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 systems
where all system coefficients are expressed as fuzzy parameters. A new consolidity chart is suggested
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 consolidity
results. Application of the proposed methodology is demonstrated through illustrative examples,
covering fuzzy impulse response of systems, fuzzy Routh–Hurwitz stability criteria, fuzzy controllability
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 systems
operating in fully fuzzy environment. |
