New Interpretation of MIMO Quantitative Feedback Theory

Horowitz´s Quantitative Feedback Theory provides a graphical control design technique for uncertain servo tracking systems. Horowitz has generalized his method to solving MIMO problems. This paper reinterpretes his MIMO design approach from the perspective of Inverse Nyquist Array method The MIMO servo design goal is reformulated to contain two objectives: reaching the demanded tracking performance in individual channels and achieving the specified degree of diagonal dominance for reducing cross coupling effects. The Nichols plots of Gershgorin or Ostrowski circles are used to deduce the needed compensation for the desired degree of diagonal dominance. Together with the Horowitz bounds for achieving the desired tracking performance, the admissible loop transmission can be determined. Thus a MIMO design is converted into an equivalent set of SISO design problems guaranteed to achieve the original MIMO performance specification.