DYNAMICS AND CONTROL IN MODAL-SPACE OF FLEXIBLE SPACECRAFT

This investigation is concerned with dynamics and control of high-order dynamical systems represented by large flexible spacecraft. The object is to develop a method of control which is particularly suitable for high-order systems. The procedure is referred to as independent modal-space control and consists of a scheme for independent control of the spacecraft modes. The decoupling of the system equations of motion is achieved via a linear transformation involving the modal matrix which reduces the system dynamics to a set of n independent equations for conjugate pairs of generalized coordinates regardless of how large the order 2n of the system is. The basic idea behind the method is that the control laws are first designed in the modal-space for each independent set in a way that the response of one pair of modes does not affect the response of any other pair of modes, i.e., the resulting modal control input vector is a modal state feedback control with a 2 x 2 block-diagonal gain matrix. The actual physical controls on the original coupled system dynamics are synthesized subsequently from the modal control laws by means of a reverse linear transformation. The approach makes it possible to design nonlinear on-off control laws as well as proportional control laws for high-order systems.; The independent modal-space control proposed in this investigation shifts the problem of high dimensionality from the control problem to the structural dynamics problem, in recognition of the fact that the capabilities of available structural dynamics computational algorithms exceed those of modern control theory by at least one order of magnitude. The controller design is modular in form. Both nongyroscopic and gyroscopic systems are being considered. It is shown that for nongyroscopic systems no control spillover exists due to the uncontrolled modes included in the mathematical model. In the case of gyroscopic systems, the method calls for a 2nth order mathematical model to control n modes independently, which results in the elimination of the truncation effects relative to the 2nth order model in controlling the n modes. The derivation of a deterministic decoupled modal observer which estimates a linear combination of the modal state is given. The formulation includes controlled and uncontrolled modes simultaneously resulting in a control free of observation spillover instabilities due to modeled uncontrolled modes without any penalty on the order of the observer. An optimal modal-space control algorithm is presented which requires the solution of a set of 2 x 2 uncoupled matrix Riccati equations regardless of the order of the coupled system dynamics.; As numerical examples, a dual-spin flexible spacecraft with a despun section is considered. If the rotor is locked, then the system is nongyroscopic and if the rotor is spinning uniformly in equilibrium, the same system is gyroscopic. The control of the nongyroscopic system is effected by means of a dual-level controller making simultaneous positional, attitude and shape control possible. The gyroscopic system is considered only in relation to the attitude and shape control. Optimal control for both types of systems is also presented.