Attitude control compensator for flexible spacecraft

An attitude control loop for a spacecraft uses a proportional-integral-derivative (PID) controller for control about an axis. The spacecraft body has at least a primary mechanical resonance. The attitude sensors are collocated, or both on the rigid portion of the spacecraft. The flexure attributable to the resonance may result in instability of the system. A compensator for the control loop has an amplitude response which includes a component which rolls off beginning at frequencies below the resonance, and which also includes a component having a notch at a notch frequency somewhat below the resonant frequency. The phase response of the compensator tends toward zero at low frequencies, and tends toward -180.degree. as frequency increases toward the notch frequency. At frequencies above the notch frequency, the phase decreases from +180.degree., becoming more negative, and tending toward -90.degree. at frequencies far above the resonance frequency. Near the resonance frequency, the compensator phase is near zero.