TABLE OF CONTENTS All switching circuits including all AC/DC rectifiers, DC/AC inverters, DC/DC converters and AC/AC (AC/DC/AC) converters are working in the discrete-time state. Therefore, they have to be described by digital control theory rather than analog control. This chapter mainly describes the mathematical modeling for these four types of converters in digital control.
Analog control theory and cybernetics describe the systems working in the continuous time process. All parameters in these systems vary from time to time continuously. The dynamic process can be described by differential equations and Laplace transform operations. If there is any element in a control system that is discrete-time circuit, then the whole system has to be treated as a discrete-time system since the signal transferring is no longer continuously varying.
All switching circuits are working in the discrete-time mode. They have not responded to the signal change in the continuous state. Therefore, any system involved in a switching circuit has to be treated as a discrete system.
Most digital control systems have the analog output functions. For example, digitally controlled variable-speed motor drive systems have analog output speed in continuous-time mode although their controllers are digital signal processor (DSP).The differences between analog and digital control systems are in the following aspects:
transfer function s form,
stability characteristics,
unit-step responses and impulse responses.
The transfer function of all analog control systems is described by the Laplace transform in the s-domain. The stability characteristics and criteria sates that if all poles of the transfer...
