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A simple Â¿minimum-fuel,Â¿ digital attitude control system requiring no rate gyros is described; the system is applicable to practically any type of orbiting space vehicle. An inertial guidance computer furnishes a quantized attitude angle to the control system. With this attitude information and a measure of time, the control computer accurately computes the vehicle's average rate. A novel switching zone arrangement in the phase plane results in decisions controlling on-off reaction jets that adjust the vehicle's attitude. Jet selection and duration of the jets' operation are determined as a function of the vehicle's angular position and average rate in relation to the switching zones in the phase plane. The system operates so that computed rates are very accurate when accurate rates are required and less accurate when accuracy is not important. The end result is a system that converges to a low-rate limit cycle while consuming near-minimum fuel. The parameters controlling the switching logic are prestored memory constants which are electronically loadable and changeable. This flexibility makes the system compatible with a wide variety of payloads and missions.