The controller in an analog control system uses analog electronic, mechanical, electromechanical, or hydraulic devices. In contrast, a digital control system uses digital electronics hardware, usually in the form of a programmed digital computer, as the heart of the controller. Like analog controllers, digital controllers normally have analog elements at their periphery to interface with the (analog) plant; thus, it is the internal workings of the controller that distinguishes a digital control system from an analog control system. As a result of using digital computers as control system controllers, the signals in the system controller must be in the form of digital signals, and the control system itself usually is treated mathematically as a discrete-time system. In this chapter, the two operations, the sampling of continuous-time signals and the reconstruction of a continuous-time signal from samples, are considered. The sampling rate is an important parameter in the design of a digital control system. The best sampling rate for a digital control system is the lowest rate that meets all performance requirements. Selection of the sampling rate to meet certain performance requirements is discussed. Because digital controllers are implemented with finite word length registers and finite precision arithmetic, their signals and coefficients can attain only discrete values. Therefore, further analysis is needed to determine if the performance of the resulting digital controller in the presence of signal and coefficient quantization is acceptable. In the final section of the chapter, we discuss error sources that exist in the digital signal processing that takes place in digital controllers. These error sources are generated by coefficient quantization, by quantization in analog-to-digital conversion, and by arithmetic operations. Limit cycles and deadbands are also discussed.
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Santina, M.S., Stubberud, A.R. (2005). Basics of Sampling and Quantization. In: Hristu-Varsakelis, D., Levine, W.S. (eds) Handbook of Networked and Embedded Control Systems. Control Engineering. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4404-0_3
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