A new adaptive identifier for second-order rotational plants with applications to underwater vehicles

Abstract

This paper reports a novel adaptive identifier for the estimation of the plant parameters of three degree-of-freedom second-order rigid-body rotational plants under the influence of externally applied torques. A second adaptive identifier is also reported which, in addition to estimating the rigid body parameters, identifies quadratic drag, and buoyancy torque parameters that arise in the rotational dynamic models of rigid-body underwater vehicles. Although a rich collection of literature exists on the problem of model-based adaptive trajectory-tracking control, these approaches are not applicable when the plant is either uncontrolled, under open-loop control, or using any control law other than a specific adaptive tracking controller. In contrast, the adaptive identifiers reported herein provide an approach to plant parameter estimation applicable to the commonly occurring cases of uncontrolled plants, plants under open-loop control, and plants using control methods prescribed to meet other considerations for an application. Local stability proofs of the new adaptive identifiers are reported. The stability analysis show that the angular velocity estimate of the adaptive identifiers converges asymptotically to the angular velocity of the actual plant, that the parameter estimates are stable, and that the parameter estimates converge asymptotically to values that provide input/output model behavior identical to that of the actual plant. A comparative experimental evaluation of the second adaptive identifier is reported using the Johns Hopkins University Remotely Controlled Underwater Vehicle. The experimental results corroborate the analytical stability analysis, showing that the angular velocity estimate of the adaptive identifier converges asymptotically to the angular velocity of the actual plant, and the adaptively estimated plant parameters asymptotically converge to values that provide plant-model input/output behavior closely approximating the input/output behavior of the actual experimental underwater vehicle. An experimental comparison of adaptive identification and conventional least squares parameter identification is also reported. The adaptively identified model was shown to be similar to the least squares identified model in its ability to match the actual vehicle's input/output characteristics. The common formulation of least squares identifiers require angular acceleration, a measurement which is not required for the adaptive identification algorithm presented herein. Since underwater vehicles are often not instrumented to measure angular acceleration, this method may provide model parameter estimates that could not be obtained by other standard methods.