Linear feedback control using quasi velocities
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abstract
A novel approach for designing feedback controllers for natural mechanical systems using quasi velocities is presented. The approach is relevant to the stabilization and regulation of finite-dimensional multibody systems. In particular the globally asymptotically stable linear feedback of Rodrigues parameters and angular velocity is taken from spacecraft attitude control and applied to a broader class of problems. This controller is shown to have good performance due to the sensitivity of the rotational kinematics to small motions near the reference configuration. Additionally, the concept is extended to systems with more than three degrees of freedom by generalizing the functional form of the three-dimensional rotational kinematics. This defines a new set of quasi velocities that allow globally asymptotically stable linear feedback for any number of degrees of freedom. An example shows that the use of these variables in controller design can lead to improved performance.
