Control Theory Applications for Dynamic Production Systems

2 Continuous-Time and Discrete-Time Modeling of Production Systems

The dynamic behavior of a production system is the result of the combined dynamic behavior of its components including the decision-making components that implement decision rules. Production system behavior is not simply the sum of component behaviors, and it only can be understood and modeled by considering the structure of the production system, the nature of interconnections between individual components, and dynamic behavior that results from these interactions. In this chapter, methods for control theoretical modeling of the dynamic behavior of production systems are introduced, both for continuous-time and discrete-time production systems and their components. Then, in subsequent chapters, methods will be introduced that can be used to combine models of production system components and design control components and decision rules that result in desired production system dynamic behavior.

A control theoretical dynamic model of a production system or component is, in the continuous-time case, a set of differential and algebraic equations or, in the discrete-time¹ case, a set of difference and algebraic equations that describe how the time-varying outputs of the production system or component are related to its time-varying inputs. The mathematical methods that will be introduced in subsequent chapters are valid for linear models, and development of these models is the focus of this chapter. Because many ...