146 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 25, NO. 1, JANUARY 2000 An Accurate Four-Quadrant Nonlinear Dynamical Model for Marine Thrusters: Theory and Experimental Validation Ralf Bachmayer, Student Member, IEEE, Louis L. Whitcomb, Member, IEEE, and Mark A. Grosenbaugh Abstract—This paper reports two specific improvements in the finite-dimensional nonlinear dynamical modeling of marine thrusters. Previously reported four-quadrant models have em- ployed thin airfoil theory considering only axial fluid flow and using sinusoidal lift/drag curves. First, we present a thruster model incorporating the effects of rotational fluid velocity and inertia on thruster response. Second, we report a novel method for experimentally determining nonsinusoidal lift/drag curves. The model parameters are identified using experimental thruster data (force, torque, and fluid velocity). The models are evaluated by comparing experimental performance data with numerical model simulations. The data indicates that thruster models incorporating both reported enhancements provide superior accuracy in both transient and steady-state responses. Index Terms—Dynamic positioning, dynamic response, hydro- dynamics, marine propulsion, marine vehicle control, thrust con- trol, thruster modeling. I. INTRODUCTION R ECENT advances in underwater position and velocity sensing enable real-time centimeter-precision position measurements of underwater vehicles [1]–[6]. With these advances in position sensing, our ability to precisely control the hovering and low-speed trajectory of an underwater vehicle is limited principally by our understanding of: 1) the vehicle’s dynamics and 2) the dynamics of the bladed thrusters com- monly used to actuate dynamically positioned marine vehicles. This paper addresses the latter problem. Recent results indicate that the transient (unsteady) dynamics of marine thrusters can be approximated by a simple nonlinear finite-dimensional lumped-parameter dynamical system [7]–[14]. Healey et al. [10] present a nonlinear model that is based on the motor electro-mechanical dynamics and thin-foil propeller hydrody- namics using sinusoidal lift and drag functions. Propeller and fluid dynamics are approximated by a two-dimensional (2-D) second-order nonlinear dynamical system with state variables of axial fluid velocity and propeller rotational velocity. We Manuscript received May 19, 1999; revised September 30, 1999. The work of R. Bachmayer and L. L. Whitcomb was supported by the Office of Naval Research under Grant N00014-97-1-0487 and by the National Science Founda- tion under Grant BES-9625143. The work of M. A. Grosenbaugh was supported by the Office of Naval Research under Grant N00014-96-1-5014. This paper is WHOI contribution #9883. R. Bachmayer and L. L. Whitcomb are with the Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218 USA. M. A. Grosenbaugh is with the Deep Submergence Lab, Woods Hole Oceano- graphic Institution, Woods Hole, MA 02543 USA. Publisher Item Identifier S 0364-9059(00)00748-2. TABLE I NOMENCLATURE will refer to this model as the “axial flow model.” In [13], the authors report experiments that corroborate the utility of the axial flow model, but also identify discrepancies between the thruster’s transient response and the model predictions. This paper examines two possible sources for the reported discrepancies: rotational fluid flow and lift/drag curve profiles. Models employing experimentally derived (nonsinusoidal) lift/drag curves are shown to more accurately agree with experimental performance than models employing sinusoidal lift/drag curves. The nomenclature is defined in Table I. We describe the experimental setup in Section II. In Section III, we report on the results of an improved hydrodynamic model and compare its results to experimental data and the axial flow model. In Section IV, we report on a novel procedure to generate lift and drag curves that is based on experimental data and our new model. Conclusions are given in Section V. 0364–9059/00$10.00 © 2000 IEEE