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  • 1. Dankowicz, H.
    et al.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Control of instabilities induced by low-velocity collisions in a vibro-impacting system with friction2009Inngår i: Vibro-Impact Dynamics of Ocean Systems and Related Problems, 2009, s. 41-52Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The onset of low-velocity collisions in vibro-impacting systems induces instabilities in the system dynamics that, when not checked, may result in sudden, and unanticipated discontinuous transitions between distinct steady-state responses. This paper illustrates this phenomenology in an example system that includes dry friction. Here, the instability is associated with the zero-velocity contact of an oscillatory unilateral constraint and a stationary mass suspended through a preloaded spring. The analysis summarizes observations on the passive response of the mass under variations in the oscillation amplitude of the constraint. A control strategy is subsequently shown to successfully suppress the instability. The paper concludes with suggestions for applications of this phenomenology as well as a description of similar observation in mechanical systems with or without friction and with rigid as well as compliant contact.

  • 2.
    Dankowicz, Harry
    et al.
    Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    On the stabilizability of near-grazing dynamics in impact oscillators2007Inngår i: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 17, nr 15, s. 1405-1429Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A constructive proof is presented for the existence of event-driven control strategies that guarantee the local persistence of system attractors with at most low-velocity contact in vibro-impacting oscillators. In particular, sufficient conditions are formulated on the linearization of the control strategies along a grazing periodic trajectory, i.e. an oscillating motion that achieves zero-relative-velocity contact with a mechanical obstacle, to ensure the asymptotic stability of the grazing trajectory and, consequently, sustained dynamics in the vicinity of the grazing trajectory even under small changes in system parameters. The implications of the methodology are illustrated with linear and nonlinear, single- and multiple-degree-of-freedom examples of vibro-impact oscillators.

  • 3.
    Edrén, Johannes
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Jonasson, Mats
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Nilsson, Andreas
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Rehnberg, Adam
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Stensson Trigell, Annika
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Modelica and Dymola for education in vehicle dynamics at KTH2009Inngår i: Proceedings from 7th Modelica Conference 2009, 2009, s. 775-783Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Dymola and Modelica has been used at KTH Vehicle Dynamics (KTHVD) for research work since 2000, see e.g. [1]. With the Vehicle Dynamics Library (VDL) [2], Modelica has become far more accessible for both researchers and students in the field of vehicle dynamics. Therefore a project aiming at introducing it as a tool in education was initiated in order to evaluate the current state of Dymola and Modelica as tools for wider use in education at the division. The work presented in this paper was realized as a part of a PhD course, where one of the tasks were to design dedicated exercises to illustrate fundamentals of vehicle dynamics for students.

  • 4.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg.
    Low-cost control of discontinuous systems including impacts and friction2007Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    For a successful design of an engineering system it is essential to pay careful attention to its dynamic response. This is particularly true, in the case of nonlinear systems, since they can exhibit very complex dynamic behaviour, including multiple co-existing stable solutions and chaotic motions, characterized by large sensitivity to initial conditions. In some systems nonlinear characteristics are desired and designed for, but in other cases they are unwanted and can cause fatigue and failure. A type of dynamical system which is highly nonlinear is discontinuous or non-smooth systems. In this work, systems with impacts are primarily investigated, and this is a typical example of a discontinuous system. To enhance or optimize the performance of dynamical systems, some kind of control can be implemented. This thesis concerns implementation of low-cost control strategies for discontinuous systems. Low-cost control means that a minimum amount of energy is used when performing the control actions, which is a desirable situation regardless of the application. The disadvantage of such a method is that the performance might be limited as compared with a control strategy with no restrictions on energy consumption. In this work, the control objective is to enforce a continuous or discontinuous grazing bifurcation of the system, whichever is desirable. In Paper A, the dynamic response and bifurcation behaviour of an impactoscillator with dry friction is investigated. For a one-degree-of-freedom model of the system, analytical solutions are found in separate regions of state space. These are then used to perform a perturbation analysis around a grazing trajectory. Through the analysis, a condition on the parameters of the system is derived, which assures a continuous grazing bifurcation. It is also shown that the result has bearing on the dynamic response of a two-degree-of-freedom model of the system. A low-cost active control strategy for a class of impact oscillators is proposed in Paper B. The idea of the control method is to introduce small adjustments in the position of the impact surface, at discrete moments in time, to assure a continuous bifurcation. A proof is given for what control parameters assures the stabilization. In Paper C, the proposed low-cost control method is implemented in a quarter-car model of a vehicle suspension, in order to minimize impact velocities with the bumpstop in case of high amplitude excitation. It is shown that the control method is effective for harmonic road excitation.

  • 5.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    On the stability and control of piecewise-smooth dynamical systems with impacts and friction2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis concerns the analysis of dynamical systems suitable to be modelled by piecewise-smooth differential equations. In such systems the continuous-in-time dynamics is interrupted by discrete-in-time jumps in the state or governing equations of motion. Not only can this framework be used to describe existing systems with strong nonlinear behaviour such as impacts and friction, but the non-smooth properties can be exploited to design new mechanical devices. As suggested in this work it opens up the possibility of, for example, fast limit switches and energy transfer mechanisms.

    Particularly, the dynamics at the onset of low-velocity impacts in systems with recurrent dynamics, so called grazing bifurcations in impact-oscillators, are investigated. As previous work has shown, low-velocity impacts is a strong source of instability to the dynamics, and efforts to control the behaviour is of importance. This problem is approached in two ways in this work. One is to investigate the influence of parameter variations on the dynamic behaviour of the system. The other is to implement low-cost control strategies to regulate the dynamics at the grazing bifurcation. The control inputs are of impulsive nature, and utilizes the natural dynamics of the system to the greatest extent.

    The scientific contributions of this work is collected in five appended papers. The first paper consists of an experimental verification of a map that captures the correction to the smooth dynamics induced by an impact, known in the literature as the discontinuity map. It is shown that the lowest order expansion of the map accurately captures the transient growth rate of impact velocities. The second paper presents a constructive proof of a control algorithm for a rather large class of impact oscillators. The proof is constructive in the sense that it gives control parameters which stabilizes the dynamics at the onset of low-velocity impacts. In the third paper a piecewise-smooth quarter-car model is derived, and the control strategy is implemented to reduce impact velocities in the suspension system. In the fourth and fifth papers the grazing bifurcation of an impact oscillator with dry friction type damping is investigated. It turns out that the bifurcation is triggered by the disappearance of an interval of stable stick solutions. A condition on the parameters of the system is derived which differentiates between stable and unstable types of bifurcation scenarios. Additionally, a low-cost control strategy is proposed, similar to the one previously mentioned, to regulate the bifurcation scenario.

  • 6.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    Controlled onset of low-velocity collisions in a vibro-impacting system with friction2009Inngår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 465, s. 3647-3665Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper investigates the onset of low-velocity, near-grazing collisions in an example vibro-impacting system with dry friction with particular emphasis on feedback control strategies that regulate the grazing-induced bifurcation behaviour. The example system is characterized by a twofold degeneracy of grazing contact along an extremal stick solution that is shown to result in a locally one-dimensional and piecewise-linear description of the near-grazing dynamics. Explicit control strategies are derived that ensure a persistent, low-impact-velocity, steady-state response across the critical parameter value corresponding to grazing contact even in instances where the dynamics in the absence ofcontrol exhibit a sudden transition to a high-impact-velocity response.

  • 7.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    Energy Transfer in Vibratory Systems with Friction Exhibiting Low-velocity Collisions2008Inngår i: Journal of Vibration and Control, ISSN 1077-5463, E-ISSN 1741-2986, nr 1-2, s. 255-284Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper investigates the dynamic response of an initially stationary part of a mechanism in the presence of a restoring force and dry friction to low-velocity collisions with a relatively more massive oscillating element. Of particular interest is the persistence of a local attractor in the motion of the less massive part as the path of the oscillating element grows to encompass the entire set of possible equilibrium positions in the absence of contact. It is argued that loss of a local attractor and the associated large-amplitude oscillations of the less massive part affords a means for energy transfer through the mechanism and a means for energy damping. The paper contains a rigorous derivation of conditions that appear sufficient for the persistence of a local attractor in the case where the massive oscillating element is replaced by an oscillating rigid unilateral constraint corresponding to an infinite mass ratio. Numerical simulations are subsequently used to investigate the response in the case where the mass ratio is assumed finite.

  • 8.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg.
    Dankowicz, Harry
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Jerrelind, Jenny
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg.
    Bumpstop control of a vehicle suspension with bilinear damping2007Rapport (Annet vitenskapelig)
  • 9.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Hamberg, J.
    Flight-path control of a missile using the Passive Normal Form2005Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper addresses the problem of controlling the flight-path angle of a missile by means of a systematic use of passivity. A simple model of a generic missile's motion in a vertical plane based on wind tunnel data is used. A variant of backstepping is introduced, based on the novel concept of Passive Normal Form, by which explicit robustness margins are obtained. The method is applied to a variety of problems, including the use of dynamical extensions.

  • 10.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Jerrelind, Jenny
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Suppression of bumpstop instabilities in a quarter-car model2009Inngår i: Non-smooth Problems in Vehicle Systems Dynamics: Proceedings of the Euromech Colloquium, Berlin Heidelberg: Springer-Verlag , 2009Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Vehicle manufacturers are constantly pushed to reduce the aerodynamic drag of vehicles, for example by constructing lower vehicles with less road clearance. This, however, reduces the available margin for oscillations within the suspension. If the oscillation amplitude exceeds a critical value, the suspension will impact a bumpstop. Under periodic excitation, the onset of low-velocity impacts is associated with a strong instability in favor of high-velocity impacts. Such impacts reduce comfort and could be damaging to the vehicle. Efforts should therefore be made to limit impact velocities with the bumpstop, for example by suppressing the instability associated with low-velocity impacts. This paper proposes a low-cost feedback-control strategy, based on making small adjustments to the position of the bumpstop, that serve to suppress the transition to high-velocity impacts with the bumpstop in the case of periodic excitation. The control law is derived from the theory of discontinuity maps. The results demonstrate that the feedback strategy works even when wheel-hop is present.

  • 11.
    Wilcox, Bryan
    et al.
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Jerrelind, Jenny
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Transient growth rates of near-grazing impact velocities: Theory and experiments2009Inngår i: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 325, nr 4-5, s. 950-958Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, nonsmooth fold bifurcations associated with the onset of low-relative- velocity (near-grazing) impacts in an oscillatory mechanical system are proposed as a potential operating principle for high-speed limit switches. Specifically, analytical, numerical, and experimental methods are employed to investigate the near-grazing transient behavior in a representative system. It is shown that the rate of growth of successive impact velocities increases beyond all bounds as the threshold parameter value is approached. A limit switch based on the proposed nonsmooth fold scenario would thus be expected to outperform one that relies on a smooth bifurcation, such as the cyclic-fold bifurcation, in terms of switching speed and sensitivity.

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