Model simulation of parametrically excited ship rolling

Tondl, A.; Nabergoj, Radoslav

doi:10.1007/bf01857784

Cited by 15 publications

(13 citation statements)

References 7 publications

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“…which is similar to equation (7) of [18] and equation (47) of [16]. For the special case of an undamped system, the instability condition of the no-roll response is then…”

Section: Conditions For Roll Instabilitymentioning

confidence: 62%

“…This is the well-known condition for the first instability region of the Mathieu equation for the undamped case, see, e.g., [5,7,11,18]. The positive sign for the second term on the right-hand side of equation (20) is associated with the response of # with B = -C, equation (17), while the negative sign is with B = C. It can easily be shown that the maximum roll, #max, is in phase with positive z if co < cob and B = C or if co > coh and B = -C, but #max is in phase with negative z if co > cob and B = C. Another important instability region, the fundamental parametric resonance region, involves harmonic roll responses; its instability conditions can be determined by substituting the following harmonic response into equation (11).…”

Section: Conditions For Roll Instabilitymentioning

confidence: 99%

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Nonlinear heave-roll coupling and ship rolling

Liaw

Bishop

1995

Nonlinear Dyn

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A nonlinear model for simulating the heave-roll motions of ships in following waves is presented. The parametric excitation is modeled by a Hill's type equation, instead of the conventional Mathieu's equation. The model includes not only the linear but also the quadratic coupling term. Instability conditions for parametrically excited rolling motions are derived using the harmonic balance method. The results are verified by numerical analyses. The effects of including the quadratic coupling term on the instability conditions and nonlinear responses are studied. The complex dynamic behaviour of the coupled system in the various instability regions is also investigated. Bifurcations of the flip, fold and pitchfork types are observed in the Poincar6 mapping of the numerically simulated responses. Chaotic motions leading to boundary crises and inevitable capsize are also reported.

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“…which is similar to equation (7) of [18] and equation (47) of [16]. For the special case of an undamped system, the instability condition of the no-roll response is then…”

Section: Conditions For Roll Instabilitymentioning

confidence: 62%

Section: Conditions For Roll Instabilitymentioning

confidence: 99%

Nonlinear heave-roll coupling and ship rolling

Liaw

Bishop

1995

Nonlinear Dyn

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“…In the present paper some results obtained by Tondl A. and Nabergoj R. [1,2] will be extended for the case of a nonlinear elastic spring and ~onlinear expansions of trigonometric functions. …”

Section: Introductionmentioning

confidence: 93%

“…Using the Lagrange equations for the system represented in Fig.l we have the following differential equations of motion: 1) where Z = x-u is the relative vertical displacement ·of the mass Af, x i~ the vertical displacemen~ of the u1ass M from its static position of equilibrium 1 u = qcoswt is the vertical displacement of the base of the spring -masS system, pis the angular displacement of the pendulum 1 ko and {3,., are the linear and nonlinear charadeilltics of the spring respectively, l is the length of the rod, ho and Co are the damping cQefficients of the linear and angular motions, respectively, g is the gravity acceleration and an overdot denotes a derivative with respect to time t. …”

Section: Motion Equationsmentioning

confidence: 99%

“…The simulation of the coupling between heave roll and pitch roll motions of a ship running in a regular longitudinal or oblique sea has been studied by Tondl A. and Nabergoj R. [1]. The proposed model consists of a mass M restrained by a linear elastic spring, which, in turn, carries a simple free oscillating pendulum made up of a mass m attached to a hinged, weightless rod {Fig.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear model simulation of ship motion

Dao¹

1992

Vietnam J. Mech.

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S~Y. Nonlinear model simulation of coupling between heave-roll and pitchroll ship mot.ions is considered by means of the asymptotic method of nonlinear mechanics. The purely vertical motion and vertical-angular motion and _their stability are studied. L INTRODUCTIONThe simulation of the coupling between heave roll and pitch roll motions of a ship running in a regular longitudinal or oblique sea has been studied by Tondl A. and Nabergoj R. [1]. The proposed model consists of a mass M restrained by a linear elastic spring, which, in turn, carries a simple free oscillating pendulum made up of a mass m attached to a hinged, weightless rod {Fig. 1). The system is forced to oscillate sinusoidally in the vertical direction by means of an exten1al driver with constant a1nplitude q and frequency w. The coupling between the vertical and angular oscillations is accomplished by connecting the two masse5 and the effect of the waves is sllnulated by means of external forcing.In the present paper some results obtained by Tondl A. and Nabergoj R. MOTION EQUATIONSUsing the Lagrange equations for the system represented in Fig.l we have the following differential equations of motion: 1) where Z = x-u is the relative vertical displacement ·of the mass Af, x i~ the vertical displacemen~ of the u1ass M from its static position of equilibrium 1 u = qcoswt is the vertical displacement of the base of the spring -masS system, pis the angular displacement of the pendulum 1 ko and {3,., are the linear and nonlinear charadeilltics of the spring respectively, l is the length of the rod, 7

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Cooperative control of networked robots on a dynamic platform in the presence of communication delays

Nguyen

Dankowicz

2016

Intl J Robust & Nonlinear

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This paper presents an analysis of the synchronization and consensus problems of networked manipulators operating on an underactuated dynamic platform in the presence of communication delays. The proposed formulation does not require detailed information about the system model. A theoretical formulation based on input-output maps of functional differential equations shows that the control system's behavior matches closely that of a non-adaptive reference system. The tracking synchronization objective is achieved despite the effects of the communication delay and the unknown dynamics of the platform. When there is no common desired trajectory, the modified controller drives all robots to average consensus for an unsigned graph and to bipartite consensus for a structurally balanced signed digraph. In addition, a leader-follower scheme is proposed that allows for the control of the constant and time-varying consensus values. Simulation results illustrate the performance of the proposed control algorithms.These strategies can be shown to produce satisfactory performance in the presence of constant communication delay. The work in [9] studies cooperative control of multi-agent systems for escorting a target with the capability of avoiding obstacles. The control scheme in [10-12] is able to synchronize a group of manipulators in the presence of time-varying communication delay and intermittent information exchange. Robot synchronization is also addressed in [13] in the presence of interaction forces on the mechanical systems from a human operator. Such cooperative control scenarios were extended to task space in [14] using passivity-based approaches discussed in [15][16][17]. Neural network-based methods are explored to solve synchronization of Lagrangian systems in [4]. The work in [18,19] studied the synchronization problem with uncertainties in both system dynamics and the Jacobian matrix. The controller was extended to drive the robots' angular velocities to their average value in [20] and was designed to account for the case of communication delay in [21]. Synchronization problem in the context of teleoperation with master and slave manipulators is studied in [22] via a communication architecture designed to cope with delays.The adaptive control algorithms in the cited literature rely on the linear-in-parameter property of Lagrangian systems. They parameterize a robot's dynamic structure as a product of a well-defined regression matrix and a vector of unknown parameters. When these assumptions apply, the unknown parameters can be estimated by appropriate adaptive laws. For fixed-base manipulators, this is typically the case. Control algorithms that do not rely on the linear-in-parameter property can be found in [23] and [24], which achieves synchronization via an adaptive sliding-mode control schemes. This work does not consider communication delays and assumes a known inertia matrix [23] or gravity cancellation [24]. For fixed-base manipulators, these are again reasonable assumptions.In contrast, when manipulator...

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Model simulation of parametrically excited ship rolling

Cited by 15 publications

References 7 publications

Nonlinear heave-roll coupling and ship rolling

Nonlinear heave-roll coupling and ship rolling

Nonlinear model simulation of ship motion

Cooperative control of networked robots on a dynamic platform in the presence of communication delays

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