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Description:
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Quantitative Feedback Theory (QFT ) method employs a two degree of freedom
control configuration that includes a feedback controller and a prefilter in the feedforward
path . When applied to multi -input multi -output (MIMO ) systems , the QFT
method calls for a special decomposition of the MIMO system . Specifically , the MIMO
system is decomposed into multiple multi -input single -output (MISO ) equivalent
systems , and is followed by the single -input single -output (SISO ) QFT design of each
equivalent system . Depending on pole -zero structure of the equivalent SISO plants so
obtained , the QFT design may become unnecessarily difficult /conservative or even
infeasible . This situation is especially true for linear time invariant (LTI ) systems with
non -minimum phase (NMP ) zero (s ) and unstable pole (s ) .
This unnecessary design difficulty and the challenge of dealing with MIMO
systems that have unstable poles and NMP transmission zeros in undesirable locations ,
when MIMO QFT is considered , is investigated and addressed in this research . A new
MIMO QFT design methodology was developed using the generalized formulation . The
key idea of the generalized formulation is to utilize appropriate modifications at the plant input and /or the output to obtain a better conditioned plant that in turn can be used to
execute a standard MIMO QFT design . The formulation is based on a more general
control structure , where input and output transfer function matrices (TFM ) are included
to provide additional degrees of freedom in the typical decentralised MIMO QFT
feedback structure , which facilitates the exploitation of directions in MIMO QFT
designs . The formulation captures existing design approaches for a fully populated
MIMO QFT controller design and provides for a directional design logic involving the
plant and controller alignment and the directional properties of their multivariable poles
and zeros . As a case in point Horowitz’s Singular -G design methodology is placed in the
context of this generalized formulation , and the Singular -G design for the X -29 is
analysed and redesigned using both non -sequential and sequential MIMO QFT
demonstrating its utility .
The results highlight a fundamental trade -off between multivariable controller
directions for stability and performance in classically formulated MIMO QFT design
methodologies , which elucidate the properties of Singular -G designed controllers for the
X -29 and validate the developed new MIMO QFT design method . |