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CivilComp Proceedings
ISSN 17593433 CCP: 89
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping
Paper 17
Multirate Sampled Data System Robustness: Frequency Analysis J. Salt, P. Albertos, C. Camiña and J. Sandoval
Department of Systems Engineering and Control, Polytechnic University of Valencia, Spain , "Multirate Sampled Data System Robustness: Frequency Analysis", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 17, 2008. doi:10.4203/ccp.89.17
Keywords: multirate systems, frequency response, discretetime systems, sampleddata systems, inferential control, multivariable control.
Summary
Frequency analysis is an appropriate tool to study the robustness of a controlled
system to either disturbances or uncertainties. When a sampleddata system (SD) is
analysed in the frequency domain, the dimension of the frequency operators often
leads to difficult implementation problems. Among the different techniques to deal
with the SD frequency response, two main approaches can be singled out. The
approach proposed by Araki and his coworkers [1], is based on the definition of an
infinite dimension frequency response (FR) operator. The SD impulse input, by the
socalled impulse modulation [2], is decomposed into an infinite sum of sinusoidal
components. Clearly, the computation of this operator is not straight forward. The
second, and also very popular, approach is the socalled continuous lifting [3],
which is based on transforming the sampleddata system to a discrete LTI system,
taking into account the input and output expansion into functional spaces. Again the
model leads to an infinite dimension operator, with the corresponding difficulty in
its computation. Both approaches allow for the steadystate computation of the
frequency response and can be used to obtain the continuous time output response,
leading to equivalent operators [4]. In this paper, the main objective is to present an
approximate analysis by assuming the addition of a fictitious high rate sampler at the
output of the system. In this way, a multirate based approach allows the
intersampling behaviour of the system to be taken into account by selecting a faster
sampling rate at the output. Following this approach, the controlled process
robustness to model uncertainties and disturbances can be derived by using the
frequency analysis of multirate systems. The proposed methodology by using
singular values of the multirate discrete lifted representation [5], greatly simplifies
the aforementioned study. The proposed methodology has been used in this paper to
compare different control structures [6,7]. As a result of this comparison it is proved,
with a counter example, that the claim that a dual rate inferential control could be
more robust than a fast single rate one assuming some kind of parametric
uncertainty [6], is not always correct. For the sake of comparison, the
control performances using a nonconventional dualrate controller are also
computed.
References
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