Digital Power Electronics and Applications

Chapter 3: Basic Mathematics of Digital Control Systems

Digital control systems are described by digital control theory. Some necessary fundamental knowledge on digital control theory is introduced in this Chapter as mathematical tools, which are used in further Chapters.

3.1 INTRODUCTION

Today, computers are more advanced and are almost inevitable in many industries. As computers operate on digital signals, the need for handling digital signals also increased proportionally. High-speed processing capabilities of modern computers attracted applications that make use of digital signals, which further accelerate the development of the use of digital signals. Hence, digital control systems have gradually become more prominent in today s industries. Accompanying the growth of digital signals, the use of switching circuits also increases tremendously for industrial applications. These switching circuits transfer energy from the source to the load in switching status. For example, the energy from the source is transferred to the load in discrete format. In the 1980 s Dr. F. L. Luo paid attention to this phenomenon, which differs from the traditional analog control methods. Note that any system that involves the switching circuits must be in the discrete-data control system and the sampling interval is the switching period T, where T = 1/ f C in which f C is the switching frequency.

Signals are variations that transport information from one place to another. There are two main types of signals: the analog signals and the digital signals. Analog signals, also known as continuous-time signals can take any value and are defined at every...

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