Rapid maneuvers of large flexible structures are proposed by integrating the singular perturbation method and the Lyapunov- based nonlinear control design. The singular perturbation technique is applied for dividing the flexural vibration of large flexible structures into a slow-model and a fast-model subsystems in two separate time scales. The fast-model states characterized by the high frequency modes are significantly active only during a short initial transient period such that they decay in the fast time scale. After that period, behaviors of the system are dominated by its slow-model states associated with the low frequency modes. Based on the linear slow-model subsystem, a linear output feedback gain can be achieved by using the linear control theory such as the optimal control law or the pole-placement method. The control input of the nonlinear fast-model subsystem can be derived through a Lyapunov-based nonlinear control design. Namely, a feedback control of the fast-model subsystem is designed to guarantee its stability by having a positive-definite Lyapunov function which is a decreasing function of time. Combination of these two parts thus ensures a stable feedback control design for nonlinear two-time-scale flexible structures in a Lyapunov sense. This approach is also effective due to its reduced-order of two-time-scale models while dealing with the nonlinear control design. A numerical example is given to demonstrate control designs for rapid slewing maneuvers of large flexible structures with coupled rotational and translational motions while simultaneously suppressing vibrational motion during the control process.
"Two-time-scale control designs for large flexible structures", Proc. SPIE 1303, Advances in Optical Structure Systems, (1 October 1990); doi: 10.1117/12.21514; https://doi.org/10.1117/12.21514