Identification Of Multivariable Ill-Conditioned Sysrems Using Virtual Transfer Function Between Inputs
In industry, processes are often multivariable, and frequently possess strong interactions among the various outputs. Such systems will be ill-conditioned due to the presence of high and low gain directions. The system will respond much more strongly if the input lies in the former than the latter....
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| Format: | Thesis |
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2016
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| Summary: | In industry, processes are often multivariable, and frequently possess strong interactions among the various outputs. Such systems will be ill-conditioned due to the presence of high and low gain directions. The system will respond much more strongly if the input lies in the former than the latter. Therefore, it is necessary for perturbation signals designed for ill-conditioned systems to sufficiently excite the low gain direction for accurate identification, especially of the smallest singular value. In view of this, the virtual transfer function between inputs (VTFBI) perturbation signal design is introduced with the aim of improving the accuracy in estimating the smallest singular value. The design takes into account the uniform excitation of all output directions with as large an output signal-to-noise ratio (SNR) as possible, subject to power constraints at the input and possible bounds at the output. Starting with a 2×2 system, the theoretical formulation of the VTFBI is developed. The VTFBI technique utilises a single correlated harmonic chosen at a frequency where the system gain is expected to be reasonably large. The relation between the outputs are made to describe a circle so that equal perturbation in all output directions is achieved, through design parameters that include the relative magnitudes and phases of the chosen correlated harmonic using information of the system’s gains and phases obtained from an a priori test. |
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