New approach for automatic control modeling and analysis using Arithmetic And Visual Fuzzy Logic-based Representations in fully fuzzy environment

The paper presents a new approach for the fuzzy modeling and analysis of automatic control systems in fully fuzzy environment. The proposed technique is based on the normalized fuzzy matrices and is an extension of the Arithmetic and Visual Fuzzy Logic-based Representations developed recently by Gabr and Dorrah. The approach is also suitable for determining the propagation of fuzziness in automatic control and 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 problems with parameters expressed in fully fuzzy environment. These problems cover 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 opens the door for a unified theory for fuzzy modeling, analysis and design of continuous and discrete automatic control systems operating in fully fuzzy environment.