Abstract - The paper presents a new approach for the fuzzy
modeling and analysis of automatic control systems in fully fuzzy
environment. The approach is based on the normalized fuzzy
matrices and an extension of the Arithmetic and Visual Fuzzy
Logic-based Representations developed recently by Gabr and
Dorrah. The approach is also suitable for fuzzy dynamical
systems where all system coefficients are expressed as fuzzy
parameters. It is simply based on the assignment of
corresponding fuzzy levels for parameters uncertainty that is
made in a heuristic way circumventing the previous difficulties in
assuming probabilistic or membership functions.
Implementations of the approach are carried out for solving
selected automatic control problem with their parameters
expressed in fully fuzzy environment. These problems involve
fuzzy impulse response of systems, fuzzy Routh-Hurwitz stability
criteria, fuzzy controllability and observability, and the
stabilization of inverted pendulum through pole placement
technique. The results demonstrated the robustness of the
proposed formulation and illustrated in a systematic way how the
system parameters fuzziness effect on output results can be
effectively tracked for monitoring and control. Finally, it is
pointed out that the suggested Arithmetic and Visual Fuzzy
Logic-based Representations will open the door for a unified
theory for fuzzy modeling, analysis and control for continuous
and discrete |
