617 research outputs found

    Steady state behaviour of stochastically excited nonlinear dynamic systems

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    Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact

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    In this paper, we will give conditions under which the equilibrium set of multi-degree-of-freedom non-linear mechanical systems with an arbitrary number of frictional unilateral constraints is attractive. The theorems for attractivity are proved by using the framework of measure differential inclusions together with a Lyapunov-type stability analysis and a generalisation of LaSalle's invariance principle for non-smooth systems. The special structure of mechanical multi-body systems allows for a natural Lyapunov function and an elegant derivation of the proof. Moreover, an instability theorem for assessing the instability of equilibrium sets of non-linear mechanical systems with frictional bilateral constraints is formulated. These results are illustrated by means of examples with both unilateral and bilateral frictional constraint

    Stability Properties of Equilibrium Sets of Controlled Linear Mechanical Systems with Dry Friction

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    The dynamics of mechanical systems with dry friction elements, modeled by set-valued force laws, can be described by differential inclusions. The switching and set-valued nature of the friction force law is responsible for the hybrid character of such models. An equilibrium set of such a differential inclusion corresponds to a stationary mode for which the friction elements are sticking. The attractivity properties of the equilibrium set are of major importance for the overall dynamic behavior of this type of systems. Conditions for the attractivity of the equilibrium set of linear MDOF mechanical systems with multiple friction elements are presented. These results are obtained by application of a generalization of LaSalle’s principle for differential inclusions of Filippov-type. Besides passive systems, also systems with negative viscous damping are considered. For such systems, only local attractivity of the equilibrium set can be assured under certain conditions. Moreover, an estimate for the region of attraction is given for these cases. The results are illustrated by means of a 2DOF example. Moreover, the value of the attractivity results in the context of the control of mechanical systems with friction is illuminated

    Parameter identification in nonlinear models using periodic equilibrium states

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    The global output regulation problem: an incremental stability approach

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    We present a global solution to the output regulation problem for a class of nonlinear systems. The solution is based on the incremental stability property. The question of existence of the proposed solution can be answered by checking solvability of the regulator equations and feasibility of certain linear matrix inequalities

    The local output regulation problem: convergence region estimates

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    In this paper, the problem of local output regulation is considered. The presented results answer the question: given a controller solving the local output regulation problem, how to estimate the set of admissible initial conditions for which this controller makes the regulated output converge to zero. Theoretical estimation results and an estimation procedure explaining the application of these results in practice are presented. An example of the disturbance rejection problem for a mechanical system (TORA system) is given as an illustration

    An error bound for model reduction of Lur'e-type systems

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    In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur’e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur’e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system

    Alternative Methods in Spectral Factorization. A Modeling and Design Tool

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    Spectral factorization can be used to recover the complex transfer function of a linear, causal, stable, minimum-phase system from merely its amplitude information. Two different approaches are presented, resulting in two consistent expressions for the complex transfer function. Firstly, an approach using Fourier theory is followed (Papoulis, 1977; Priestley, 1981). Secondly, a new approach using potential theory results is presented. Spectral factorization can be successfully used as a modeling tool. Moreover, its capability to serve as a design tool is emphasized. These fields of application are illustrated by means of examples

    Control and observer design for non-smooth systems

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