In the preceding chapter we used the Laplace transform to obtain transfer function
models representing linear, time-invariant physical systems described by ordinary
differential equations. This method is attractive because it provides a practical approach
to design and analysis and allows us to utilize block diagrams to interconnect
subsystems. In this chapter we turn to an alternative method of system modeling
using time-domain methods. As before, we will consider physical systems described
by an nth-order ordinary differential equation. Utilizing a (nonunique) set of variables,
known as state variables, we can obtain a set of first-order differential equations. We
group these first-order equations using a compact matrix notation in a model known
as the state variable model. The time-domain state variable model lends itself readily
to computer solution and analysis. The relationship between signal-flow graph
models and state variable models will be investigated. Several interesting physical
systems, including a printer belt drive, are presented and analyzed. The chapter concludes
with the development of a state variable model for the Sequential Design Example:
Disk Drive Read System.
