Design of control systems by a linear fractional transformation

선형분수변환을 이용한 제어계설계

The fundamental objective of this paper has been to develop a means for incoporating the concept of the linear fractional transformation more generally and easily into multivariable feedback design procedure. When we design a continuous system, generally, we are constrained by design methods which arise specifically for the system. Also, in the design of descrete systems, it is the same concept. But the approach developed in this paper is very flexible in the view that in spite of being the continuous or discrete, the design can be done using a well known design method in both cases. That is, when we design a contnuous system or discrete system, the design can be done by a standard design method of continuous systmes or discrete ones, depending on the choice of the linear fractional transformation. Therefore, it is noted that this concept has broken the unflexibility of the conventional design rules for multivariable control system. In essence, the concept shows that if a given system is controllable, some desirable design, for examples, pole assignment within prespecified region, optimal controllers with poles within prespecified region etc., could be done easily by transforming a desirable region into a standard region, such as the complex left-half plane or the unit disk, by the chosen linear fractional transformation, and then by designing the transformed system using the well known standard results.