Indirect Controls Of Temperature For Reaction-diffusion Processes

This thesis explores indirect controls of temperature for reaction-diffusion processes.The system considered is the cascade of ordinary differential equations and partial differential equations and control input is designed in ordinary differential equations.In industrial production,the system can be used to represent the cascade of chemical reactions and biological fermentation and other issues.The research of the system has a certain value in engineering technology.For reaction-diffusion system,we deal with the cascaded boundary condition(,)= (3()as control input.In this paper,using Backstepping method can design the controller and the stabilization of reaction-diffusion system.Through Backstepping transformation,the reaction-diffusion system is transformed into the exponentially stable target system.In this process,one kernel function is derived.Then the solution of the kernel function is solved,or the well posedness of the kernel function is proved.Output-feedback controller is designed according to the characteristics of the system.Secondly,by inverse transformation,the target system is transformed into the original reaction-diffusion system.Finally,the exponential stability of the closed-loop system is proved by the boundedness of the transformation and its inverse transformation.For indirect controls of temperature for reaction-diffusion processes,the existing results are boundary control of partial differential equations.Compared with the existing results,this thesis is to solve the cascaded system with control input in ordinary differential equations.In this paper,two indirect controls of temperature are proposed for one-dimensional reaction-diffusion process and two-dimensional reaction-diffusion process.Besides,two numerical simulations are carried out to verify the effectiveness of the method.