| 1. |
- Dankowicz, H., et al.
(författare)
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Control of near-grazing dynamics in impact oscillators
- 2005
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 461:2063, s. 3365-3380
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Tidskriftsartikel (refereegranskat)abstract
- A method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontiunities. In particular, it is shown that a discrete, linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory, such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact. The implementation relies on a local analysis of the near-grazing dynamics using the concept of discontinuity mappings. Numerical results are presented for a linear and a nonlinear oscillator.
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| 2. |
- Jerrelind, Jenny, et al.
(författare)
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A global control strategy for efficient control of a Braille impact hammer
- 2006
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Ingår i: Journal of Vibration and Acoustics-Transactions of the ASME. - : American Society of Mechanical Engineers. - 1048-9002 .- 1528-8927. ; 128:2, s. 184-189
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Tidskriftsartikel (refereegranskat)abstract
- A combined control scheme relying on feedback-based local control in the vicinity of periodic system responses and global control based on a coarse-grained approximation to the nonlinear dynamics is developed to achieve a desirable dynamical behavior of a Braille printer impact hammer The proposed control methodology introduces discrete changes in the position of a system discontinuity at opportune moments during the hammer motion while the hammer is away from the discontinuity, thereby exploiting the recurrent contacts with the discontinuity to achieve the desired changes in the transient dynamics. It is argued that, as the changes in the position of the discontinuity affect the motion only indirectly through changes in the timing and state at the subsequent contact, the control actuation can be applied over an interval of time during the free-flight motion as long as it is completed prior to contact. A forced, piecewise smooth, single-degree-of freedom model of a Braille impact hammer is used to illustrate the methodology and to yield representative numerical results.
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| 3. |
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| 4. |
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| 5. |
- Svahn, Fredrik, 1978-
(författare)
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Low-cost control of discontinuous systems including impacts and friction
- 2007
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 6. |
- Svahn, Fredrik, 1978-
(författare)
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On the stability and control of piecewise-smooth dynamical systems with impacts and friction
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 7. |
- Svahn, Fredrik, et al.
(författare)
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Suppression of bumpstop instabilities in a quarter-car model
- 2009
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Ingår i: Non-smooth Problems in Vehicle Systems Dynamics. - Berlin Heidelberg : Springer-Verlag. - 9783642013553
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 8. |
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| 9. |
- Wilcox, Bryan, et al.
(författare)
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Transient growth rates of near-grazing impact velocities: Theory and experiments
- 2009
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Ingår i: Journal of Sound and Vibration. - London : Academic Press. - 0022-460X .- 1095-8568. ; 325:4-5, s. 950-958
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Tidskriftsartikel (refereegranskat)abstract
- 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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