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The application of linear optimal control and least square filtering theory to the design of a control system for the Saturn V launch vehicle is described. System performance is evaluated on the basis of the ratio of the standard deviations of structural load, engine deflection, and lateral velocity drift to their design limits. An optimal linear control is derived from a quadratic performance index in ratios of these critical variables to their design limits. It is shown that this essentially eliminates trial and error search for suitable quadratic index weighting coefficients. It is also shown that the standard deviations are only slightly degraded when feedback gains on actuator states and bending and slosh modes are eliminated, leaving feedback gains on only the three rigid-body states and feed-forward gains on the wind-induced angle of attack and wind-shear velocity. A new method of reducing the state estimation filter dimension to yield suboptimal estimation of the three rigid-body states and two wind model states is applied and shown to cause only a slight additional increase in the standard deviations of the critical system variables.
Date of Publication: Dec 1971