Modeling of Digital Control Systems

This chapter explores the modeling concept of digital control systems. The configuration includes a digital-to-analog converter (DAC), an analog subsystem, and an analog-to-digital converter (ADC). The DAC converts numbers calculated by a microprocessor or computer into analog electrical signals that can be amplified and used to control an analog plant. The analog subsystem includes the plant as well as the amplifiers and actuators necessary to drive it. The output of the plant is periodically measured and converted to a number that can be fed back to the computer using an ADC. It begins by developing models for the ADC and DAC, then for the combination of DAC, analog subsystem, and ADC. Following this, it develops models for the various components of this digital control configuration. Many other configurations that include the same components can be similarly analyzed. It then describes the procedure of obtaining the transfer function of an analog system with analog-to-digital and digital-to-analog converters including systems with a time delay. Finally, it describes the steady-state tracking error for a closed-loop control system and the steady-state error caused by a disturbance input for a closed-loop control system.