ABSTRACT
An accurate mathematical model that describes a system completely must be determined in order to analyze a dynamic system. The derivation of this model is based upon the fact that the dynamic system can be completely described by known differential equations (Chapter 6) or by experimental test data (Section 11.1). The ability to analyze the system and determine its performance depends on how well the characteristics can be expressed mathematically. Techniques for solving linear differential equations with constant coefficients are presented in Chapters 6 and 7. However, the solution of a time-varying or nonlinear equation often requires a numerical, graphic, or computer procedure [1]. The systems considered in this chapter are described completely by a set of linear constant coefficient differential equations. Such systems are said to be linear time-invariant (LTI) [2]; that is, the relationship between the system input and output is independent of time. Since the system does not change with time, the output is independent of the time at which the input is applied. Linear methods are used because there is extensive and elegant mathematics for solving linear equations. For many systems, there are regions of operation for which the linear representation works very well.
