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Über dieses Buch

This open access brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon has a view of the whole. Each concept is illustrated by detailed examples and graphics. The full software code for each example is available, providing the basis for experimenting with various assumptions, learning how to write programs for control analysis, and setting the stage for future research projects. The topics focus on robustness, design trade-offs, and optimality. Most of the book develops classical linear theory. The last part of the book considers robustness with respect to nonlinearity and explicitly nonlinear extensions, as well as advanced topics such as adaptive control and model predictive control. New students, as well as scientists from other backgrounds who want a concise and easy-to-grasp coverage of control theory, will benefit from the emphasis on concepts and broad understanding of the various approaches.

Inhaltsverzeichnis

Frontmatter

Open Access

Chapter 1. Introduction

Abstract
This book introduces the basic principles of control theory in a concise self-study guide. The introductory chapter provides an overview of the three parts of the book: basic principles, design tradeoffs, and common challenges.
Steven A. Frank

Basic Principles

Frontmatter

Open Access

Chapter 2. Control Theory Dynamics

Abstract
The mathematics of classical control theory depends on linear ordinary differential equations, which commonly arise in all scientific disciplines. Control theory emphasizes a powerful Laplace transform expression of linear differential equations that helps in the conceptual understanding and analysis of complex systems.
Steven A. Frank

Open Access

Chapter 3. Basic Control Architecture

Abstract
This chapter introduces the common alternative structures of control systems, with emphasis on feedback control. Error-correcting feedback plays a central role in robust control systems. The classic example of proportional, integral, and derivative control is used to illustrate the sensitivities of control systems and the design tradeoffs that arise between alternative performance goals.
Steven A. Frank

Open Access

Chapter 4. PID Design Example

Abstract
This chapter continues to develop the example of proportional, integral, and derivative control. The analysis illustrates the classic responses to a step change in input and a temporary impulse perturbation to input. The techniques for analyzing and visualizing dynamics and sensitivities are emphasized, particularly the Bode gain and phase plots.
Steven A. Frank

Open Access

Chapter 5. Performance and Robustness Measures

Abstract
A theory of design tradeoffs requires broadly applicable measures of cost, performance, stability, and robustness. This chapter introduces the key measures of performance. The following chapters apply these measures to the analysis of particular systems.
Steven A. Frank

Design Tradeoffs

Frontmatter

Open Access

Chapter 6. Regulation

Abstract
This chapter develops the techniques needed to analyze how quickly a system can return to its setpoint after disturbance. The analysis also considers the design tradeoffs that arise with respect to other measures of performance, such as system stability or responsiveness to a change in setpoint.
Steven A. Frank

Open Access

Chapter 7. Stabilization

Abstract
The previous chapter assumed that the intrinsic system process has a given unvarying form. The actual process may differ from the given form or may fluctuate over time. Designing a control system that can perform well when the intrinsic dynamics are uncertain raises new challenges. This chapter introduces the fundamental concepts of designing stable systems under uncertainty.
Steven A. Frank

Open Access

Chapter 8. Tracking

Abstract
The previous chapters focused on a system’s ability to reject perturbations and to remain stable with respect to uncertainties. This chapter focuses on a system’s ability to track external changes in the environment or changes in the system’s desired setpoint.
Steven A. Frank

Open Access

Chapter 9. State Feedback

Abstract
Earlier chapters focused on the inputs into a system and the outputs produced by a system. This chapter considers the internal dynamics of the system. For example, in the regulation of an organism’s body temperature, we could model performance and cost in terms of the system’s body temperature output. Alternatively, the internal dynamics of the system may include the burning of stored energy, the rise and fall of various signaling molecules, the dilation of blood vessels.
Steven A. Frank

Common Challenges

Frontmatter

Open Access

Chapter 10. Nonlinearity

Abstract
Real systems are nonlinear. This chapter begins with three reasons why the core theory of control focuses on linear analysis. The chapter continues by introducing various design methods that explicitly consider nonlinear system dynamics.
Steven A. Frank

Open Access

Chapter 11. Adaptive Control

Abstract
The parameters of a process may be unknown or may change slowly over time. This chapter discusses how one can control a process with unknown parameters. Adaptive methods adjust parameters in response to information about external inputs and system outputs. Adaptive error-correcting techniques often provide a good approach to coping with unknown nonlinear system dynamics.
Steven A. Frank

Open Access

Chapter 12. Model Predictive Control

Abstract
Control design often seeks the best trajectory along which to move a system from its current state to a target state. Most control methods consider only the first step of the full trajectory toward the target state. Model predictive control considers the full sequence of steps required to move the system optimally from its current state to a future target. The control system then applies the first inputs to start the system along that optimal trajectory. However, rather than continuing, the system takes new inputs and recalculates a new optimal trajectory based on its updated information. The system then begins to move along the new trajectory, updates again, and adjusts its trajectory again. By repeated updating, the system can often perform very well with limited information about nonlinear dynamics and other uncertainties.
Steven A. Frank

Open Access

Chapter 13. Time Delays

Abstract
Delays often occur between an input into a system and the output from that system. Delays complicate dynamics, create system instabilities, and reduce the information that systems can use to respond to the environment. Adjusting for delays often requires systems to predict future states based on past inputs. Error-correcting feedback can enhance a system’s predictions and improve its ability to cope with delays.
Steven A. Frank

Open Access

Chapter 14. Summary

Abstract
This chapter summarizes the three key topics of feedback, robust control, and design tradeoffs.
Steven A. Frank

Backmatter

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