Consequences of the digitization on the performance of a fuzzy logic controller

The consequences of the finite wordlength on the performance of a digital fuzzy logic controller (FLC) based on Mamdani´s inference algorithm are investigated. Digital implementations of FLCs involve three main types of errors due to the finiteness of the wordlength: analog-to-digital errors, membership function errors, and arithmetic errors. First, a statistical evaluation of the consequences of these errors is performed. The effects of the digital resolution on the controller response are discussed. Then, the dynamic behavior of a closed-loop fuzzy system composed of a digitized FLC and a second-order plant is evaluated; a qualitative evaluation of time-domain parameters as a function of the universe discretization is carried out. The results show that, as in the case of conventional control strategies, bias effects and limit cycles are generated as a consequence of the digitization. Although these distortions diminish when the discretization is sufficiently refined, they are very difficult to predict because of the nonlinear nature of both quantization and fuzzy operation. In this sense, the availability of computer-aided design (CAD) tools that permit the specification of the wordlength is essential to validate the design