Nonlinear control of flexible spacecraft based on LMI constrained convex optimization

In this paper, a class of nonlinear controllers is proposed for rotational maneuvers of spacecraft with a pair of flexible appendages attached. With the application of proposed nonlinear feedback torque, dynamic equations of the flexible spacecrafts are converted into the linear parameter-varying (LPV) form. Regional pole assignment for the resultant LPV system is performed via secondary linear state feedback, and the feedback gain is computed through convex optimization constrained by linear matrix inequalities (LMI). It is shown that exponential closed-loop stability of the original spacecraft system can be achieved. Numerical simulations show that the rotational maneuvers can be performed precisely and the vibration is suppressed as well.