Fuzzy PI vibration suppression control strategy for space double flexible telescopic manipulator with fractional disturbance observer

The space double flexible telescopic manipulator (SDFTM) with time-varying length, is called the space flexible manipulator and can carry out reciprocating linear telescopic motion along its axis. It possesses characteristics such as lightweight flexibility, small space occupation, large turning radius, and a wide working range. These features can assist astronauts in performing complex tasks in dangerous outer space environments and offer broad application prospects. However, due to the highly nonlinear and time-varying length characteristics of the space flexible manipulator, its dynamic modeling becomes more complex and challenging. Moreover, during the rotation of the space flexible manipulator, its inherent flexible behavior can trigger vibration phenomena, significantly impacting the execution accuracy of on-orbit tasks. Therefore, proposing control methods to address vibration issues is an effective approach. Thus, achieving stable and precise operation of the space flexible manipulator necessitates the precise establishment of its dynamic model and the development of high-precision control algorithms, which have become key research directions. Firstly, a time-varying dynamic modeling method of the space manipulator is proposed by combining the Lagrange principle and flexible beam vibration theory. Unlike the traditional method, which only considers the limit length of the space manipulator under static conditions, the dynamic process of the space manipulator presented during actual operation is fully considered, which greatly improves the modeling accuracy. Then, a time-varying model based on the fuzzy PI real-time control strategy (FD-FZPI) with fractional order disturbance observer (FO-DOB) is proposed. Based on the robust stability principle, a more accurate FO-DOB is proposed based on integer order DOB, coupled with a fuzzy PI controller to compensate for the external disturbance and modeling error of the space manipulator. Finally, numerical simulation analysis is carried out, and the results show that the average parameter difference between the time-varying dynamic model and the static dynamic model can reach about 5.2 %, which indicates the accuracy of the proposed dynamic modeling method. At the same time, the proposed FD-FZPI control strategy achieves about 14.6 % performance improvement over the traditional DOB-PI control method, indicating that the proposed control strategy can effectively suppress the flutter fluctuation of the space manipulator and achieve accurate and stable dynamic tracking.