TABLE OF CONTENTS The content of this book is closely related to system theory, a scientific discipline devoted to the study of mathematical properties of various physical systems. System theory has become an extensive and rapidly growing field that overlaps and interrelates with other fields of study, such as information theory, signal theory, stability and control theory, and others. There are many problems and areas covered by system theory, including mathematical modeling, system identification, dynamic system analysis, control system synthesis, and optimization, among others. In this chapter, two elements of system theory, mathematical modeling and system identification, will be discussed, with an emphasis on application to aircraft.
Mathematical modeling is the process of developing an adequate mathematical representation of some aspects of a physical system. Mathematical models can take various forms. One form that often results from direct application of physical laws is a set of differential equations relating input to output. An equivalent and more preferable form of the model is the state-space representation, which relates three variables: input, output, and state. The input u , output y, and state x can be vector or scalar quantities.
The input excites the system and can usually be specified by the experimenter. It is therefore an external disturbance that can be directly measured. The input must be distinguished from unmeasured disturbances, which are observed only through their influence on the system response. In some cases, the experimenter may not have the capability to specify the input, so that...
