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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Control Theory Applications for Dynamic Production Systems Apply the fundamental tools of linear control theory to model, analyze, design, and understand the behavior of dynamic production systems In Control Theory Applications for Dynamic Production Systems: Time and Frequency Methods for Analysis and Design, distinguished manufacturing engineer Dr. Neil A. Duffie delivers a comprehensive explanation of how core concepts of control theorical analysis and design can be applied to production systems. Time-based perspectives on response to turbulence are augmented by frequency-based perspectives, fostering new understanding and guiding design of decision-making. The time delays intrinsic to decision making and decision implementation in production systems are addressed throughout. Readers will discover methods for calculating time response and frequency response, modeling using transfer functions, assessing stability, and design of decision making for closed-loop production systems. The author has included real-world examples emphasizing the different components of production systems and illustrating how practical results can be quickly obtained using straightforward Matlab programs (which can easily be translated to other platforms). Avoiding unnecessary theoretical jargon, this book fosters an in-depth understanding of key tools of control system engineering. It offers: * A thorough introduction to core control theoretical concepts of analysis and design of dynamic production systems * Comprehensive and integrated explorations of continuous-time and discrete-time models of production systems, employing transfer functions and block diagrams * Practical discussions of time response, frequency response, fundamental dynamic behavior, closed-loop production systems, and the design of decision-making * In-depth examples of the analysis and design of complex dynamic behavior requiring approaches such as matrices of transfer functions and modeling of multiple sampling rates Perfect for production, manufacturing, industrial, and control system engineers, Control Theory Applications for Dynamic Production Systems will also earn a place in the libraries of students taking advanced courses on industrial system digitalization, dynamics, and design.
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Control Theory Applications for Dynamic Production Systems
Time and Frequency Methods for Analysis and Design
Neil A. DuffieUniversity of WisconsinMadison, Wisconsin
This edition first published 2022
© 2022 John Wiley & Sons, Inc.
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A catalogue record for this book is available from the Library of Congress
Hardback ISBN: 9781119862833; ePub ISBN: 9781119862857; ePDF ISBN: 9781119862840; Obook ISBN: 9781119862864
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Set in 9.5/12pt and STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India
To Hans-Peter Wiendahl (1938–2019)
Contents
Cover
Title page
Copyright
Dedication
Preface
Acknowledgments
1 Introduction
1.1 Control System Engineering Software
2 Continuous-Time and Discrete-Time Modeling of Production Systems
2.1 Continuous-Time Models of Components of Production Systems
2.2 Discrete-Time Models of Components of Production Systems
2.3 Delay
2.4 Model Linearization
2.4.1 Linearization Using Taylor Series Expansion – One Independent Variable
2.4.2 Linearization Using Taylor Series Expansion – Multiple Independent Variables
2.4.3 Piecewise Approximation
2.5 Summary
3 Transfer Functions and Block Diagrams
3.1 Laplace Transform
3.2 Properties of the Laplace Transform
3.2.1 Laplace Transform of a Function of Time Multiplied by a Constant
3.2.2 Laplace Transform of the Sum of Two Functions of Time
3.2.3 Laplace Transform of the First Derivative of a Function of Time
3.2.4 Laplace Transform of Higher Derivatives of a Function of Time Function
3.2.5 Laplace Transform of Function with Time Delay
3.3 Continuous-Time Transfer Functions
3.4 Z Transform
3.5 Properties of the Z Transform
3.5.1 Z Transform of a Sequence Multiplied by a Constant
3.5.2 Z Transform of the Sum of Two Sequences
3.5.3 Z Transform of Time Delay dT
3.5.4 Z Transform of a Difference Equation
3.6 Discrete-Time Transfer Functions
3.7 Block Diagrams
3.8 Transfer Function Algebra
3.8.1 Series Relationships
3.8.2 Parallel Relationships
3.8.3 Closed-Loop Relationships
3.8.4 Transfer Functions of Production Systems with Multiple Inputs and Outputs
3.8.5 Matrices of Transfer Functions
3.8.6 Factors of Transfer Function Numerator and Denominator
3.8.7 Canceling Common Factors in a Transfer Function
3.8.8 Padé Approximation of Continuous-Time Delay
3.8.9 Absorption of Discrete Time Delay
3.9 Production Systems with Continuous-Time and Discrete-Time Components
3.9.1 Transfer Function of a Zero-Order Hold (ZOH)
3.9.2 Discrete-Time Transfer Function Representing Continuous-Time Components Preceded by a Hold and Followed by a Sampler
3.10 Potential Problems in Numerical Computations Using Transfer Functions
3.11 Summary
4 Fundamental Dynamic Characteristics and Time Response
4.1 Obtaining Fundamental Dynamic Characteristics from Transfer Functions
4.1.1 Characteristic Equation
4.1.2 Fundamental Continuous-Time Dynamic Characteristics
4.1.3 Continuous-Time Stability Criterion
4.1.4 Fundamental Discrete-Time Dynamic Characteristics
4.1.5 Discrete-Time Stability Criterion
4.2 Characteristics of Time Response
4.2.1 Calculation of Time Response
4.2.2 Step Response Characteristics
4.3 Summary
5 Frequency Response
5.1 Frequency Response of Continuous-Time Systems
5.1.1 Frequency Response of Integrating Continuous-Time Production Systems or Components
5.1.2 Frequency Response of 1st-order Continuous-Time Production Systems or Components
5.1.3 Frequency Response of 2nd-order Continuous-Time Production Systems or Components
5.1.4 Frequency Response of Delay in Continuous-Time Production Systems or Components
5.2 Frequency Response of Discrete-Time Systems
5.2.1 Frequency Response of Discrete-Time Integrating Production Systems or Components
5.2.2 Frequency Response of Discrete-Time 1st-Order Production Systems or Components
5.2.3 Aliasing Errors
5.3 Frequency Response Characteristics
5.3.1 Zero-Frequency Magnitude (DC Gain) and Bandwidth
5.3.2 Magnitude (Gain) Margin and Phase Margin
5.4 Summary
6 Design of Decision-Making for Closed-Loop Production Systems
6.1 Basic Types of Continuous-Time Control
6.1.1 Continuous-Time Proportional Control
6.1.2 Continuous-Time Proportional Plus Derivative Control
6.1.3 Continuous-Time Integral Control
6.1.4 Continuous-Time Proportional Plus Integral Control
6.2 Basic Types of Discrete-Time Control
6.2.1 Discrete-Time Proportional Control
6.2.2 Discrete-Time Proportional Plus Derivative Control
6.2.3 Discrete-Time Integral Control
6.2.4 Discrete-Time Proportional Plus Integral Control
6.3 Control Design Using Time Response
6.4 Direct Design of Decision-Making
6.4.1 Model Simplification by Eliminating Small Time Constants and Delays
6.5 Design Using Frequency Response
6.5.1 Using the Frequency Response Guidelines to Design Decision-Making
6.6 Closed-Loop Decision-Making Topologies
6.6.1 PID Control
6.6.2 Decision-Making Components in the Feedback Path
6.6.3 Cascade Control
6.6.4 Feedforward Control
6.6.5 Circumventing Time Delay Using a Smith Predictor Topology
6.7 Sensitivity to Parameter Variations
6.8 Summary
7 Application Examples
7.1 Potential Impact of Digitalization on Improving Recovery Time in Replanning by Reducing Delays
7.2 Adjustment of Steel Coil Deliveries in a Production Network with Inventory Information Sharing
7.3 Effect of Order Flow Information Sharing on the Dynamic Behavior of a Production Network
7.4 Adjustment of Cross-Trained and Permanent Worker Capacity
7.5 Closed-Loop, Multi-Rate Production System with Different Adjustment Periods for WIP and Backlog Regulation
7.6 Summary
References
Bibliography
Index
End User License Agreement
List of Figures
Chapter 1
Figure 1.1 Replanning cycle with...
Figure 1.2 Adjustment of permanent...
Figure 1.3 Regulation of backlog...
Figure 1.4 Adjustment of deliveries...
Figure 1.5 Control of force...
Chapter 2
Figure 2.1 Continuous variables in...
Figure 2.2 Response of WIP...
Figure 2.3 Backlog regulation in...
Figure 2.4 Mixture outlet temperature...
Figure 2.5 Experimental results obtained...
Figure 2.6 Discrete variables in...
Figure 2.7 Response of WIP...
Figure 2.8 Discrete-time decision...
Figure 2.9 Response of change...
Figure 2.10 Exponential filter for...
Figure 2.11 Response of desired...
Figure 2.12 Lead time and...
Figure 2.13 Adjustment of permanent...
Figure 2.14 Linear approximation of...
Figure 2.15 Production work system...
Figure 2.16 Percent error in...
Figure 2.17 Actual production capacity...
Chapter 3
Figure 3.1 Unit step function...
Figure 3.2 Exponential function with...
Figure 3.3 Decaying sine function...
Figure 3.4 Function with time...
Figure 3.5 Mixture temperature regulation...
Figure 3.6 Sequence...
Figure 3.7 Ideal sampler with...
Figure 3.8 Unit step sequence.
Figure 3.9 Exponential sequence.
Figure 3.10 Decaying sinusoidal sequence.
Figure 3.11 Example of delayed...
Figure 3.12 Continuous-time and...
Figure 3.13 Summing and differencing...
Figure 3.14 Block diagram for...
Figure 3.15 Block diagram for...
Figure 3.16 Transfer functions and...
Figure 3.17 Result of combining...
Figure 3.18 Transfer functions and...
Figure 3.19 PID decision rule...
Figure 3.20 Transfer functions in...
Figure 3.21 Production system with...
Figure 3.22 Block diagram for...
Figure 3.23 Closed-loop transfer...
Figure 3.24 Computer-controlled actuator...
Figure 3.25 Block diagrams for...
Figure 3.26 Block diagram for...
Figure 3.27 Block diagrams showing...
Figure 3.28 Pressing operation with...
Figure 3.29 Equivalent block diagrams...
Figure 3.30 Simplified block diagram...
Figure 3.31 Block diagrams for...
Figure 3.32 Closed-loop production...
Figure 3.33 Warehouse with Product...
Figure 3.34 Block diagram for...
Figure 3.35 Block diagram for...
Figure 3.36 Block diagram for...
Figure 3.37 Zero-order hold...
Figure 3.38 Discrete-time transfer...
Figure 3.39 Block diagram with...
Figure 3.40 Block diagram for...
Figure 3.41 Replacement of zero...
Figure 3.42 Production network with...
Chapter 4
Figure 4.1 First-order continuous...
Figure 4.2 Examples of second...
Figure 4.3 Production system with...
Figure 4.4 Examples of first...
Figure 4.5 Examples of second...
Figure 4.6 Production system with...
Figure 4.7 Block diagram for...
Figure 4.8 Block diagram for...
Figure 4.9 Transient and steady...
Figure 4.10 Response of continuous...
Figure 4.11 Response of discrete...
Figure 4.12 Response of actuator...
Figure 4.13 Characteristics of step...
Figure 4.14 Block diagram for...
Figure 4.15 Response of mixture...
Figure 4.16 Unit step response...
Chapter 5
Figure 5.1 Example of transient...
Figure 5.2 Example of response...
Figure 5.3 Frequency response of...
Figure 5.4 Bode plot of...
Figure 5.5 Frequency response of...
Figure 5.6 Production system with...
Figure 5.7 Frequency response of...
Figure 5.8 2nd-order continuous...
Figure 5.9 Frequency response of...
Figure 5.10 Frequency response of...
Figure 5.11 Frequency response of...
Figure 5.12 Frequence response of...
Figure 5.13 Block diagram for...
Figure 5.14 Frequency response of...
Figure 5.15 Frequency response of...
Figure 5.16 Frequency response of...
Figure 5.17 Aliasing errors result...
Figure 5.18 Aliasing errors in...
Figure 5.19 Zero-frequency magnitude...
Figure 5.20 Continuous-time or...
Figure 5.21 Block diagrams for...
Figure 5.22 Open-loop frequency...
Figure 5.22 (
b
...
Chapter 6
Figure 6.1 Closed-loop decision...
Figure 6.2 Production system with...
Figure 6.3 Block diagram for...
Figure 6.4 Response to a...
Figure 6.5 Step response with...
Figure 6.6 Actuator with proportional...
Figure 6.7 Step response with...
Figure 6.8 Block diagram for...
Figure 6.9 Response to step...
Figure 6.10 Response to step...
Figure 6.11 Proportional plus integral...
Figure 6.12 Block diagram with...
Figure 6.13 Response of backlog...
Figure 6.14 Benchmark relationship between...
Figure 6.15 Open-loop block...
Figure 6.16 Open-loop frequency...
Figure 6.17 Closed-loop error...
Figure 6.18 Production system with...
Figure 6.19 Open-loop frequency...
Figure 6.20 Open-loop frequency...
Figure 6.21 Closed-loop frequency...
Figure 6.22 Block diagram for...
Figure 6.23 Open-loop frequency...
Figure 6.24 Open-loop frequency...
Figure 6.25 Closed-loop mixture...
Figure 6.26 PID control topologies...
Figure 6.27 Decision-making divided...
Figure 6.28 Block diagrams for...
Figure 6.29 Response lead-time...
Figure 6.30 Example of a...
Figure 6.31 Example of discrete...
Figure 6.32 Cascade computer control...
Figure 6.33 Block diagram for...
Figure 6.34 Cascaded discrete-time...
Figure 6.35 Response of cascaded...
Figure 6.36 Feedforward control. (a...
Figure 6.37 Discrete-time regulation...
Figure 6.38 Feedforward control added...
Figure 6.39 Response of cascade...
Figure 6.40 Discrete-time closed...
Figure 6.41 Smith Predictor topology...
Figure 6.42 Response to step...
Chapter 7
Figure 7.1 Replanning cycle for...
Figure 7.2 Block diagram of...
Figure 7.3 Recovery time 4...
Figure 7.4 Galvanizing lines share...
Figure 7.5 Block diagram for...
Figure 7.6 Variation in galvanizing...
Figure 7.7 Amplitude of variation...
Figure 7.8 Example of a...
Figure 7.9 Block diagram for...
Figure 7.10 Block diagram for...
Figure 7.11 Change in WIP...
Figure 7.12 Change in WIP...
Figure 7.13 Case where 37...
Figure 7.14 Change in WIP...
Figure 7.15 Frequency range and...
Figure 7.16 Block diagram for...
Figure 7.17 Magnitude of frequency...
Figure 7.18 Example of order...
Figure 7.19 Example of order...
Figure 7.20 Block diagram with...
Figure 7.21 Sampler decomposition. (a...
Figure 7.22 Response to a...
Figure 7.23 Response to a...
List of Tables
Chapter 3
Table 3.1 Laplace transforms of common....
Table 3.2 Z transforms of common sequences.
Chapter 4
Table 4.1 Settling times for various ratios...
Chapter 7
Table 7.1 Improvement of recovery time...
Table 7.2 Amplitude of variation of difference...
Table 7.3 Summary of results for cases...
Guide
Cover
Title page
Copyright
Dedication
Table of Contents
Preface
Acknowledgments
Begin Reading
Bibliography
Index
End User License Agreement
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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 1Introduction. 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 2Continuous-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 3Transfer 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 4Fundamental 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 5Frequency 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 6Design 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 7Application 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, and designing 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.
Figure 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 ToolboxTM 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 ToolboxTM. For purposes of brevity and compatibility between platforms, some programming details are omitted in the examples in this book.
References
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
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
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
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
Production systems include the physical equipment, procedures, and organization needed to supply and process inputs and deliver products to consumers.
2
MATLAB
®
and Control System Toolbox
TM
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
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.
