Synthesis of controllers for non-minimum phase and unstable systems using non-sequential MIMO quantitative feedback theory

Abstract

Considered Are multi-input multi-output (MIMO) systems with non-minimum phase (NMP) zeros and unstable poles, where some of the unstable poles are located to the right of, or close to, the NMP zeros. In the single-input single-output (SlSO) case such systems pose serious difficulties in controller synthesis for performance and stability. In spite of the added degrees of freedom the MIMO case also poses difficulties, as has been shown in the stabilization of the X-29 aircraft. When using the MIMO QFT technique, the design procedure proceeds by decomposing the MIMO design problem into multiple multi-input single-output (MISO) design problems, with the equivalent SISO plants q/sub ii/, where (P/sup -1/)/sub ii/ = 1/q/sub ii/, employed in each MISO design. Developed is a transformation scheme that can be used to condition the equivalent SISO plants so that the difficult problem of NMP zeros lying to the left of, or close to, unstable poles may be avoided. Examples illustrate the use of the proposed transformation.