Semi‐active damping optimization of vibrational systems using the parametric dominant pole algorithm

In this work we consider the problem of semi-active damping optimization of mechanical systems with fixed damper positions. Our goal is to compute a damping that is locally optimal with respect to the H∞-norm of the transfer function from the exogenous inputs to the performance outputs. We make use of a new greedy method for computing the H∞-norm of a transfer function based on rational interpolation. In this paper, this approach is adapted to parameter-dependent transfer functions. The interpolation leads to parametric reduced-order models that can be optimized more efficiently. At the optimizers we then take new interpolation points to refine the reduced-order model and to obtain updated optimizers. In our numerical examples we show that this approach normally converges fast and thus can highly accelerate the optimization procedure. Another contribution of this work are heuristics for choosing initial interpolation points.

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“…According to [27,5], a transfer function F (s) = H 1 (s 2 M + sC + K) −1 E 2 ∈ R(s) m× can be written in pole/residue representation as…”

Section: Choice Of the Initial Interpolation Pointsmentioning

confidence: 99%

“…which is widely used in the literature, see, e. g., [12,8,5]. Note that this choice makes the unforced system (1a) asymptotically stable.…”

Section: Choice Of the Initial Interpolation Pointsmentioning

confidence: 99%

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Semi‐active ℋ∞ damping optimization by adaptive interpolation

Tomljanović

Voigt

2020

Numerical Linear Algebra App

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“…One criterion for systems described by would be to minimize the H 2 norm of the system as the penalty function. In particular, damping optimization using the H 2 norm was considered in [] as well as in [], where the authors considered model order reduction approaches in order to determine the optimal damping parameters efficiently. Also, one can consider damping optimization using the

H_{\infty}

norm.…”

Section: Introductionmentioning

confidence: 99%

“…(1 ∶ 5, 1 ∶ 5) = diag(5,4,3,2,1), while all the other entries are equal to zero. This means that the input is applied to the first 5 masses on the left-hand side of the considered -mass oscillator, hence the masses on the left-hand side od the oscillator have a larger influence on the input.Moreover, we are interested in the 10 displacements and velocities in the middle of the -mass oscillator.…”

mentioning

confidence: 99%

Mixed control of vibrational systems

Nakić¹,

Tomljanović²,

Truhar³

2019

Z Angew Math Mech

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We consider new performance measures for vibrational systems based on the H2 norm of linear time invariant systems. New measures will be used as an optimization criterion for the optimal damping of vibrational systems. We consider both theoretical and concrete cases in order to show how new measures stack up against the standard measures. The quality and advantages of new measures as well as the behaviour of optimal damping positions and corresponding damping viscosities are illustrated in numerical experiments.

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Fast optimization of viscosities for frequency‐weighted damping of second‐order systems

et al. 2022

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We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the imaginary axis. To this end, we present two complementary techniques.First, we propose new frameworks using nonsmooth constrained optimization problems, whose solutions both damp undesirable frequency bands and maintain the stability of the system. These frameworks also allow us to weight, which frequency bands are the most important to damp. Second, we also propose a fast new eigensolver for the structured quadratic eigenvalue problems (QEPs) that appear in such vibrating systems. In order to be efficient, our new eigensolver exploits special properties of diagonal-plus-rank-one (DPR1) complex symmetric matrices, which we leverage by showing how each QEP can be transformed into a short sequence of such linear eigenvalue problems. The result is an eigensolver that is substantially faster than standard techniques. By combining this new solver with our new optimization frameworks, we obtain our overall algorithm for fast computation of optimal viscosities. The efficiency and performance of our new approach are verified and illustrated on several numerical examples.

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Semi‐active damping optimization of vibrational systems using the parametric dominant pole algorithm

Cited by 17 publications

References 26 publications

Semi‐active ℋ∞ damping optimization by adaptive interpolation

Semi‐active ℋ∞ damping optimization by adaptive interpolation

Mixed control of vibrational systems

Fast optimization of viscosities for frequency‐weighted damping of second‐order systems

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