Research On Fault Detection And Isolation For Dynamic Systems Based On Interval Observers

With the increasing scale and complexity of modern control systems,safety and reliability of the systems are more and more concerned.Therefore,fault diagnosis technique has attracted much wider attention.Fault diagnosis mainly consists of fault detection,fault isolation and fault identification.Fault detection and isolation has become an important subject in fault diagnosis field due to detection of the occurrence of faults and localization of different faults.The key technique of the classical model-based fault detectionscheme is to generate the residual signal and compute the threshold.The remaining taskis to determine the occurrence of faults by designing the residual evaluation function andcomparing it to the threshold.Fault isolation is implemented by a bank of residual generators and thresholds.In particular,observer has developed into an effective residual generator because of estimation ability.Besides the constant threshold,how to design the time-varying threshold for the dynamic systems subject to exogenous disturbanceshas become a research focus in recent years.Rising and developing of interval observer theory in the control field provide a new idea for fault detection and isolation.On the basis of the previous work,this dissertation further studies fault detection and isolation problems for several linear and nonlinear systems.Interval observer based fault detection and isolation schemes are proposed in this dissertation.Compared with the classical method based on state estimation,the interval observers proposed in this paper are able to both generate the residual signals and imply the thresholds.As a result,the scheme need not design the residual evaluation functions and the threshold generators,but it's enough for detection and isolation purposes.Parts of the developed theories are applied to the fault detection and isolation of the one-track model,the benchmark mass-spring system,ship steering model,double-inverted pendulums model and single-link direct-drive manipulator actuated by a permanent magnet brush dc motor.Simulation examples illustrate the effectiveness and superiority of proposed approaches.The main contents are outlined as follows:Chapter 1 systematically analyzes and summarizes the development of fault detection and isolation and the fundamental principle of interval observers.Preliminaries and research methods about the considered problem are also given.Chapter 2 provides an event-triggered fault detection method based on interval observer and investigates the effects of sampling on fault detection performance.First,a novel event-triggering mechanism is developed.Then,an event-triggered interval observer is proposed by taking into account the influence of the disturbances and the event error.Furthermore,the robustness of the residual interval and the fault sensitivity are improved by introducing l₁ and H_? performances.Slack matrices are used to decouple the Lyapunov matrices from the system matrices.The observer design conditions are obtained in the formulation of LMIs.This technique allows removing the constraints on Lyapunov matrices and provides less conservative design conditions.It is shown that the information communication burden is reduced,while the fault detection performance can still be guaranteed.Finally,a simulation example demonstrates the effectiveness and advantages of the proposed method.Chapter 3 investigates the fault detection problem for linear parameter-varying systems.A parameter-dependent interval observer is designed by taking into account the bounds of disturbances.The disturbance attenuation,fault sensitivity and nonnegative conditions are presented by translating the parameter-dependent LMIs into finite ones.In contrast to the existing results based on parameter-independent Lyapunov and slack matrices,the proposed method provides less conservative design conditions.Finally,simulation examples are presented for showing the effectiveness and superiority of the proposed method.Chapter 4 studies the fault isolation problem for fuzzy interconnected systems with unknown interconnections.First,the output-space of each subsystem is partitioned into operating and interpolation regions.Then for each subsystem,a piecewise fault isolation interval observer is constructed by taking into account the bounds of the unknown inter-connections and subsystem disturbances.Accordingly,the effects of the other subsystem faults and disturbances introduced by the interconnections are considered fully.Further-more,l₁ performance is introduced to improve the robustness of the residual intervals against their own disturbances and the interconnections.Meanwhile,H? performance is introduced to increase the sensitivity to their own faults.Finally,the interval observer design conditions are obtained based on piecewise Lyapunov functions,slack matrices and LMI technique.The obtained conditions are less conservative than the existing results with the common and diagonal Lyapunov functions.Simulation examples illustrate the effectiveness and merits of the proposed method.Chapter 5 presents an interval observer based fault isolation method for discrete-time multi-agent systems.For the output feedback based closed-loop MASs with a certain node fault,a bank of fault isolation interval observers are constructed by taking into account the outputs of the neighbor agents,the bounds of one node fault signal and the whole disturbances.Under such framework,each node has the capacity to determine which neighbor node is faulty.Then,the observer gains can be determined by solving the disturbance attenuation,fault sensitivity and non-negativity conditions,simultaneously.Finally,the fault isolation decision is made by determining whether the zero value is included in a certain interval and excluded from the others.The developed techniques are demonstrated in a simulation example.Chapter 6 investigates the fault detection problem for uncertain nonlinear strict-feedback systems with unmeasurable states and unmatched nonlinear fault functions andproposes the prescribed performance based fault detection method.Unlike the method proposed in the previous chapters,the observer-based residual generator in this chapter is proposed by developing the recursive algorithm.In each step,the undetermined function in the observer is designed into two parts,one part of it is a responsibility to offset cross term,and the other part is an assignment to finish correction action by the residual.It turns out that the residual signal satisfies the prescribed performance and all the estimation errors are uniformly bounded in the fault-free case.Furthermore,the fault detection thresholds are computed by using the prescribed performance bound of the residual signal.The fault detection scheme is presented with the fault detectability analysis following close behind.Similar to the previous chapters,the prescribed performance based method can generate the upper and lower residual signals.That is,the observer in this chapter could be regarded as a generalized interval observer.Compared with the fault detection method without considering the prescribed performance bound,the proposed scheme improves the fault detection performance with fewer false alarms caused by overshoot during the transient process.Finally,two comparative examples illustrate the superiority of the proposed method.Finally,the results of the dissertation are summarized and further research topics are pointed out.