A new approach for automatic control modeling, analysis and design in fully fuzzy environment

Abstract

The paper presents a new approach for the modeling, analysis and design of automatic control systems in fully fuzzy environment based on the normalized fuzzy matrices. The approach is also suitable for determining the propagation of fuzziness in automatic control and dynamical sys- tems where all system coefficients are expressed as fuzzy parameters. A new consolidity chart is sug- gested based on the recently newly developed system consolidity index for testing the susceptibility of the system to withstand changes due to any system or input parameters changes effects. Implementation procedures are elaborated for the consolidity analysis of existing control systems and the design of new ones, including systems comparisons based on such implementation consolid- ity results. Application of the proposed methodology is demonstrated through illustrative examples, covering fuzzy impulse response of systems, fuzzy Routh-Hurwitz stability criteria, fuzzy con- trollability and observability. Moreover, the use of the consolidity chart for the appropriate design of control system is elaborated through handling the stabilization of inverted pendulum through pole placement technique. It is also shown that the regions comparison in consolidity chart is based on type of consolidity region shape such as elliptical or circular, slope or angle in degrees of the centerline of the geometric shape, the centroid of the geometric shape, area of the geometric shape, length of principal diagonals of the shape, and the diversity ratio of consolidity points for each region. Finally, it is recommended that the proposed consolidity chart approach be extended as a unified theory for modeling, analysis and design of continuous and digital automatic control sys- tems operating in fully fuzzy environment. � 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).