Operational modal analysis coupled controller for space flexible-joint flexible-link manipulator using complex mode approach

In this paper, the operational mode coupled controller analysis theory and method for space flexible-joint flexible-link (FJFL) manipulator is proposed completely, and the coupling problem of control and structure is solved. Firstly, the vibration partial differential equation (PDE) based on the Rayleigh-Ritz method is modelled; then, the complicated boundary condition including joint rigidity and controller gain parameters is obtained via state feedback constraint and bending moment balance modus. In order to solve the operational mode frequency and shape function, the Laplace transform and complex mode approach are both significantly employed. The solution shows that the controller significantly influence the rigidity and damping coefficients and alters the dynamics response characteristic. Especially, the state feedback of the joint velocity introduces extra structure damping into the system, thus it lowers the natural frequency and makes the phase non-zero, which is extremely different from the conventional vibration features. Finally, a large number of numerical simulations are performed to verify the validity and rationality of the proposed programme.