An exploration of active hard mount vibration isolation for precision equipment

Poel, G.W. van der

doi:10.3990/1.9789036530163

Cited by 8 publications

(7 citation statements)

References 77 publications

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“…The tertiary path P 3 (q) ∈ RH n a ×n a ∞ , that relates a 0 (k) to a measurement of a 0 (k) is considered unity. 16 The signal a s (k) ∈ R n a is the exogenous disturbance, whose measurement ã0 (k) is corrupted by sensor noise n 0 (k) and the input-disturbance interaction signal a a (k). The measurement ã0 (k) is used for the feedforward controller C FF (q) ∈ RH n u ×n a ∞ .…”

Section: F I G U R Ementioning

confidence: 99%

“…a(k), (16) and a(k) ∈ R n a , Ψ(k) ∈ R n u ×n a n e n u . The parameter vector w = col(W) ∈ R n a n u n e ×1 , and w d ∈ R n a n u n e ×n a n u n e is the zero matrix with w on the diagonal.…”

Section: F I G U R Ementioning

confidence: 99%

“…We emphasize that Beijen et al 6 did not consider the presence of

{\boldsymbol{P}}_4(q)

. The tertiary path

{\boldsymbol{P}}_3(q)\in \mathbb{R}{H}_{\infty}^{n_a\times {n}_a}

, that relates

{\boldsymbol{a}}_0(k)

to a measurement of

{\boldsymbol{a}}_0(k)

is considered unity 16 . The signal

{\boldsymbol{a}}_s(k)\in {\mathbb{R}}^{n_a}

is the exogenous disturbance, whose measurement

{\tilde{\boldsymbol{a}}}_0(k)

is corrupted by sensor noise

{\boldsymbol{n}}_0(k)

and the input‐disturbance interaction signal

{\boldsymbol{a}}_a(k)

.…”

Section: Problem Descriptionmentioning

confidence: 99%

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Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward

Spanjer,

Köroğlu,

Hakvoort

2024

Adaptive Control & Signal

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SummaryThe convergence of filtered error and filtered reference adaptive feedforward is limited by three effects: model mismatch, unintended input‐disturbance interaction and too fast parameter adaptation. In this article, the first two effects are considered for MIMO systems under the slow parameter adaptation assumption. The convergence with model mismatch is conventionally guaranteed using a strictly positive‐real condition. This condition can be easily verified in the frequency domain, but due the high‐frequency parasitic dynamics of real systems, it is hardly ever satisfied. Nevertheless, filtered error and filtered reference adaptive feedforward have successfully been implemented in numerous applications without satisfying the strictly positive‐real condition. It is shown in this article that the strictly positive‐real condition can be relaxed to a power‐weighted integral condition, that is less conservative and provides a practical check for the convergence of filtered error adaptive feedforward for real systems in the frequency domain. The effects of input‐disturbance interaction are analysed and conditions for the stability are given in the frequency domain. Both conditions give clear indicators for frequency domain filter tuning, and are verified on an experimental active vibration isolation system.

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Section: F I G U R Ementioning

confidence: 99%

Section: F I G U R Ementioning

confidence: 99%

“…We emphasize that Beijen et al 6 did not consider the presence of

{\boldsymbol{P}}_4(q)

. The tertiary path

{\boldsymbol{P}}_3(q)\in \mathbb{R}{H}_{\infty}^{n_a\times {n}_a}

, that relates

{\boldsymbol{a}}_0(k)

to a measurement of

{\boldsymbol{a}}_0(k)

is considered unity 16 . The signal

{\boldsymbol{a}}_s(k)\in {\mathbb{R}}^{n_a}

is the exogenous disturbance, whose measurement

{\tilde{\boldsymbol{a}}}_0(k)

is corrupted by sensor noise

{\boldsymbol{n}}_0(k)

and the input‐disturbance interaction signal

{\boldsymbol{a}}_a(k)

.…”

Section: Problem Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward

Spanjer,

Köroğlu,

Hakvoort

2024

Adaptive Control & Signal

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show abstract

“…A common method to reduce vibration is to mount the sensitive equipment on a suspended platform which attenuates the vibrations above the frequency of the suspension modes [10,11].…”

Section: Introductionmentioning

confidence: 99%

Active damping of rotating platforms using integral force feedback

Dehaeze

Collette

2021

Eng. Res. Express

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This paper investigates the use of Integral Force Feedback (IFF) for the active damping of rotating mechanical systems. Guaranteed stability, typical benefit of IFF, is lost as soon as the system is rotating due to gyroscopic effects. To overcome this issue, two modifications of the classical IFF control scheme are proposed. The first consists of slightly modifying the control law while the second consists of adding springs in parallel with the force sensors. Conditions for stability and optimal parameters are derived. The results reveal that, despite their different implementations, both modified IFF control scheme have almost identical damping authority on suspension modes.

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“…An alternative approach is to use active hard mounts [2][3][4]. These provide a much stiffer support.…”

Section: Introductionmentioning

confidence: 99%