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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.