Fault Estimation Design Based On Iterative Learning Scheme

In the modern complex control systems,the increasing demand for safety and reliability has motivated the need for fault detection and isolation(FDI).Fault estimation is an important part of FDI,which is supplementary to give the exact information of faults,thereby helping to reconstruct fault signals.Therefore,more and more scholars have paid attention on the fault estimation methods.Due to batch reciprocating,most of the industrial production systems repeat the same task and the cycle start all over again with the same initial condition and system structure.However,the existing fault estimating methods are proposed for continuous operation system and igore the repetitive nature.Affected by environmental factors inevitably,the time delay,parameter uncertainty and randomly trial length have occurred in the repetitive system,which seriously affect the operation performance and fault estimation results.Iterative learning approaches have attracted more and more attention because that the fault information obtained from previous iteration can be utilized in current iteration to get more precise fault estimating results.These motivate our study.This paper proposes fault estimation approaches using iterative learning scheme for reconstructing the actual fault signal in different repetitive systems.Different from existing fault estimating schemes,the state error information and fault estimating information in the previous iteration are used in the current iteration to improve the estimating results.The stability and convergence of iterative learning observer and uniformly boundedness of dynamic error system are achieved by using Lyapunov function and optimal function design.Simultaneously,an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality(LMI)and norm theory.Iterative learning observer based fault estimation method is presented for repetitive system with measurement noise.It can perfectly track the fault trajectory and reconstruct the magnitude and shape of the fault simultaneously.Firstly,state observer is proposed to reconstruct the state and output.Then Lyapunov function is designed to guarantee the stability of error distributed system.By making use of iterative learning scheme,the error item in the traditional fault estimation is substituted by the integrated error composed of state predictive error and tracking error in the previous iteration.Further,optimal function is proposed to prove the convergences of iterative learning fault estimator.Such that the tracking error converges to an interval value after several iterations.To deal with the time-delay and estimation overshoot caused by the P-type iterative learning fault estimator,an improved PD-type method based on time-delay term is proposed.On the one hand,time-delay term is considered in state observer to reduce the state and output time-delay.On the other hand,time-delay term is imported in fault estimator design to eliminate the time delay of fault estimation results.As a result,the system function can be rewritten to ensure the convergence of the output and restrict the influence of time delay.Iterative learning scheme based fault estimation method is presented to accurately estimate the intermittent fault of uncertain system.Reconstruction error in time domain and estimation error in iteration domain are both used to design fault estimator.The Lyapunov function is constructed to reduce the influence of system state and output reconstruction result caused by parameter uncertainties.The optimal function contains robust factor and iteration factor is proposed to proven the convergence of the proposed fault estimation method.Compared with traditional adaptive fault estimation method,the proposed method can obtain more accurate results than the adaptive observer-based fault estimation algorithm.Iterative learning scheme based fault estimation observer is designed for a class of nonlinear systems with randomly changed trial length.An average factor is defined to deal with the lack and redundancy in tracking information caused by randomly trial length.In linear system,only average factor is used in fault estimation method.Due to the constant length of average factor,the iterative learning error converges to a finate range.In nonlinear system,a forgetting factor is proposed in fault estimation method.Then iterative learning fault estimation error converanges to a constant value after serveral iterations.The observer gains and iterative learning law indexes are computed by solving the proposed conditions under constraints.Finally,numerical examples are proposed to illustrate the effectiveness of the proposed method and comparability examples are presented to demonstrate the superiority of the algorithm.The simulation results show that the proposed methods have good performance for fault estimation and have certain reference value for safety and reliability.Simultaneously,the proposed fault estimation theory has wide industrial applications prospect.