Control Theory Fundamentals PDF Download

This book contains a set of notes accompanying a short seminar in elementary control theory. An aim of the seminar is to present the fundamentals of control theory in a way accessible to engineers whose principal area of expertise may lie elsewhere. The purpose of the book is to provide an additional resource for the audience. Chapter 1 presents a review of the elementary mathematical results necessary for our further study. The concept of a linear system is introduced together with a review of differential equations and their solution using the method of Laplace transforms. The behaviour of classical first and second order systems is described in both the time and frequency domain. Chapter 2 examines the application of negative feedback from the perspective of the frequency domain. The Nyquist plot is developed as a powerful design tool in feedback control. We focus particularly on the role of the open loop transfer function in determining the ability of the control loop to follow a reference trajectory and to reject unwanted disturbances. A brief description of model uncertainty and robust control is also given. Chapter 3 is concerned with control system performance in the time domain. This is typically visualised in terms of a transient step response, the features of which are required to be optimised by adjusting terms in the controller. We then describe the root locus design method: a semi-graphical technique which provides insight into transient response based on the location of the closed loop roots in the complex plane. Chapter 4 deals with the theory of sampled systems, including an explanation of the z transform. An overview is provided of the mapping of the complex plane under discrete time transformation. Chapter 5 briefly covers the design of closed loop digital controllers. Two fundamental approaches are described: design using emulation attempts to replicate the performance of an existing prototype controller, while direct design methods conduct the entire design process in the digital domain. Finally, chapter 6 describes several issues and pit-falls which may confront the designer of digital control systems. Among the topics discussed are sample rate selection, phase shift arising from sample-to-output delay, signal reconstruction and aliasing.