Combined design of structures and controllers for optimal maneuverability

1 I n t r o d u c t i o n Large space structures such as antennas or space stations will be very flexible, not only because of the high cost of transportation of structures from earth to space, but also because they will be constructed or deployed in orbit and will not need to withstand large launching and gravity loads. However, when a space structure is very flexible, its active control system can excite and otherwise significantly interact with its flexible modes. Thus, the idea arises of achieving simultaneous vibration mode suppression with at t i tude maneuver of flexible spacecraft. The control design for rotational maneuvers and vibration mode suppression of flexible spacecraft has received extensive attention (e.g. Breakwell 1981; Van der Velde and He 1983; Turner and Chun 1984; Hale and Lisowski 1985; Vadali 1986; Fujii and Ishijima 1989; BenAsher et al. 1987; Barbieri and Ozguner 1988; Thompson et al. 1989, 1990; Singh et al. 1989). For certain applications, it will be desirable that such a spacecraft slew as rapidly as possible, within the operating limits of the control actuators. Flexible spacecraft are modelled with a finite number of vibration modes, and optimal control theory is then applied to obtain the time optimal control history for quiescent terminal conditions of the vibration modes (see, for example, Barbieri and Ozguner 1988; Thompson el al. 1989, 1990; Singh et al. 1989). Singh et al. (1989) observe quantitatively that the difference between the minimum time for a rigid body and the actual time required for a flexible spacecraft is small for large-angle maneuvers of systems of low flexibility and low authority control torques. However, all of these authors only consider control design based on a specific structure. It is expected that by adjusting the design parameters of the spacecraft itself we may obtain even bet ter results, especially for large flexible structures. As a consequence, structural optimization is considered so as to further minimize the maneuver time and achieve vibration mode suppression. The design process is thus a combined design of controllers/structures applied to spacecraft. This paper is concerned with developing a theoretical and practical framework for solving this problem. Traditionally, the overall design for actively controlled space structures is t reated via an iterative two-part scheme. The redesign of the structure including sensor and actuator placement is performed in one stage, and then the control law is modified for the resulting system to complete an iteration cycle. Generally different design objectives apply in the separate steps. More recently, the need to integrate the design of a structure and its control system has been recognized. An integrated approach is justified simply on the basis that structural and control purposes are substantially coupled. Bodden and Junkins (1985) presented a method for eigenvalue optimization with sequential or simultaneous design of structure and control. Khot el al. (1985a, b) and Khot el al. (1988) considered structural optimization, including constraints on control gain norm and transient behaviour of the control system, based on a linear-quadratic model of the controller. Hale and Lisowski (1983) and Hale c t a l . (1984) treated the problem o~simultaneous structure and control design for a maneuvering spacecraft which resulted in a linear-quadratic optimization problem. Bends¢e et al. (1987) presented an algorithm for integrated design of the structure and its control system which includes a constraint to limit the controller spillover from the unmodelled modes. Lust and Schmit (1988) presented a control-augmented structural synthesis methodology in which the structural member sizes and active control system feedback gains are treated simultaneously as independent design variables. Onoda and Haftka (1987) and ttaftka el al. (1985) considered the optimization of the total cost of the structure and control system subject to constraints on the magnitude of the response to a given disturbance involving both rigid-body and elastic modes. Lim and Junkins