Design of multivariable systems using unity-rank feedback†

Existing pole-assignment methods are inadequate as a complete design technique for linear multivariable systems since other design factors such as zero positions, steady-state characteristics, integrity, etc., must also be taken into account. This paper extends an existing pole-assignment technique, employing unity-rank feedback, to account for such additional design features. For an nth-order multivariable system with m inputs and l outputs, it is shown that there are essentially m − 1 independent variables available in the design process. When complete state feedback or output feedback with l = n is used, these m − 1 degrees of freedom are available to meet specifications in addition to pole assignment. When incomplete state feedback or output feedback with l less than n is used, these m − l degrees of freedom must be shared between pole-assignment and the other design features. The method is computationally fast and is well suited to the computer-aided design of control systems. A number of illustrative examples are given.