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Low-cost control of discontinuous systems including impacts and friction
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
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.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , viii, 48 p.
Series
Trita-AVE, ISSN 1651-7660 ; 2007:79
Keyword [en]
nonlinear dynamics, discontinuities, nonlinear control, impacts, friction, vehicle suspensions
National Category
Vehicle Engineering
Identifiers
URN: urn:nbn:se:kth:diva-4581ISBN: 978-91-7178-830-6 (print)OAI: oai:DiVA.org:kth-4581DiVA: diva2:12975
Presentation
2007-12-18, D3, D-huset, Lindstedtsvägen 5, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20101118Available from: 2007-12-14 Created: 2007-12-14 Last updated: 2010-11-18Bibliographically approved
List of papers
1. On the stabilizability of near-grazing dynamics in impact oscillators
Open this publication in new window or tab >>On the stabilizability of near-grazing dynamics in impact oscillators
2007 (English)In: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 17, no 15, 1405-1429 p.Article in journal (Refereed) Published
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.

Keyword
grazing bifurcations, vibro-impact oscillators, stabilizability, control
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-7835 (URN)10.1002/rnc.1252 (DOI)000250093000004 ()2-s2.0-34848816213 (Scopus ID)
Note
QC 20100811Available from: 2007-12-14 Created: 2007-12-14 Last updated: 2017-12-14Bibliographically approved
2. Bumpstop control of a vehicle suspension with bilinear damping
Open this publication in new window or tab >>Bumpstop control of a vehicle suspension with bilinear damping
2007 (English)Report (Other academic)
Series
TRITA-AVE, ISSN 1651-7660 ; 2007:74
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-7836 (URN)
Note

Uppdaterad från manuskript till rapport(20101118). QC 20101118

Available from: 2007-12-14 Created: 2007-12-14 Last updated: 2017-03-29Bibliographically approved
3. Energy Transfer in Vibratory Systems with Friction Exhibiting Low-velocity Collisions
Open this publication in new window or tab >>Energy Transfer in Vibratory Systems with Friction Exhibiting Low-velocity Collisions
2008 (English)In: Journal of Vibration and Control, ISSN 1077-5463, E-ISSN 1741-2986, no 1-2, 255-284 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Thousand Oaks: SAGE Publications Inc., 2008
Keyword
nonlinear dynamics, non-smooth dynamics, impacts, friction
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-11077 (URN)10.1177/1077546307079390 (DOI)000252947600013 ()2-s2.0-38149128709 (Scopus ID)
Note
QC 20100811Available from: 2009-09-15 Created: 2009-09-15 Last updated: 2017-12-13Bibliographically approved

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