Finite Wordlength Controller Realizations Using the Specialized Implicit Form Thibault Hilaire, Philippe Chevrel, James F. Whidborne

A specialized implicit state-space representation is introduced to deal with finite wordlength effects in controller implementations. This specialized implicit form provides a macroscopic description of the algorithm to be implemented. So, it constitutes a unifying framework, allowing to encompass various implementation forms, such as the δ-operator, the ρDirect Form II transposed, observer-based and many other realizations considered usually separately in the literature. Different measures quantifying the finite wordlength effects on the overall closed loop behaviour, are defined in this new context. They concern both stability and performance. The gap with the infinite precision case is evaluated classically through the coefficient sensitivity and roundoff noise analysis. The problem of determining a realization with minimum finite wordlength effects can subsequently be solved using appropriate numerical methods. The approach is illustrated with two examples. Key-words: Digital Control, Finite Wordlength Effects, Digital Controller Implementation, Optimal Realization