Chapter 3 - Modeling of digital control systems

Abstract

As in the case of analog control, mathematical models are needed for the analysis and design of digital control systems. A common 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 and 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. In this chapter, we develop models for the various components of this digital control configuration. Many other configurations that include the same components can be similarly analyzed. We begin by developing models for the ADC and DAC, then for the combination of DAC, analog subsystem, and ADC. We also show how to calculate the steady-state tracking error for standard test inputs and the error due to a disturbance. Next, we show how to simulate a digital control system using SIMULINK. Finally, we discuss the sensitivity function and how it can be used to assess the effect of modeling errors.