Analytical Stability Analysis of Surface Vessel Trajectories for a Control-Oriented Model

An analytical stability analysis of the steady trajectory for a surface vessel with various damping models is presented in this work. The analysis is based on a control-oriented, three degrees-of-freedom model that considers vessel motion only in the horizontal plane. The goal of this study is to understand the vessel trajectories predicted by this reduced order model for model-based control design. Straight line and circular motion stability conditions for each trajectory are derived and presented for the various damping models. The results of this analysis show that either a straight line or a circular steady trajectory is possible, depending on the magnitude of the surge force and the form of the damping model used to represent viscous drag, vortex shedding, and losses due to the surface wake generated by the vessel motion. However, the straight line motion is much less likely for the vessel considered in this work.

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Brake squeal noise due to disc run-out

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1243/09544070jauto342 ◽

2007 ◽

Vol 221 (7) ◽

pp. 811-821 ◽

Cited By ~ 6

Author(s):

J-P Park ◽

Y-S Choi

Keyword(s):

Stability Analysis ◽

Degrees Of Freedom ◽

Experimental Results ◽

Brake System ◽

Brake Squeal ◽

Friction Characteristic ◽

Linear Friction ◽

Brake Dynamometer ◽

Squeal Noise ◽

Three Degrees Of Freedom

To understand brake squeal noise, the sound and vibration of an automobile brake system were measured using a brake dynamometer. The experimental results show that an important factor in squeal generation is the run-out due to disc misalignment. A three-degrees-of-freedom model is developed for the brake system, where the run-out effect and non-linear friction characteristic are included. A stability analysis of the model was also performed to predict the generation of squeal with the modification of the brake system. The results show that squeal generation is dependent on the run-out rather than the friction characteristic between the pad and disc.

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Limit Points Behavior in Electrostatically Actuated Initially Curved Micro Plate

Volume 4: 21st Design for Manufacturing and the Life Cycle Conference; 10th International Conference on Micro- and Nanosystems ◽

10.1115/detc2016-59457 ◽

2016 ◽

Author(s):

Lior Medina ◽

Rivka Gilat ◽

Slava Krylov

Keyword(s):

Degrees Of Freedom ◽

Mechanical Load ◽

Electrostatic Force ◽

Equilibrium Path ◽

Buckling Modes ◽

Reduced Order ◽

Electrostatically Actuated ◽

Base Functions ◽

Three Degrees Of Freedom ◽

Good Agreement

The axisymmetric snap-through of an initially curved circular micro plate, subjected to a transversal distributed electrostatic force is studied. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition, with buckling modes of a flat plate used as the base functions. In order to check the validity of the RO model, the corresponding problem for a displacement-independent (“mechanical”) load is solved, and a comparison between the RO model and those obtained using finite elements (FE) analysis is carried out. It is shown, that the two are in good agreement, indicating that the RO model can be used for a plate undergoing electrostatic loading. However, the study shows that at least three degrees of freedom (DOF) are required for an accurate prediction of the equilibrium path and bistability. The coupled electromechanical analysis shows that due to the nonlinearity of the electrostatic load, the snap-through occurs at a lower displacement than in the case of the “mechanical” load. Moreover, the study concludes that actuation of plates of realistic dimensions can be achieved by reasonably low voltages.

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Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

Mathematical Problems in Engineering ◽

10.1155/s1024123x97000598 ◽

1997 ◽

Vol 3 (4) ◽

pp. 329-371

Author(s):

Henryk Flashner ◽

Ramesh S. Guttalu

Keyword(s):

Stability Analysis ◽

Degrees Of Freedom ◽

Mapping Method ◽

Periodic Systems ◽

Resonance Problem ◽

Point Mapping ◽

Analytical Stability ◽

Functional Relations ◽

Ground Resonance ◽

The Stability

Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

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The stability analysis for the motion of a nonlinear damped vibrating dynamical system with three-degrees-of-freedom

Results in Physics ◽

10.1016/j.rinp.2021.104561 ◽

2021 ◽

pp. 104561

Author(s):

T.S. Amer ◽

M.A. Bek ◽

S.S. Hassan ◽

Sherif Elbendary

Keyword(s):

Dynamical System ◽

Stability Analysis ◽

Degrees Of Freedom ◽

The Stability ◽

Three Degrees Of Freedom

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Reduced-Order Model of a Mistuned Multi-Stage Bladed Rotor

Volume 5: Turbo Expo 2007 ◽

10.1115/gt2007-27277 ◽

2007 ◽

Cited By ~ 8

Author(s):

Alok Sinha

Keyword(s):

Degrees Of Freedom ◽

Maximum Amplitude ◽

Reduced Order Model ◽

Order Model ◽

Mass Model ◽

Reduced Order ◽

Multi Stage ◽

Bladed Rotor ◽

The Impact ◽

Three Degrees Of Freedom

This paper deals with a reduced-order model of a multi-stage rotor in which each stage has a different number of blades. In particular, it is shown that a reduced-order model can be developed on the basis of tuned modes of certain bladed disks. The validity of this algorithm is shown for a spring-mass model with three degrees of freedom per sector. In addition, the statistical distributions of the peak maximum amplitude are generated via Monte Carlo simulations, and the impact of mistuning is examined for a two-stage rotor.

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Linear coupled model for floating wind turbine control

Wind Engineering ◽

10.1177/0309524x18756970 ◽

2018 ◽

Vol 42 (2) ◽

pp. 115-127 ◽

Cited By ~ 10

Author(s):

Alessandro Fontanella ◽

Ilmas Bayati ◽

Marco Belloli

Keyword(s):

Degrees Of Freedom ◽

Coupled Model ◽

Control Design ◽

Offshore Wind ◽

Order Model ◽

Reduced Order ◽

Offshore Wind Turbines ◽

Wind Turbine Control ◽

Floating Offshore Wind Turbines ◽

Three Degrees Of Freedom

This work deals with an analytical linear coupled model describing the integrated aero-hydrodynamics of floating offshore wind turbines. Three degrees of freedom (platform surge, platform pitch and rotor azimuth) were considered with the goal of building a reduced-order model suitable for being integrated in control design algorithms as well as to be used for a straightforward evaluation and comprehension of the global system dynamics.

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Consecutive Compensator in Station-Keeping of a Surface Vessel

Mekhatronika Avtomatizatsiya Upravlenie ◽

10.17587/mau.21.566-574 ◽

2020 ◽

Vol 21 (10) ◽

pp. 566-574

Author(s):

O. I. Borisov ◽

A. R. Dahl ◽

A. A. Pyrkin ◽

F. B. Gromova ◽

R. Skjetne

Keyword(s):

Degrees Of Freedom ◽

External Disturbance ◽

High Gain ◽

Longitudinal Motion ◽

Station Keeping ◽

External Disturbances ◽

Set Up ◽

Surface Vessel ◽

Thrust Allocation ◽

Three Degrees Of Freedom

This paper addresses the problem of station-keeping of a surface vessel by means of the consecutive compensator approach. The horizontal motion of the vessel is described by a dynamic model. The model is set up in vessel parallel coordinates, with three degrees of freedom: longitudinal, transverse and rotational motion. It is assumed that the vessel is fully actuated, i.e. there is a sufficient number and type of actuators and a thrust allocation system to ensure full manoeuvrability. Thus, the control can be designed with the assumption of three independent inputs and three output signals. The longitudinal motion can be considered separately, but a cross-coupling exists between the transverse and rotational kinetics. There is uncertainty both in parameters and signals, due to the vessel mass, inertia, and damping, as well as the unmeasured derivatives. The proposed control ensures station-keeping when the vessel is subjected to external disturbances. The consecutive compensator, which is based on high-gain feedback, provides robustness. Stability analysis is presented considering the cross-terms as limited disturbances. This allows proof of exponential stability. Experimental results are included from the Marine Cybernetics Laboratory (MC lab) at the Centre for Autonomous Marine Operations and Systems (A MOS) at the Norwegian University of Science and Technology (Norges teknisk-naturvitenskapelige universitet, NTNU ). Two scenarios are investigated: the scaled vessel is subjected to external disturbance, and the vessel executes the " four corner test". The experiments illustrate the applicability of the method.

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