Control Theory Applications for Dynamic Production Systems. Neil A. Duffie

1.1 Replanning cycle with significant delays.

      Figure 1.2 Adjustment of permanent, temporary, and cross-trained employee capacity based on frequency content of variation in order input rate.

In the planning and scheduling system shown in Figure 1.3, failure to understand the interactions between backlog regulation and work-in-progress (WIP) regulation when designing their decision rules can lead to unexpected and adverse combined dynamic behavior. Design guided by modeling and analysis achieves system behavior that reliably meets goals of effective backlog and WIP regulation. In the four-company production network shown in Figure 1.4, modeling and analysis of interactions between companies allows decision rules to be designed for individual companies that result in favorable combined dynamic behavior. Benefits and dynamic limitations of information sharing between companies can be quantified and used in evaluating the merits and costs of information sharing and designing the structure in which it should be implemented. In the production operation shown in Figure 1.5, control theoretical modeling and analysis of the interacting components enables design of control components that together result in favorable, efficient behavior.

      Figure 1.3 Regulation of backlog and WIP.

      Figure 1.4 Adjustment of deliveries based on feedback of backlog information.

      Figure 1.5 Control of force and position in a pressing operation.

There has been considerable research in the use of control theoretical methods to improve understanding of the dynamics behavior of production systems and supply chains [1–4], but many production engineers are unfamiliar with the application of the tools of control system engineering in their field, tools that are well-developed and used extensively by electrical, aerospace, mechanical, and chemical engineers for mathematically modeling, analyzing, and designing control of electro-mechanical systems and chemical processes. The tools of control system engineering include a daunting variety of mathematical approaches, but even the most basic control theoretical methods for modeling, analysis, and design can be important additions to the productions system engineer’s toolbox, complementing tools such as discrete event simulation. The content of this book has been chosen to be immediately relevant to practicing production engineers, providing a fundamental understanding of both continuous-time and discrete-time control theory while avoiding unnecessary material. Some aspects of control theory covered in traditional texts are omitted here; for example, the principles of obtaining discrete-time models from continuous-time models are discussed, but the variety of mathematical methods for doing so are not because practicing production engineers rarely or never use these methods; instead, practicing production engineers need to obtain results quickly with the aid of control system engineering software. Similarly, practicing production engineers rarely or never need to find explicit solutions for differential and difference equations, and such solutions are only discussed in this book when they support important practical developments. Straightforward examples are presented that illustrate basic principles, and software examples are used to illustrate practical computation and application. The goal throughout this book is to provide production engineers and managers with valuable and fundamental means for improving their understanding of the dynamic behavior of modern production systems and guiding their design of future production systems. A brief biography is included at the end of this book for readers who are interested in further study including additional theoretical derivations, alternative methods of analysis and design, other application areas, and advanced topics in the ever-evolving field of control system engineering.

      1.1 Control System Engineering Software

      Control system engineering software is an essential tool for control system designers. MATLAB^® and its Control System Toolbox^TM from The MathWorks, Inc.² is one of the more widely used, and MATLAB^® programs have been included in many of the examples in this book to illustrate how such software can be used to obtain practical results quickly using transfer functions and control theoretical methods.³ Computations that would be very tedious to perform by hand can be performed by such software using a relatively small number of statements, and numerical and graphical results can be readily displayed. Programming control system engineering calculations on platforms other than MATLAB^® often uses functions and syntax that are similar to those in the Control System Toolbox^TM. For purposes of brevity and compatibility between platforms, some programming details are omitted in the examples in this book.

      References

      1 1 Ortega, M. and Lin, L. (2004). Control theory applications to the production–inventory problem: a review. International Journal of Production Research 42 (11): 2303–2322.

      2 2 Sarimveis, H., Patrinos, P., Tarantilis, C., and Kiranoudis, C. (2008). Dynamic modeling and control of supply chain systems: a review. Computers & Operations Research 35 (11): 3530–3561.

      3 3 Ivanov, D., Dolgui, A., and Sokolov, B. (2012). Applicability of optimal control theory to adaptive supply chain planning and scheduling. Annual Reviews in Control 36 (1): 73–84.

      4 4 Duffie, N., Chehade, A., and Athavale, A. (2014). Control theoretical modeling of transient behavior of production planning and control: a review. Procedia CIRP 17: 20–25. doi: 10.1016/j.procir.2014.01.099.

      Notes

      1 1 Production systems include the physical equipment, procedures, and organization needed to supply and process inputs and deliver products to consumers.

      2 2 MATLAB® and Control System ToolboxTM are trademarks of The MathWorks, Inc. The reader is referred to the Bibliography and documentation available from The MathWorks as well as many other publications that address the use of MATLAB® and other software tools for control system analysis and design.

      3 3 Other software such as Simulink®, a trademark of The MathWorks, Inc., facilitates modeling and time-scaled simulations. While such tools are commonly used by control system engineers, production engineers often find that discrete-event simulation software is more appropriate for detailed modeling of production systems. The reader is referred to the Bibliography and many publications that describe discrete-event and time-scaled simulation.

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,