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

Preface

      Production planning, operations, and control are being transformed by digitalization, creating opportunities for automation of decision making, reduction of delays in making and implementing decisions, and significant improvement of production system performance. Meanwhile, to remain competitive, today’s production industries need to adapt to increasingly dynamic and turbulent markets. In this environment, production engineers and managers can benefit from tools of control system engineering that allow them to mathematically model, analyze, and design dynamic, changeable production systems with behavior that is effective and robust in the presence of turbulence. Research has shown that the tools of control system engineering are important additions to the production system engineer’s toolbox, complementing traditional tools such as discrete event simulation; however, many production engineers are unfamiliar with application of control theory in their field. This book is a practical yet thorough introduction to the use of transfer functions and control theoretical methods in the modeling, analysis, and design of the dynamic behavior of production systems. Production engineers and managers will find this book a valuable and fundamental resource for improving their understanding of the dynamic behavior of modern production systems and guiding their design of future production systems.

      This book was written for a course entitled Smart Manufacturing at the University of Wisconsin-Madison, taught for graduate students working in industry. It has been heavily influenced by two decades of industry-oriented research, mainly in collaboration with colleagues in Germany, on control theory applications in analysis and design of the dynamic behavior of production systems. Motivated by this experience, the material in this book has been selected to

       explain and illustrate how control theoretical methods can be used in a practical manner to understand and design the dynamic behavior of production systems

       focus application examples on production systems that can include production processes, machines, work systems, factories, communication, and production networks

       present both time-based and frequency-based analytical and design approaches along with illustrative examples to give production engineers important new perspectives and tools as production systems and networks become more complex and dynamic

       apply control system engineering software in examples that illustrate how dynamic behavior of production systems can be analyzed and designed in practice

       address both open-loop and closed-loop decision-making approaches

       present discrete-time and continuous-time theory in an integrated manner, recognizing the discrete-time nature of adjustments that are made in the operation of many production systems and complementing the integrated nature of supporting tools in control system engineering software

       recognize that delays are ever-present in production systems and illustrate modeling of delays and the detrimental effects that delays have on dynamic behavior

       show in examples how information acquisition, information sharing, and digital technologies can improve the dynamic behavior of production systems

       “bridge the gap” between production system engineering and control system engineering, illustrating how control theoretical methods and control system engineering software can be effective tools for production engineers.

      This material is organized into the following chapters:

      Chapter 1 Introduction. The many reasons why production engineers can benefit from becoming more familiar with the tools of control system engineering are discussed, including the increasingly dynamic and digital environment for which current and future production systems must be designed. Several examples are described that illustrate the opportunities that control theoretical time and frequency perspectives present for understanding and designing the dynamic behavior of production systems and their decision-making components.

      Chapter 2 Continuous-Time and Discrete-Time Models of Production Systems. Methods for modeling the dynamic behavior of production systems are introduced, both for continuous-time and discrete-time production systems and components. The result of modeling is differential equations in the continuous-time case or difference equations in the discrete-time case. These describe how the outputs of a production system and its components vary with time as a function of their time-varying inputs. The concepts of linearizing a model around an operating point and linearization using piecewise approximations also are presented.

      Chapter 3 Transfer Functions and Block Diagrams. Use of the Laplace transform and Z transform to convert continuous-time differential equation models and discrete-time difference equation models, respectively, into relatively more easily analyzed algebraic models is introduced. The concept of continuous-time and discrete-time transfer functions is introduced, as is their use in block diagrams that clearly illustrate dynamic characteristics, cause–effect relationships between the inputs and outputs of production systems and their components, delay, and closed-loop topologies. Transfer function algebra is reviewed along with methods for defining transfer functions in control system engineering software.

Chapter 4 Fundamental Dynamic Characteristics and Time Response. Fundamental dynamic characteristics of production system and component models are defined including time constants, damping ratios, and natural frequencies. The significance of the roots of characteristic equations obtained from transfer functions is reviewed, including using the roots to assess stability. Methods are presented for using continuous-time and discrete-time transfer functions to calculate the response of production systems as a function of time and determine characteristics such as settling time and overshoot in oscillation, with practical emphasis on use of control system engineering software.

      Chapter 5 Frequency Response. Methods are presented for using transfer functions to calculate the response of production systems and their components to sinusoidal inputs that represent fluctuations in variables such as demand. Characteristics of frequency response that are important in analysis and design are defined including bandwidth, zero-frequency magnitude, and magnitude and phase margins. Theoretical foundations are presented, with practical emphasis on using control system engineering software to calculate and analyze frequency response.

      Chapter 6 Design of Decision Making for Closed-Loop Production Systems. Approaches for design of decision making for closed-loop production systems using time response, transfer functions, and frequency response are introduced. Design for common closed-loop production system topologies is reviewed, and approaches such as PID control, feedforward control, and cascade control are introduced. Challenges and options for decision making in systems with significant time delays are addressed, and the use of control system engineering software in design is illustrated with examples.

      Chapter 7 Application Examples. Examples are presented in which analysis and design of the dynamic behavior is of higher complexity, requiring approaches such as use of matrices of transfer functions and modeling using multiple sampling rates. The examples illustrate analysis and design from both the time and frequency perspectives. In the first application example, the potential for improving performance by using digital technologies to reduce delays in a replanning cycle is explored. Other application examples then are presented that illustrate analysis and design production systems with multiple inputs and outputs, networks of production systems with information sharing, and production systems with multiple closed loops.

After becoming familiar with the material presented in this book, production engineers can expect to be able to apply the basic tools of control theory and control system engineering software in modeling, analyzing,