SENSITIVITY REDUCTION LIMITATIONS IN MIMO NON-MINIMUM PHASE FEEDBACK SYSTEMS

摘要

Limitations and design trade-offs of the closed-loop sensitivity/performance of linear-time-invariant non-minimum-phase MIMO plants, with l inputs and m outputs, where m ≤ l are investigated. It is shown that if rows i_1,..., i_k of the plant transfer function form a k × l non-minimum phase transfer matrix, and if the design is such that the sensitivity gain of k - 1 rows among the rows i_1,..., i_k of the closed-loop transfer function is low, then by necessity the sensitivity gain of the remaining row is high. This sensitivity constraint is quantified with the help of the cross-over frequency restriction of a specially constructed SISO transfer function that includes the right half plane zeros and poles of the k × l transfer matrix.