Control Theory Applications for Dynamic Production Systems

3 Transfer Functions and Block Diagrams

Modeling as described in Chapter 2 results in a set of differential, difference, or algebraic equations that describe the dynamic behavior of the components and interactions between the components of a production system. Analysis of the dynamic behavior of a production system and design of decision-making rules that result in favorable dynamic behavior requires combining the models of the production system’s components. However, it can be a challenge to combine these equations: there may be a mix of continuous-time and discrete-time models; the structure of the production system may be complicated and this structure will be present in the equations; and while low-order differential or difference equations may describe the dynamic behavior of individual components in a satisfactory manner, combined models may be of significantly higher order. Fortunately, Laplace transforms and Z transforms can be used to convert differential and difference equations, respectively, into algebraic forms that are easily manipulated and readily support mathematical analysis and design tools implemented in control system engineering software.

Transfer functions that represent cause-and-effect relationships between the components can be obtained after transformation of continuous-time and discrete-time models of components of production systems. The structure of these relationships is important and must be well understood in order to proceed to dynamic analysis ...