Extreme inputs/outputs for multiple input multiple             output linear systems.

Smallwood, David O.

doi:10.2172/875611

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…1. The TRFs for the five Responses with respect to each of the two Inputs were experimentally determined using methods mentioned by Trudnowski and Pierre (2009) and Smallwood (2005). 2.…”

Section: Sequence Of Experimentsmentioning

confidence: 99%

“…Further details of each step are provided in the subsequent section on Experimental Procedure.1. The TRFs for the five Responses with respect to each of the two Inputs were experimentally determined using methods mentioned by Trudnowski and Pierre (2009) and Smallwood (2005).2. The Responses were measured with both actuators exciting the beam, similar to research conducted by Mckelvey and Moheimani (2005), Nestorovic et al (2012), and Saunders et al (1994).…”

Section: Introductionmentioning

confidence: 99%

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Error analyses of a Multi-Input-Multi-Output cantilever beam test

Maji¹,

Moreu

Woodall

et al. 2021

Journal of Vibration and Control

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Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

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“…1. The TRFs for the five Responses with respect to each of the two Inputs were experimentally determined using methods mentioned by Trudnowski and Pierre (2009) and Smallwood (2005). 2.…”

Section: Sequence Of Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error analyses of a Multi-Input-Multi-Output cantilever beam test

Maji¹,

Moreu

Woodall

et al. 2021

Journal of Vibration and Control

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“…The development is essentially the same as in the previous section. Details are given in Smallwood [13].…”

Section: Derivation Of the Minimum/maximum Output Tracementioning

confidence: 99%

Multiple‐Input Multiple‐Output (MIMO) Linear Systems Extreme Inputs/Outputs

Smallwood¹

2006

Shock and Vibration

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A linear structure is excited at multiple points with a stationary normal random process. The response of the structure is measured at multiple outputs. If the autospectral densities of the inputs are specified, the phase relationships between the inputs are derived that will minimize or maximize the trace of the autospectral density matrix of the outputs. If the autospectral densities of the outputs are specified, the phase relationships between the outputs that will minimize or maximize the trace of the input autospectral density matrix are derived. It is shown that other phase relationships and ordinary coherence less than one will result in a trace intermediate between these extremes. Least favorable response and some classes of critical response are special cases of the development. It is shown that the derivation for stationary random waveforms can also be applied to nonstationary random, transients, and deterministic waveforms.

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