Dynamics of Underactuated Multibody Systems

Seifried, Robert

doi:10.1007/978-3-319-01228-5

Cited by 75 publications

(38 citation statements)

References 11 publications

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“…The derivation of the structural Equations of Motion (EQM) follows the Newton-Euler approach, as opposed to the Lagrangian approach, which is often found in wind turbine research [57,93]. The method allows for a user-defined MBS layout, independent of the configuration of bodies and DoFs; see [75] or [79]. Therefore the derivation, which is here shown for a FOWT, holds also for any other multibody system with the same assumptions.…”

Section: Structural Modelmentioning

confidence: 99%

“…In the same way as for rigid bodies, the flexible body velocity and acceleration vectors z II,i and z III,i of Eq. (1) can be written in terms of the generalized coordinates q with the Jacobian matrices J t,i and J r,i following [79] as…”

Section: Flexible Bodiesmentioning

confidence: 99%

“…Therefore we omit the derivation of h ω . It can be found in [77, p. 296] (for a reference in English, see [79]). Nonetheless, in the present model, we implement the quadratic velocity vector.…”

Section: Quadratic Velocity Vectormentioning

confidence: 99%

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Multibody modeling for concept-level floating offshore wind turbine design

Lemmer

Luhmann³

et al. 2020

Multibody Syst Dyn

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Existing Floating Offshore Wind Turbine (FOWT) platforms are usually designed using static or rigid-body models for the concept stage and, subsequently, sophisticated integrated aero-hydro-servo-elastic models, applicable for design certification. For the new technology of FOWTs, a comprehensive understanding of the system dynamics at the concept phase is crucial to save costs in later design phases. This requires low-and medium-fidelity models. The proposed modeling approach aims at representing no more than the relevant physical effects for the system dynamics. It consists, in its core, of a flexible multibody system. The applied Newton-Euler algorithm is independent of the multibody layout and avoids constraint equations. From the nonlinear model a linearized counterpart is derived. First, to be used for controller design and second, for an efficient calculation of the response to stochastic load spectra in the frequency-domain. From these spectra the fatigue damage is calculated with Dirlik's method and short-term extremes by assuming a normal distribution of the response. The set of degrees of freedom is reduced, with a response calculated only in the two-dimensional plane, in which the aligned wind and wave forces act. The aerodynamic model is a quasistatic actuator disk model. The hydrodynamic model includes a simplified radiation model, based on potential flow-derived added mass coefficients and nodal viscous drag coefficients with an approximate representation of the second-order slow-drift forces. The verification through a comparison of the nonlinear and the linearized model against a higher-fidelity model and experiments shows that even with the simplifications, the system response magnitude at the system eigenfrequencies and the forced response magnitude to wind and wave forces can be well predicted. One-hour simulations complete in about 25 seconds and even less in the case of the frequency-domain model. Hence, large sensitivity studies and even multidisciplinary optimizations for systems engineering approaches are possible.

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Section: Structural Modelmentioning

confidence: 99%

Section: Flexible Bodiesmentioning

confidence: 99%

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Multibody modeling for concept-level floating offshore wind turbine design

Lemmer

Luhmann³

et al. 2020

Multibody Syst Dyn

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“…The considered approaches are based on different model-based feedforward control designs [1] which are supported by additional feedback controllers.…”

Section: Introductionmentioning

confidence: 99%

Experimental studies of control concepts for a parallel manipulator with flexible links

2015

Self Cite

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Control of flexible multibody systems, such as flexible manipulators, is a challenging task. This is especially true if end-effector trajectory tracking is aspired. On the one hand, these systems require a large number of generalized coordinates to describe their dynamical behavior accurately. On the other hand, only a small subset of these values can be measured or reconstructed on-the-fly. Hence, it is difficult, if not nearly impossible, to use a state controller. In addition, flexible systems are underactuated, i.e. they possess less control inputs than generalized coordinates. In case of a non-collocated output controller, which is the case for end-effector trajectory tracking, the closed loop of the system might lose passivity and is non-minimum phase. In order to achieve end-effector trajectory tracking, exact and approximate feed-forward controls can be applied. In this work, two different versions of such concepts are compared experimentally. These model-based concepts are computed off-line and they supply, next to the required input values, a C 1 -continuous solution of the complete state vector which can be used for feedback control. If the system is non-minimum phase, a two-sided boundary value problem has to be solved and the solution includes a pre-actuation as well as a post-actuation phase. While the exact method incorporates all dynamical effects of the flexible multibody system, the approximate concepts neglect certain implications, for example the dynamical effects due to the flexibility. In addition to the presentation of the theoretical basics of the control approaches and the underlying models, this contribution addresses some of the crucial obstacles, which have to be overcome for the operation of the test bench, e.g., signal conditioning, state reconstruction and friction compensation. Since the installed sensors do not allow the direct measurement of the endeffector position, image tracking is used to judge the quality of the different control approaches.

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“…That is, it has fewer control inputs than the degrees-of-freedom (DOF) to be controlled. This presents a tough problem frequently encountered by researchers, i.e., control design for underactuated mechanical systems [8].…”

Section: Introductionmentioning

confidence: 99%

Controlling an Underactuated Two-Wheeled Mobile Robot: A Constraint-Following Approach

Yin

Chen

2019

Journal of Dynamic Systems, Measurement, and Control

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Controlling underactuated systems is a challenging problem in control engineering. This paper presents a novel constraint-following approach for control design of an underactuated two-wheeled mobile robot (2 WMR), which has two degrees-of-freedom (DOF) to be controlled but only one actuator. The control goal is to drive the 2 WMR to follow a set of constraints, which may be holonomic or nonholonomic constraints. The constraint is considered in a more general form than the previous studies on constraint-following control (hence including a wider range of constraints). No auxiliary variables or pseudo variables are required for the control design. The proposed control only uses physical variables. We show that the proposed control is able to deal with both holonomic and nonholonomic constraints by forcing the constraint-following error to converge to zero, even if the system is not initially on the constraint manifold. Using this control design, we investigate two cases regarding different constraints on the 2 WMR motion, one for a holonomic constraint and the other for a nonholonomic constraint. Simulation results show that the proposed control is able to drive the 2 WMR to follow the constraints in both cases. Furthermore, the standard linear quadratic regulator (LQR) control is applied as a comparison in the simulations, which reflects the advantage of the proposed control.

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Dynamics of Underactuated Multibody Systems

Cited by 75 publications

References 11 publications

Multibody modeling for concept-level floating offshore wind turbine design

Multibody modeling for concept-level floating offshore wind turbine design

Experimental studies of control concepts for a parallel manipulator with flexible links

Controlling an Underactuated Two-Wheeled Mobile Robot: A Constraint-Following Approach

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