Research On Stability And Boundary Feedback Control Of Coupled PDE-ODE System

Many complex engineering processes can be modeled as parameter systems for coupled hyperbolic partial differential equations(PDE)and ordinary differential equations(ODE).Control analysis and design are more complicated due to the infinite dimensionality of the state space of the distributed parameter system and the complexity of the system itself,as well as the inevitable uncertainty and disturbance of the system.In this paper,we consider a class of hyperbolic systems with distributed parameters,and select interconnected continuous stirred tank reactors(CSTR)and plug flow reactors(PFR)systems,which interact with systems with lumped parameters through dynamic boundary conditions effect.Firstly,the operating characteristics,dynamics modeling basis of PFR system and CSTR system are described in detail.Secondly,the three coupling modes of PFR and CSTR systems are analyzed.The coupled hyperbolic PDE-ODE system is modeled for the coupling mode of PFR-CSTR.Analyze the steady state of the coupled system.In order to facilitate understanding and simplify the calculation,the system is linearized according to the steady state to construct the deviation system.Finally,the deviation system is standardized.Secondly,using the model to design the proportional feedback controller of the PDE right system state variable measured by the sensor,it can be used to return to ODE to construct a closed-loop system;the definition and characteristics of input-state stability(ISS)and ISS Lyapunov are introduced in detail.The construction of the equation further defines the definition of the system ISS stability.Finally,considering the uncertainty and external disturbance of the system,the input-state stability of the closed-loop system is analyzed,and the sufficient conditions for the stability of the system are given.Finally,an actual chemical reaction process is described.Firstly,the sufficient conditional solution based on the spatial distribution is solved.The inequality of the spatial distribution is reduced by the polyhedral technique.According to the actual parameters,the range of the relevant control coefficients is determined by MATLAB.Further,under the action of the controller the PFR-CSTR model was used to simulate the experiment.The feasibility and effectiveness of the controller and the rationality of the input-state stability analysis of the system were verified by the evolution of each reactant concentration and reaction temperature.