Research On Nonlinear Fault Diagnosis And Fault-Tolerant Control

The increasing reliability and safety requirements of modern technological systems have motivated enormous research activities in search for new design methodologies, for detecting and identifying the instrument malfunction, accommodating the component fail-ures and maintaining the acceptable system stability and performances. These types of control strategies are often known as fault diagnosis(FD) and fault-tolerant control(FTC) methodologies. Due to the universal existence of autologous nonlinearities of nonlinear systems and unknown environmental disturbance, fault diagnosis and fault-tolerant con-trol for nonlinear systems brings more increased safety and reliability demands beyond what conventional methods in this field can offer.Most of the exiting results about nonlinear fault diagnosis observer always focus on ensuring the accuracy of fault estimation and the sensitivity of fault detection. Given the increasing needs of modern industry systems for safety and reliability, the require-ments for the real-time characteristic, quickness, robustness and isolability of fault di-agnosis cannot be neglected any more. The increasing requirements bring a lot of new difficult research issues to be solved for fault diagnosis observer design method, which are classified as unknown disturbance decoupling-based diagnosis method and parameter estimation-based diagnosis method. For example, the unknown disturbance decoupling-based diagnosis method can hardly maintain the diagnosis robustness when dealing with the systems with unstructured uncertainties and disturbance(e.g., stochastic variables); the parameter estimation-based diagnosis method is not able to guarantee the real-time char-acteristic and the quickness when dealing with uncertain nonlinear systems; the unknown disturbance decoupling-based diagnosis method is only able to detect the occurrence of faults and not able to do isolation, meanwhile the parameter estimation based diagnosis method is difficult to guarantee the diagnosis robustness when dealing with fault isolation; in some industry systems such as paper-making equipment fault diagnosis is difficult be-cause the measurement is only probability distribution function of output etc. In general, the research for improving high performances, e.g., the real-time characteristic, quick- ness, robustness, isolability of nonlinear fault diagnosis methods meets the needs of the developing more safe complex industrial control procedures.As the same time, the research of nonlinear fault-tolerant control is closely related to the research of nonlinear fault diagnosis. For the increasing scale and complexity of industrial production systems, the existing nonlinear fault-tolerant control methods reveal more and more unsolved problems, because of the increasing nonlinearity of the con-cerned industrial control systems, the diversity of appearing fault, the backwardness of the applied controller design and the improving performance requirement. For example, the nonlinear passive optimal fault-tolerant controller designs are always formulated into difficult HJI(Hamilton-Jacobi inequality) which usually has no efficient solution; the ac-tuator deadzone fault in uncertain systems with polynomial growth rate in unmeasurable states causes the construction of adaptive output feedback controller very difficult; the integrated diagnosis and fault-tolerant control problem for uncertain systems is lack of efficient observe design method, at the same time the fault diagnosis is lack of quali-tative analysis on robustness, real-time characteristic, sensitivity and quickness of fault compensation; how to detect and deal with actuator losing-efficiency fault and stuck fault (especially when the stuck value is time-varying) is an open problem mentioned in the existing literature; the reliable cooperative controller design method is expected for net-work communication perturbation in large-scale multi-agent control systems etc. In such situations, the research into developing new fault-tolerant controller design method to deal with the aforementioned fault-tolerant control problems is of great theoretical and applicable importance.For fault diagnosis, this thesis studies several kinds of systems which have indus-trial backgrounds, i.e., gaussian stochastic time-delay systems, non-gaussian uncertain stochastic systems and a class of non-exact-linearizable uncertain nonlinear systems. On the basis of ensuring the accuracy and sensitivity, the robustness of diagnosis is consid-ered together with real-time characteristic and quickness, isolability according to different systems’characteristic. The fault diagnosis methods proposed in this thesis use the non-linear high-gain observer technique to ensure the robustness and sensitivity, and use the nonlinear adaptive observer technique to achieve the estimation and isolation of faults. The designs of fault diagnosis observer implements constructive methods. Though non-linear coordinates transformation, the turning in parameters is completed based on Lya-punov theory and stochastic analysis method. The set of faults which can be detected and isolated, the time for detection and diagnosis, the robustness and the sensitivity are rigorously qualitatively analyzed. For fault-tolerant control, this thesis deals with several representative nonlinear systems, i.e., polynomial systems, strong nonlinear systems with polynomial growth rate in nonlinearities, strict feedback nonlinear systems with uncer-tainties, strong nonlinear systems with nonlinearities in unmeasurable states and complex multi-agent cooperative systems.For nonlinear optimal passive fault-tolerant control problem, a numerical compu-tation method for HJI equation is developed to give a solvable optimization approach; for the strong nonlinear systems with actuator dead-zone fault, a novel numerical con-struction is proposed for an adaptive output feedback controller; for the strict feedback systems with uncertainties, an integrated fault diagnosis-fault tolerant control framework is newly developed by rigorous analysis for robustness and sensitiveness of fault diag-nosis and fault-tolerant strategy; for strong nonlinear systems with actuator stuck fault, a universal fault model is proposed and a new fault diagnosis and fault-tolerant control method is developed by a logic-based adaptive output feedback controller, for strongly coupled multi-agent complex systems, a reliable cooperative controller is given by a net-work communication based adaptive method. Parts of the developed theories are applied to the fault detection filter or fault-tolerant controller designs of biochemical reactors, induction motors, paper machines, surface-mounted permanent magnet synchronous mo-tors (PMSM), F-18HARV-like wing-rock model, single-link flexible-joint robot, multiple motor cart group systems by simulations. Simulation examples illustrate the advantages and effectiveness of our approaches.The main research contents are outlined as follows:Chapter1summarizes the development and main research methods in fault diagnosis and fault-tolerant control literature.Chapter2proposes a high-gain nonlinear observer based fault diagnosis approach for nonlinear stochastic systems with time delays. The system model under consider-ation contains parameter uncertainties, stochastic disturbances, time delays, as well as Lipschitz-like nonlinearities. The objective is to design a robust filter such that the dy-namics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in a sense of mean square. A new high-gain filter idea is introduced to solve the stochastic filtering problem by using the Lyapunov method and stochastic analysis tech-niques. The design of the proposed filter does not necessitate the resolution of any dynam-ics systems and its expression is explicitly given, i.e., its calibration is achieved through the choice of a single parameter, and does not rely on solving any matrixes inequalities by numerical computation.A simulation example is given to illustrate the performance of the proposed filter.Chapter3studies a high-gain nonlinear observer based fault diagnosis (FD) approach for a class of non-Gaussian uncertain systems with measurable output probability density functions (PDFs).The objective of the presented FD algorithm is to use the measurable output probability density functions (PDFs) and the input of the system to construct an exponential observer-based residual generator such that the fault can be detected and diag-nosed. The main result is given in a constructive manner by developing a novel nonlinear observer, without resort to any linearization. By a coordinates transformation, the design of the proposed observer does not need to solve any kind of linear matrix inequalities (LMIs) and its expression is explicitly given. The exponential convergence of the errors in the presence of uncertainties is proved to guarantee the fastness of the proposed fault diagnosis scheme by employing a class of quadratic Lyapunov functions. Furthermore, the bound of the estimation errors in the presence the faults is minimized by appropriately choosing the parameters of the presented observer. Finally a simulation example is given to illustrate the effectiveness of the proposed fault diagnosis method.Chapter4investigates a high-gain nonlinear observer based residual generation method for fault detection and isolation (FDI) in a class of nonlinear systems. The non-linear systems under consideration contain Lipschitz-like nonlinearities, modeling uncer-tainties, and may be harmed by time-varying faults. Based on some appropriate assump-tions on the monitored faults and a persistent excitation condition, a residual for fault diagnosis is designed in a constructive way by developing a novel nonlinear adaptive observer. Moreover, three design functions are given for the choice of the gain of the observer, which can maintain prescribed levels of the speed of convergence of error sys-tems, the insensitivity to the complement faults and the sensitivity to the monitored faults, respectively. The number of faults which can be completely diagnosed is independent of the number of output sensors. Given a set of possible faults, the sensitivity of the residuals to the monitored faults and the insensitivity to the other complement faults are rigorously analyzed. A simulation example is given to illustrate the effectiveness of the proposed fault diagnosis method.Chapter5studies the fault tolerant control (FTC) problem for nonlinear systems, with guaranteed cost or L2performance objective in the presence of actuator faults. The faulty mode is built as a multi-model framework of the typical aberration in actuator effec-tiveness. The novelty of this chapter is that the effect of the nonlinear terms is described as an index in order to transform the FTC design problem into a semi-definite programming (SDP). The proposed optimization approach is to find zero optimum for this index. Com-bined with other performance indexes, the conceived multiobjective optimization problem is solved by using sum of squares method (SOS) in a reliable and efficient way. Numerical examples are included to verify the applicability of this new approach for the nonlinear FTC synthesis.Chapter6deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone actuator fault. The nonlinear system model considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which ensures the boundedness of all the signals in the adaptive closed-loop without knowing the growth rate of the uncertainties. An example is presented to show the effectiveness of the proposed approach.Chapter7presents a systemic methodology for fault diagnosis and adaptive fault compensation control strategy for a class of nonlinear systems subjected to an unknown time-varying fault vector. Based on a nonlinear extended observer, which can provide the estimation of system states as well as the derivatives of the system output, detectability conditions are derived to design a fault diagnosis scheme. Furthermore, a fault-tolerant control component is designed to compensate the effect of actuator faults. To empha-size the sensitivity of fault detection, the upper bound of the detection time is rigorously analyzed. Under certain assumptions, the newly proposed fault information-based com-pensation controller can guarantee the boundedness of all the system signals during the whole process of detection and accommodation. It is shown that the rapidity of detection and accommodation of the proposed fault-tolerant mechanism can be ensured by tuning some parameters of the proposed observer. The theoretical results are illustrated by a sim-ulation example of surface-mounted permanent magnet synchronous motors (PMSM).Chapter8deals with the problem of fault-tolerant control (FTC) for a class of nonlin-ear uncertain systems against actuator faults using adaptive logic based-switching control method. The uncertainties under consideration are assumed to be dominated by a bound-ing system which is linear growth in the unmeasurable states but can be a continuous function of the system output, with unknown growth rates. Several types of common ac-tuator faults, e.g., bias, loss-of-effectiveness, stuck and hard-over faults are integrated by a unified fault model. By utilizing a novel adaptive logic-based switching control scheme, the actuator faults can be detected and automatically accommodated by switching from the stuck actuator to the healthy or even partly-losing-effectiveness one with bias, in the presence of large parametric uncertainty. In particular, two switching logics for updating the gain in the output feedback controllers are designed to ensure the global stability of the nominal (fault-free) system and the boundedness of all closed-loop signals of the faulty system, respectively. Two simulation examples of aircraft wing model and single-link flexible-joint robot are given to show the effectiveness of the proposed FTC controller.Chapter9is concerned with the decentralized and distributed estimation and reli-able cooperative control problem for a formation of agents with strongly couplings. The collected agents of the formation are modeled by a class of uncertain nonlinear systems communicating information between each other through unidirectional links with a fixed communication topology. Carrying an estimate of the entire formation state in each agent, the proposed hybrid control strategy relies on the possibility of making discrete on-line adjustments of parameter in the updating law of gain by a monitor signal. A crucial step in our proofs is finding an appropriate switching logic for the parameter and establishing a special set of measurement function in the updating law of gain. By a Lyapunov-based analysis of closed-loop equilibrium dynamics, a constructive design procedure results in the consensus of the estimation error dynamics and the stability of all signals in the closed-loop systems simultaneously.Finally, the results of the dissertation are summarized and further research topics are pointed out.