Robust Command Filtered Backstepping Control for FJR Using Reduced-Order GPI Observers

This brief addresses the trajectory tracking control of a category of n-link disturbed flexible joint robots (FJRs). First of all, two reduced-order generalized proportional integral observers (ROGPIOs) are constructed to estimate not only matched disturbances but also mismatched disturbances. Next on, with the assistance of estimations provided by the ROGPIOs, a newly robust tracking controller is recursively designed with the command filtered backstepping (CFBS) method. Meanwhile, second-order filters are employed to overcome the obstacle of "explosion of complexity" and an error compensation mechanism is developed to mitigate the adverse effect of filter errors on tracking performance. A rigorous theoretical analysis guarantees that the closed-loop system consisting of error compensation signals, estimation errors, compensated tracking errors, and tracking errors is uniformly ultimately bounded. Numerical tests on a two-link FJR are carried out to validate the viability of the presented strategy. The results confirm that the proposed control scheme has a solid ability to suppress both matched and mismatched disturbances.