| Time-optimal control refers to the design of a control algorithm which accomplishes a desired task in the shortest possible time. Typically, a time-optimal control algorithm makes optimal use of the maximum input available for rapid maneuvers. It is an important field for many applications, especially in the aerospace industry where fast system response is required. Precision pointing control and rapid maneuvering capabilities have long been part of many space missions; examples include military observation platforms, communications satellites, and exploratory space missions. Consequently, research in attitude maneuvers and time-optimal controls has been a consistently strong field of study. There are many other applications as well, such as in manipulators, disk-drive heads or pointing systems.; In this work, a new mathematical procedure is developed with the objective of designing a feedback time-optimal control law, based on Gulko's strategy for fourth-order systems with and without damping. These systems include one rigid-body mode and one flexible mode, with one collocated control input, and represent rather typical simplified structural models used for large-angle rotational maneuvers of flexible spacecraft and flexible robotic arms.; Since, in practice, it is difficult, if not impossible, to implement bang-bang control action, the design of time-optimal control input with a finite rate of change during a switching time is investigated.; Since the time-optimal control of multimodal models of flexible structures is difficult to solve analytically, we also outline a direct numerical technique for finding open-loop time-optimal controls for general linear and nonlinear systems based on collocation method and differential inclusion concept. Then these numerical techniques are used to obtain the thrusting firing sequence for the Gamma Ray Observatory (GRO) satellite for the purpose of raising its orbit in minimum time. |
