Dynamic Modeling And Control Of The Electrical Behavior Of Solid Oxide Fuel Cell Using Fractional Calculus

Solid oxide fuel cell (SOFC) is a clean and high efficient energy source with a remarkable prospect in future. However, the SOFC stack is a complex object consisted of a lot of physicochemical characteristics such as fluxion, heat transfer, mass transfer process and electrochemical reaction. The control technology of SOFC stack is a difficult and unsolved subject at present. As a result of experimental analysis, the electrochemical reaction of SOFC is a fractional calculus process. It is more suitable to describe and control the SOFC pile with fractional order systems. The fractional calculus is a subject of integration and differentiation to an arbitrary order, and it reflects the gradual changes of integral and differential order, so it is flexible. In these recent years, fractional calculus has been introduced to the field of control science but the theory of fractional order system has not consummated even until now.This thesis is trying to introduce and study this theory and make applications on SOFC.This thesis is based on the"863"national major project"Development of the Mesothermal Planar Solid Oxide Fuel Cell Power Systems". Firstly, this thesis summarily introduces the definition and basic properties of fractional calculus and how to describe objects with fractional order systems. Secondly, the analytical and discrete numerical solution of fractional order differential equations are summarized.Through the study of dynamic experimental model and mechanism model of electrical characteristic of SOFC,the fractional dynamic experimental model of the SOFC stack's output electrical characteristic is established.Then the bottle-neck that SOFC stack's electrical characteristic of dynamic experimental model can't be accurately described and used in real-time control is broken; Thirdly, a novel genetic algorithm (NGA) is introduced and improved, and a new method of fractional order system identification based on the simple model and NGA is presented.Then it is used to identify the electrical characteristic model of SOFC, and the result of its application on SOFC shows a good performance. Fourthly, two numerical approaching methods of fractional order PIλDμcontroller are introduced,and compared in frequency-domain with Bode diagram in detail.The model of fractional order PIλDμcontroller is realized with Matlab/Simulink, and a simulated example that NGA is used to optimize the five parameters of PIλDμcontroller is given. Finally, the applications that using PIλDμand PID controllers to control integral SOFC model and fractional SOFC model separately imply that the performance of PIλDμcontroller is better than PID controller.The study of this thesis provides some new key technology and methods to improve the performance of control unit about SOFC stack's output electrical characteristic which require speedy dynamic response, good stability and small overshoot.