ABSTRACT
This chapter discusses three error sources that may occur in digital processing of controllers. These error sources are coefficient quantization, quantization in AID conversion, and arithmetic operations. The chapter discusses limit cycles and deadbands and presents the reviews of fixed and floating point number arithmetic. It describes the major sources of error caused by finite word length and then determine their effects on the behavior of digital controllers. These errors are coefficient quantization, quantization errors in A/D converters and quantization errors in arithmetic operations. There are many choices of arithmetic that can be used to implement digital controllers. The two most popular ones are fixed-point and floating-point binary arithmetic. One approach for analyzing roundoff and truncation errors generated in digital processing of controllers is to derive deterministic upper bounds on the maximum errors that can possibly result from roundoff or truncation.
