ABSTRACT
Historically, control theory has been well established for linear systems, and numerous analysis and synthesis tools are available for control system design and evaluation. Yet most chemical processes are known to exhibit nonlinear behavior. Since there are many instances where nonlinear processes remain near a particular operating point, a linear approximation of the process model in this region may be sufficiently accurate. Such local models can provide significant intuition and insight into the problem and lead to practical control strategies. This chapter presents a discussion of the linear approximation of process models described by nonlinear differential equations. To facilitate the construction of input–output (I/O) relationships from linear models, the Laplace transform is introduced. A major benefit is that this transformation converts the linear differential equations into algebraic equations, thus simplifying the mathematical manipulations required to develop an I/O model. Such an algebraic model, called the transfer function, is used exclusively in control system design and analysis.
