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

Abstract

The consequences of the finite wordlength on the performance of a digital fuzzy logic controller (FLC) based on the Mamdani's inference algorithm are investigated. Digital implementations of FLC's involve three main types of errors due to the finiteness of the wordlength: the analog-to-digital errors, the membership function errors, and the 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 timedomain 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.

A real-time fuzzy hardware structure for disparity map computation

“…One basic type of error due to the word length finiteness in digital implementations of FISs is the membership function errors. These errors result from the digitization of the membership function values [24]. An increased number of bits improve the accuracy, but hardware complexity also increases, complicating the implementation of the system.…”

Uma Nova Arquitetura Modular para Circuitos Geradores de Função de Pertinência com uso em Projeto de Microprocessador Difuso

“…A implementação analógica deste circuito foi escolhida pelas vantagens anteriormente citadas. Também, em grande parte das situações onde um microcontrolador lógico difuso é utilizado, os sinais de entrada são provenientes de sensores que produzem sinais analógicos como saídas.. Por esta razão, o microcontrolador sendo analógico evita-se a necessidade do uso de conversores A/D em suas entradas e os consequentes erros relacionados com os mesmos [10].…”

Mixed-Signal Neuro-Fuzzy Processor Implementations: Sequential Architectures and Circuit-Level Description

“…5-6. takes advantage of the large-signal transconductance characteristics of two MOS-transistor differential pairs to obtain the required bell-shaped function, inherently transconducing external voltage signals into current-mode signals. Both position and slope are digitally programmable with 6-bit resolution, being this resolution adequate for this closed-loop controller application [33]. The use of transistor arrays as input compound transistors in the differential pairs makes their transconductance digitally tuneable to adjust the slope of the characteristic transfer function.…”

“…Although precision requirements for the learning phase of neural and neuro-fuzzy systems can be high, for the recall phase they are less than 8 equivalent bits in most neural [4] and fuzzy [33] applications. Therefore, proper analog circuits can be used to perform this phase.…”