Engineering topics

Bach, Ralph

Publications and source records attributed to Bach, Ralph.

4 records

NASA NTRS1995

Inversion Of Dynamical Equations For Control Of Attitude

Method of inverting nonlinear equations of rotational dynamics of rigid body used to design feedback control of orientation of body. Applicable to both direction-cosine and quaternion formulations suitable for large-angle maneuvers. Exploiting some apparently little-known properties of direction cosine and quaternion formulations, method leads to equations for model-follower control system that exhibits exactly linear attitude-error dynamics. Quarternion system more robust in responding to large roll-angle commands.

Bach, Ralph↗

NASA NTRS1993

Linearization of Attitude-Control Error Dynamics

Direction cosines and quaternions are useful for representing rigid-body attitude because they exhibit no kinematic singularities. Each utilizes more variables than the minimum three degrees of freedom required to specify attitude. Therefore, application of a nonlinear inversion procedure to either formulation introduces singularities. Furthermore, in designing an attitude-control system, it is not appropriate to express attitude error as a difference of direction cosines (or quaternions). One should employ a measure of attitude error that not only is minimal but preserves orthogonal rotation properties as well. This note applies an inversion procedure to an appropriate measure of attitude error, so that the singularity occurs when the error reaches +/- 180 deg. This approach leads to the realization of a new model-follower attitude-control system that exhibits exact linear attitude-error dynamics.

Bach, Ralph↗

NASA NTRS1990

Direct inversion of rigid-body rotational dynamics

The global linearization (inversion) of rigid-body rotational dynamics is reviewed and representations in terms of quaternions and direction cosines are compared. Certain properties common to quaternions and direction cosines that make their use preferable to Euler angles and that simplify the inversion procedure are described. Applications of the inversion procedure for state estimation and attitude control are discussed. To avoid complexities caused by aerodynamics, an example of direct inversion for linear feedback control of spacecraft attitude is given.

Bach, Ralph↗

NASA NTRS1990

Direct inversion of rigid-body rotational dynamics

The global linearization (inversion) of rigid-body rotational dynamics is reviewed, and representations in terms of quaternions and direction cosines are compared. Certain properties common to quaternions and direction cosines that make their use preferable to Euler angles and that simplify the inversion procedure are described. Applications of the inversion procedure for state estimation and attitude control are discussed. To avoid complexities caused by aerodynamics, an example of direct inversion for linear feedback control of spacecraft attitude is given.

Bach, Ralph↗