A novel feedback design method for mimo QFT with application to the X-29 flight control problem
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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.