Introduction to System Science with MATLAB, 2nd Edition

4Single‐Input Systems

Because of their relative simplicity and universal importance in the study of systems, the major analytical solution methods associated with single‐input systems will be examined in detail in this chapter. With access to adequate computing facilities and appropriate software (e.g., MATLAB and MAPLE) support, the system investigator can use computer‐based software packages for analysis that may reduce the need for the analytical‐based methods presented in this chapter for single‐input systems and Chapter 5 for multiple‐input systems. However, definite advantages do accrue from understanding and using the analytical methods described in these two chapters. Furthermore, the symbolic computational packages also provided by MATLAB and MAPLE permit quasi‐analytical means of assessing and evaluating system equations, particularly those with single inputs.

4.1 Definition and Significance of a Single‐Input System

The single‐input system model is applicable to any system that can be reasonably assumed to have only one significant or dominant input or independent variable and one or more outputs or dependent variables. For a system with more than one input, it is necessary to reduce all inputs to the system to a single dominant or representative input in order to utilize the single‐input system model. This reduction requirement may appear to be an unrealistic and incorrect assumption, but, as we will see in Chapter 8, it is usually possible to reduce multiple‐inputs ...