On the choice of overall transfer functions

The linear algebra method for designing rational control systems consists of two steps: Selecting an overall transfer function and then designing the controller. Once an overall transfer function is chosen, the rest of the design is straightforward. This paper will discuss how to select a suitable overall transfer function for linear plant with time delay. The problem can be formulated as: Given a linear proper plant with time delay, search an overall transfer function such that the overall system is internally stable and has some other desired properties. Sufficient and necessary conditions are given and constructing procedure is developed. Numerical examples are provided to illustrated the proposed method.