Boundary control of a flexible spacecraft considering shear deformation and rotary inertia of the appendage

This study investigates the planar motion control of a spacecraft with a single flexible appendage. The objective is to simultaneously control the rigid-body motion of the spacecraft and structural vibrations of the appendage by using only the control actuators on the central hub. The appendage is modeled by using Timoshenko beam theory, which is more accurate and has a wider range of applications than Euler–Bernoulli beam theory because it considers shear deformation and rotary inertia. The governing equations of motion that comprise partial differential equations (PDEs) and ordinary differential equations (ODEs) are obtained by using Hamilton's principle. Following this, boundary control laws are designed based on the coupled PDE–ODE model without discretizing the PDEs to avoid the spillover phenomenon. The closed-loop system is proven to be exponentially stable by using Lyapunov’s direct method. Finally, numerical simulations are performed to validate the effectiveness of the boundary control laws proposed in this work.