Bending feedback control Final report

3 ,12.-0 The results of a lZ-month study of the application of quadratic optimal control, least squares state, and parameter estimation to the stability and control problem of the flexible launch vehicle are presented. The feasibility of using optimal control on a few states cf a high-order system to control the damping in the bending modes is demonstrated. State estimation (Kalman) filters are shown to be capable of stabilizing the higher-order bending modes. Combined state and parameter estimation is shown to be straightforward, although rather complex in mechanization. A set of control gains and filters is derived for a particular model vehicle provided by NASA-MFSC. This model, based on the general characteristics of Saturn V, is specifically tailored to make it difficultto stabilize. It is shown that the methods described can stabilize this model at three sample flight conditions which represent the extremes in the environment. A set of design guides, or principles, for the application of these techniques is presented. It is suggested that these techniques raise the capacity of the control system designer to the consideration of better and higher-order systems than have been readily tractable heretofore. PRECEDING PAGE I_[_ANK NOT FILMED. iii 1966022830-003