Identification And Control Of Distributed System Of Indoor Carbon Dioxide Concentration

Indoor space is the main place for people to live in.The quality of indoor air has a direct impact on people's health.As one of the indoor pollutants,high concentration of carbon dioxide(CO2)may cause people to suffer headache,palpitation,high blood pressure and other symptoms.Since CO2 always has a stable source and its concentration can reflect the changes of indoor people's state in real time,its concentration is often considered as a good indicator of indoor air quality.Partial differential equation(PDE)system is a form of distributed parameter system(DPS),and belongs to infinite dimensional state space system.PDE system,which reflects the dynamic relationship about time and space,has complex but special regularities and characteristics.It has been widely used in thermal,chemical,aerospace and other engineering systems,as well as ecological systems and social systems.Because of its wide applications,it is of great significance for the research of PDE system.Taking the control of indoor CO2 concentration system as the research objective,a PDE model of indoor CO2 concentration is constructed in this thesis.The parameter identification and control problems are studied in detail based on this model.The main contents of this thesis are as follows:Firstly,according to the advection-diffusion process and the working principle of heating ventilation air conditioning(HVAC),a PDE model of indoor CO2 concentration is constructed for the working condition that both supply vent and return vent are on the ceiling of the room.The physical significance and selection principle of the terms in the model,initial condition as well as boundary condition.In order to prove the validity of the model,we simulate the dynamic process of the models with three different initial conditions and boundary conditions.The results show that the dynamic development of the model is consistent with the real physical process.For the case of model with unknown parameters,the finite difference method and the least square method are combined to estimate the values of the unknown parameters.The effectiveness of this method is verified by simulation.Secondly,based on the constructed model,the PDE system is transformed into a low order ordinary differential equation(ODE)system through the characteristic spectrum method and Galerkin method.For the linear PDE system without disturbance,an output feedback control law with state observer is designed based on the low order model,which makes the closed-loop PDE system converge at a given rate.Also,we analyze the control spillover and observation spillover problems which may occur in this control method.The simulation results show that the controller can accelerate the convergence rate of CO2 concentration in the room.In addition,if there are multiple control sources existed,the fluctuation of dynamic process will be smaller and the overall convergence will speed up.For the PDE system subjected to disturbance,the system is decomposed into slow mode and fast mode by orthogonal projection on system state.The fast mode is treated as the perturbation term based on the singular perturbation theory.For the slow mode,a robust control law is designed to reduce the impact of the disturbance towards the output of the closed-loop PDE system.It guarantees the state robust stability and convergence performance of the system.The effectiveness of this method is verified by the numerical simulation.Finally,we summarize the whole thesis and point out the future research of the CO2 concentration problem.