81×10−3 rad, superior to the other three control strategies. The results illustrate the effectiveness of the proposed control method.