This paper will establish the importance and significance of studying the fractional-order control of nonlinear dynamical systems. The foundation and the sources related to this research scope is going to be set. Then, the paper incorporates a brief overview on how this study is performed and p resent the organization of this study. The present work investigates the effectiveness of the physical-fractional and biological-genetic operators to develop an Optimal Form of Fract ional-order PID Controller (O2Fo-PIDC). The newly developed Fo-PIDC with optimal structure and parameters can, also, imp rove the performances required in the modeling and control of modern manufacturing-industrial process (MIP). The synthesis methodology of the proposed O2Fo-PIDC can be viewed as a mu lti-level design approach. The hierarchical Multiobject ive genetic algorith m (M GA), adopted in this work, can be visualized as a comb ination of structural and parametric genes of a controller orchestrated in a h ierarch ical fashion. Then, it is applied to select an optimal structure and knowledge base of the developed fractional controller to satisfy the various design specification contradictories (simplicity, accuracy, stability and robustness).

-Designing an effective criterion and learning algorithm for find the best structure is a major problem in the control design process. In this paper, the fuzzy optimal control methodology is applied to the design of the feedback loops of an Exothermic Continuous Stirred Tank Reactor system. The objective of design process is to find an optimal structure/gains of the Robust and Optimal Takagi Sugeno Fuzzy Controller (ROFLC). The control signal thus obtained will minimize a performance index, which is a function of the tracking/regulating errors, the quantity of the energy of the control signal applied to the system, and the number of fuzzy rules. The genetic learning is proposed for constructing the ROFLC. The chromosome genes are arranged into two parts, the binary-coded part contains the control genes and the real-coded part contains the genes parameters representing the fuzzy knowledge base. The effectiveness of this chromosome formulation enables the fuzzy sets and rules to be optimally reduced. The performances of the ROFLC are compared to these found by the traditional PD controller with Genetic Optimization (PD_GO). Simulations demonstrate that the proposed ROFLC and PD_GO has successfully met the design specifications.

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A fuzzy logic controller with the fuzzy knowledge base: scaling factors of the input/output variables, membership functions and the rules are optimized by the use of the genetic algorithms, is presented in this work, and its application in the highly nonlinear systems. The fuzzy structure is specified by a combination of the mixed Sugeno's and Mamdani's fuzzy reasoning. The mixed, binary-integer, coding is utilized to construct the chromosomes, which define the set of necessary prevailing parameters for the conception of the desired controller. This new controller stands out by a non standard gain (output scaling factor) which varies linearly with the fuzzy inputs. Under certain conditions, it becomes similar to the conventional PID controller with non-linearly variable coefficients. The results of simulation show, well, the efficiency of the proposed controller.

In this paper, the harmonic response of an electric system under imbalance conditions is established. Symmetrical harmonic components are proposed to give a new way of interpreting resonance occurrence in three-phase power systems. A three-phase harmonic bus impedance matrix (THBIM) for a simple distribution system is derived using analytical procedures. The development of frequency scans for the THBIM elements in both phase and sequence reference frames is carried out. Simulation results show the benefits of the harmonic sequence components for characterization of the harmonic resonance conditions in unbalanced distribution systems, and for characterizing the effectiveness of the mitigating techniques. This method offers a new way to conduct harmonic analysis and diagnosis in unbalanced power systems.