Partial Feedback Linearization on a Harmonically Excited Beam With One-Sided Spring

Heertjes, Marcel; Molengraft, van de Mjg René; Nijmeijer, H.

doi:10.1006/jsvi.1998.2472

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…In [26,27], for a similar piecewise linear system, resonance/vibration attenuation is realized in a wider frequency band, using an observer-based state feedback controller. In [28,29], again for a similar, periodically excited, piecewise linear beam system, partial feedback linearization was used. However, in [28,29], the control objective was different compared to the control objectives of the current paper.…”

Section: Introductionmentioning

confidence: 99%

“…In [28,29], again for a similar, periodically excited, piecewise linear beam system, partial feedback linearization was used. However, in [28,29], the control objective was different compared to the control objectives of the current paper. For a specific excitation frequency, the uncontrolled piecewise linear system shows a stable 1/2 subharmonic resonance coexisting with an unstable harmonic solution with low amplitude.…”

Section: Introductionmentioning

confidence: 99%

“…For a specific excitation frequency, the uncontrolled piecewise linear system shows a stable 1/2 subharmonic resonance coexisting with an unstable harmonic solution with low amplitude. In [28,29], the control objective was to control the 1/2 subharmonic solution to the harmonic solution and to stabilize this solution.…”

Section: Introductionmentioning

confidence: 99%

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Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system

2009

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A control using Proportional and/or Derivative feedback (PD-control) is applied on a piecewise linear beam system with a flushing one-sided spring element for steady-state vibration amplitude mitigation. Two control objectives are formulated: (1) minimize the transversal vibration amplitude of the midpoint of the beam at the frequency where the first harmonic resonance occurs, (2) achieve this in a larger (low) excitation frequency range, where the lowest nonlinear normal mode dominates the response. Experimentally realizable combinations of PD-control are evaluated for both control objectives. Eventually objective (1) is realized by applying proportional control only, whereas derivative control is selected to realize objective (2). The vibration reduction that is achieved in simulations and validated by experiments is very significant for both objectives. Current results obtained with active PD-control are compared with

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system

2009

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On convergence properties of piecewise affine systems

Pavlov¹,

Pogromsky²,

Wouw³

et al. 2007

International Journal of Control

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In this paper convergence properties of piecewise affine (PWA) systems are studied. In general, a system is called convergent if all its solutions converge to some bounded globally asymptotically stable steady-state solution. The notions of exponential, uniform and quadratic convergence are introduced and studied. It is shown that for non-linear systems with discontinuous right-hand sides, quadratic convergence, i.e., convergence with a quadratic Lyapunov function, implies exponential convergence. For PWA systems with continuous right-hand sides it is shown that quadratic convergence is equivalent to the existence of a common quadratic Lyapunov function for the linear parts of the system dynamics in every mode. For discontinuous bimodal PWA systems it is proved that quadratic convergence is equivalent to the requirements that the system has some special structure and that certain passivity-like condition is satisfied. For a general multimodal PWA system these conditions become sufficient for quadratic convergence. An example illustrating the application of the obtained results to a mechanical system with a one-sided restoring characteristic, which is equivalent to an electric circuit with a switching capacitor, is provided. The obtained results facilitate bifurcation analysis of PWA systems excited by periodic inputs, substantiate numerical methods for computing the corresponding periodic responses and help in controller design for PWA systems.

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Partial Feedback Linearization on a Harmonically Excited Beam With One-Sided Spring

Cited by 2 publications

References 21 publications

Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system

Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system

On convergence properties of piecewise affine systems

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