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

Abstract

Considered in this thesis is 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 the NMP zeros. In the single-input single-output (SISO) 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 synthesis starts by considering a set of equivalent SISO plants derived from the plant transfer function matrix that are used to develop a controller. In effect the design problem is reduced to several MISO designs with the diagonal entries of as the equivalent SISO plants. Developed is a transformation scheme that can be used to condition the resulting equivalent SISO plants so that the difficult problem of NMP zeros lying to the left of unstable poles is avoided. Examples illustrate the use of the proposed transformation.