Before applying any design, or synthesis, technique to determine an appropriate control scheme for a given system, the properties of the system under consideration, such as the controllability or observability of a state-space model, the open-loop system stability, and the existence of any right half-plane transmission zeros, must first be established. Chapter 7 of Control System Professional gives a full exposition of the controllability and observability of state-space systems. In this chapter, the related concepts of functional controllability, coprimeness, and decoupling zeros, for the objects TransferFunction, LeftMatrixFraction, RightMatrixFraction, and SystemMatrix, respectively, are introduced. The finite poles and zeros of multivariable systems are also defined, and standard forms associated with the objects TransferFunction and SystemMatrix are introduced, as these are used by several of the analysis facilities to be presented. Since all the control system model objects can be converted to any other model object, this allows easy access to these additional tools and standard (or canonical) forms. Although the functions defined in this chapter are introduced in the continuous-time notation, most of them can be defined, and work similarly, in the case of discrete-time systems. |
