Fault Detection And Fault-tolerant Control For Several Kinds Of Parabolic Systems

With the complexity and interconnection of automation system,the probability of system component failure is increasing.According to the fault location,system faults can be divided into three types:actuator fault,sensor fault and component fault.Among them,because the actuator is linked to the control signal and needs to frequently achieve the physical movement of a specific target,it has a high failure rate,which is also the focus of this paper.The occurrence of faults often causes the performance degradation of the whole system,and may even lead to the major disaster.Therefore,when the system is running,detecting the potential failure as early as possible and taking action before the failure occurs can minimize the economic loss and avoid the dangerous accident.Accord-ingly,fault detection technology is also widely concerned.The fundamental purpose of fault detection is fault-tolerant control,that is,once a fault is detected in a closed-loop system,it is necessary to compensate the impact of the fault,so that the system has a fault-tolerance performance.Therefore,in recent decades,both fault detection technol-ogy and fault-tolerant control technology have been a hot control design topic in system reliability control design,and its theoretical research provides an important guarantee for the safe operation of automation system.Ordinary differential systems have been systematically studied in fault detection and fault-tolerant control technology.However,controllers are often used to adjust spatial variables such as pressure,concentration or temperature in practical engineering opera-tions.So it is necessary to study the fault and fault-tolerant control of partial differential systems.Parabolic system is widely used in heat transfer,water pollution prevention,flu-id dynamics and so on,which is an important partial differential system.Therefore,this paper studies the fault detection and fault-tolerance control of several parabolic systems.The considered fault-tolerant control problem combines the cost-reducing sampled-data control strategy and boundary control strategy.The passive fault-tolerant control based on spatial sampled-data,passive fault-tolerant control based on spatio-temporal sampled-data and active adaptive fault-tolerant control based on boundary control are studied respec-tively,and the conclusions obtained are applied to thermal detection of shallow geother-mal system and thermal fault-tolerant control of CPU chip.The specific research contents of this paper are as follows:Firstly,for a class of disturbed parabolic system,using the peak-to-peak technique,inequality technique and Description method,a robust adaptive threshold for fault detec-tion based on interval estimation is given by the constructed Lyapunov functional under the condition of bounded disturbances.The theoretical criterion is expressed only through system parameters,making the fault detection mechanism easy to calculate and imple-ment.In addition,since disturbance exists,the obtained robust adaptive threshold can effectively reduce the false alarm rate.Secondly,for a class of stochastic parabolic system,the state vector and error vector are combined to extend the original system to a new stochastic augmented system when the actuator fails.On this basis,an observer-based H_∞fault-tolerant controller is proposed to compensate the effects of fault and disturbance.Furthermore,the obtained sufficient conditions can be solved by linear matrix inequalities.Thirdly,for stochastic parabolic systems,a spatial sampled-data fault-tolerant con-troller is designed under the actuator with failure fault.In the case of stochastic term,boundary disturbance,spatial diffusion,discrete term and actuator fault coexistence,sev-eral criteria are proposed for the system to achieve mean square exponential stability and robust mean square finite-time stability.Results are further extended to stochastic reaction convection(advection)diffusion systems.In addition,the mean square H_∞performance of stochastic parabolic systems with boundary disturbance is studied.By means of bound-ary homogeneous transformation and Lyapunov functional method,sufficient conditions are obtained to guarantee the H_∞performance.Then,for a class of delay parabolic system,a spatio-temporal sampled-data con-troller is further designed under the actuator with failure.A like-Lyapunov functional is constructed to analyze system performance due to the difficulty of time discrete term in spatio-temporal sampled-data.The criterion of system stability is obtained by using Ha-lanay inequality,Description method and Razumikhin method.The effects of maximum spatial sampled-data interval and delay on system stability are also revealed:The smaller the sampling interval and delay,the more beneficial the system stability is.Finally,a boundary fault-tolerant controller is designed for a class of stochastic parabolic system with boundary actuator faults.Without accurate fault information,the indirect adaptive method and direct adaptive method are used respectively to obtain the asymptotic stability of the system.The considered actuator failures include interrupt,failure,offset and non-parametric stuck.In addition,all the theoretical results are verified by numerical examples or practical examples.