Abstract: A method is described for avoiding gyroscopic singularities during attitude correction to a system, such as a spacecraft having a CMG array. The method receives a corrective torque vector ? and gimbal angle values ? for each of at least three gimbals within the CMG array. The method generates a Jacobian matrix A as a function of gimbal angle values ?. The method calculates a determinant D of Jacobian matrix A. If the determinant is not equal to zero, it is not singular, and the method calculates a gimbal rate {dot over (?)} using a pseudo-inverse steering law equation. If the determinant is equal to zero, it is singular, and the method calculates a gimbal rate {dot over (?)} using a singularity avoidance steering law equation. The gimbal rate {dot over (?)} is output and can be applied to a CMG array resulting in applied torque to a spacecraft and attitude correction.

Abstract: Noise effects in a signal for driving a plant are reduced by generating a reference signal from the error signal. A signal generator generates a reference signal for input to a finite impulse response (FIR) filter. The error signal is produced by differencing the transfer function output and a disturbance signal. The error signal is input to the signal generator and to a least mean square calculator. The reference signal is input to a copy of the transfer function that outputs a modified reference signal. The modified reference signal is input to least mean square calculator. An LMS signal that updates the filter coefficients to minimize the mean square error is calculated and the LMS signal and the reference signal are input to the FIR filter with the FIR filter being arranged to process the LMS signal and the reference signal to minimize the error signal.

Abstract: A system and method for attitude control in a geosynchronous satellite to compensate for roll and yaw pointing errors consequent to orbit inclination variation from the nominal equatorial orbit plane provides for an inertially fixed momentum vector coupled to the satellite through a gimbal system providing a one and preferably two degree-of-freedom relationship with the momentum vector. In a two degree-of-freedom embodiment, the momentum vector is established by spinning the satellite about an axis or providing an independent momentum wheel with the gimbal axes provided along the roll and yaw axes. Gimbal torquers torque the satellite about the inertially fixed momentum vector in a time-varying manner to effect correction of the roll and yaw pointing errors. Roll and yaw pointing errors consequent to orbit inclination drift from the nominal equatorial orbit are corrected in a fuel-efficient manner to extend the operating life of the satellite.