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

the dynamic behavior of production systems, as well as significantly contribute to control system engineering applications in production industries.

Acknowledgments

I am grateful to many former graduate students and international research associates in my laboratory for the fruitful discussions and collaboration we have had on topics related to this book. I am particularly indebted to Professor Hans-Peter Wiendahl (1938–2019) for his inspiring encouragement of the research that culminated in this book, which is dedicated to him; he is greatly missed. Professor Katia Windt provided indispensable feedback regarding the contents of this book and its focus on production systems, and I owe much to collaborations with her and Professors Julia Arlinghaus, Michael Freitag, Gisela Lanza, and Bernd Scholz-Reiter. I thank the Department of Mechanical Engineering of the University of Wisconsin-Madison for the environment that made this book possible and, above all, I am deeply indebted to my wife Colleen for her companionship and her unwavering support of my research and the writing of this book.

1 Introduction

      To remain competitive, today’s industries need to adapt to increasingly dynamic and turbulent markets. Dynamic production systems¹ and networks need to be designed that respond rapidly and effectively to trends in demand and production disturbances. Digitalization is transforming production planning, operations, control, and other functions through extensive use of digitized data, digital communication, automatic decision-making, simulation, and software-based decision-making tools incorporating AI algorithms. New sensing, communication, and actuation technologies are making new types of measurements and other data available, reducing delays in decision-making and implementing decisions, and facilitating embedding of models to create more “intelligent” production systems with improved performance and robustness in the presence of turbulence in operating conditions.

      In this increasingly dynamic and digital environment, production engineers and managers need tools that allow them to mathematically model, analyze, and design production systems and the strategies, policies, and decision-making components that make them responsive and robust in the presence of disturbances in the production environment, and mitigate the negative impacts of these disturbances. Discrete event simulation, queuing networks, and Petri nets have proved to be valuable tools for modeling the detailed behavior of production systems and predicting how important variables vary with time in response to specific input scenarios. However, these are not convenient tools for predicting fundamental dynamic characteristics of production systems operating under turbulent conditions. Large numbers of experiments, such as discrete event simulations with random input scenarios, often must be used to draw reliable conclusions about dynamic behavior and to subsequently design effective decision rules. On the other hand, measures of fundamental dynamic characteristics can be obtained quickly and directly from control theoretical models of production systems. Dynamic characteristics of interest can include

       time required for a production system to return to normal operation after disturbances such as rush orders or equipment failures (settling time)

       difference between desired values of important variables in a production system and actual values (error)

       tendency of important variables to oscillate (damping) or tendency of decision rules to over adjust (overshoot)

       whether disturbances that occur at particular frequencies cause excessive performance deviations (magnification) or do not significantly affect performance (rejection)

       over what range of frequencies of turbulence in operating conditions the performance of a production system is satisfactory (bandwidth).

      Unlike approaches such as discrete event simulation in which details of decision rules and the physical progression of entities such as workpieces and orders through the system often are modeled, control theoretical models are developed using aggregated concepts such as the flow of work. The tools of control system engineering can be applied to the simpler, linear models that are obtained, allowing decision-making to be directly designed to meet performance goals that are defined using characteristics such as those listed above. Experience has shown that the fidelity of this approach often is sufficient for understanding the fundamental dynamic behavior of production systems and for obtaining valuable, fundamentally sound, initial decision-making designs that can be improved with more detailed models and simulations.

      Production engineers can significantly benefit from becoming more familiar with the tools of control system engineering because of the following reasons:

       The dynamic behavior of production systems can be unexpected and unfavorable. For example, if AI is incorporated into feedback with the expectation of improving system behavior, the result instead might be unstable or oscillatory. If a control theoretical model is developed for such a system, even though it is an approximation, it can be an effective and convenient means for understanding why such a system behaves the way it does. A control theoretical analysis can replace a multitude of simulations from which it may be difficult to draw fundamental conclusions and obtain initial guidance for design and implementation of decision-making.

       Many useful decision-making topologies already have been developed and are commonly applied in other fields but are unlikely to be (re)invented by a production engineer who is unfamiliar with control system engineering. Well-known practical design approaches arising from control theory can guide production engineers toward systems that are stable, respond quickly, avoid oscillation, and are not sensitive to day-to-day variations in system operation and variables that are difficult to characterize or measure.

       Delays and their effects on a production system can be readily modeled and analyzed. While delay often is not significant in design of electro-mechanical systems, delay can be very significant in production systems. The implications of delay need to be well understood, including the penalties of introducing delay and the benefits of reducing delay.

       Analysis and design using frequency response is an important additional perspective in analysis and design of dynamic behavior. Production systems often need to be designed to respond effectively to lower-frequency fluctuations such as changes in demand but not respond significantly to higher-frequency fluctuations such as irregular arrival times of orders to be processed. Analysis using frequency response is not a separate theory; rather, it is a fundamental aspect of basic control theory that complements and augments analysis using time response. Production engineers, who are mostly familiar with time domain approaches such as results of discrete-event simulation, can significantly benefit from this alternative perspective on dynamic behavior and analysis and design using frequency response.

In this book, emphasis is placed on analysis and examples that illustrate the opportunities that control theoretical time and frequency perspectives present for understanding and designing the behavior of dynamic production systems. The dynamic behavior of the components of these systems and their interactions must be understood first before decision-making can be designed and implemented that results in favorable overall dynamic behavior of the production system, particularly when the structure contains feedback. In the replanning system with the topology in Figure 1.1, control theoretical modeling and analysis reveal that relationships between the period between replanning decisions and delays in making and implementing decisions can result in undesirable oscillatory behavior unless these relationships are taken into account in the design of replanning decision-making. Benefits of reducing delays using digital technologies can be quantified and used to guide replanning cycle redesign. In the production capacity decision-making approach shown in Figure 1.2, modeling and analysis from a frequency perspective can be used to guide design of the decision rules used to adjust capacity provided by permanent, temporary, and cross-trained employees, but also reveals that these decision rules can work at cross-purposes unless phase differences are explicitly considered.