Implementation of Digital Controllers using Fixed Point Arithmetic; Some Stability Consideration

The analysis and design of digital controllers on microprocessors using fixed point arithmetic have been considered from the point of view of the stability specifications. Simple formulae for estimating R.M.S. and absolute bounds on limit cycles, if they arise, are provided. It is shown that the limit cycle level can be neglected or can be brought down to within the specification of the system performance. The Claasen et al. criterion for testing the absence of limit cycles is introduced and applied if the system cannot tolerate certain types of limit cycles. Finally the Vidal-Wegrazin criterion is modified and applied as a stability test whenever the absolute stability of the system is crucial.