Higher Order Models

The preceding sections were concerned with modeling first-order continuous-time systems (the ideal mass in particular) using first-order discrete-time models. Advantages of this approach include (1) minimized computational expense, (2) an alias-free mapping of the $s$ plane to the $z$ plane, and (3) the possibility of preserving a physical intepretation of the state variables (which can lead to superior numerical performance). However, to achieve a better match to certain characteristics, such as the system frequency response, one may use arbitrarily high model orders. Such a ``filter design'' approach is discussed in §Q.3 below.