UIO design for singular delayed LPV systems with application to actuator fault detection and isolation

In this paper, the unknown input observer (UIO) design for singular delayed linear parameter varying (LPV) systems is considered regarding its application to actuator fault detection and isolation. The design procedure assumes that the LPV system is represented in the polytopic framework. Existence and convergence conditions for the UIO are established. The design procedure is formulated by means of linear matrix inequalities (LMIs). Actuator fault detection and isolation is based on using the UIO approach for designing a residual generator that is completely decoupled from unknown inputs and exclusively sensitive to faults. Fault isolation is addressed considering two different strategies: dedicated and generalised bank of observers’ schemes. The applicability of these two schemes for the fault isolation is discussed. An open flow canal system is considered as a case study to illustrate the performance and usefulness of the proposed fault detection and isolation method in different fault scenarios.     

Designing fault detection observers for linear systems with mismatched unknown inputs

Algebraic unknown input observers (UIOs) that have been previously reported in the literature can be constructed under the assumption that linear systems with unknown inputs satisfy the so-called observer matching condition. This condition restricts practical applications of UIOs for fault detection and isolation (FDI). We present an algebraic design for fault detection observers (FDOs) for the case in which the observer matching condition is not satisfied. To loosen the restriction imposed by the observer matching condition, the UIO design method combined with the unknown input modeling technique is proposed to design an FDO that decouples the effect of mismatched unknown inputs. To do this, first, unknown inputs that denote the faults of no interest and process disturbances are decomposed into algebraically rejectable unknown inputs and modeled unknown inputs such that the observer matching condition is satisfied. Under the assumption that mismatched unknown inputs are deterministic and can be expressed as the responses of fictitious autonomous dynamical systems, an augmented system is obtained by combining the original system model with the unknown input model. Finally, through the design technique of a UIO for the augmented system, a reduced-order FDO is constructed to estimate an augmented state vector that consists of both the original state variables and the augmentative state variables. The estimated state is then used to generate the residual, which should be designed to be insensitive to unknown inputs while being sensitive to the faults of interest. Two numerical examples are provided to show the usefulness and the feasibility of the presented approach.     

A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.     

On linear observers and application to fault detection in synchronous generators

This work introduces an observer structure and highlights its distinct advantages in fault detection and isolation. Its application to the issue of shorted turns detection in synchronous generators is demonstrated. For the theoretical foundation, the convergence and design of Luenberger-type observers for disturbed linear time-invariant （LTI） single-input single-output （SISO） systems are reviewed with a particular focus on input and output disturbances. As an additional result, a simple observer design for stationary output disturbances that avoids a system order extension, as in classical results, is proposed.     

Design of unknown input functional observers for nonlinear systems with application to fault diagnosis

This paper considers the design of low-order unknown input functional observers for robust fault detection and isolation of a class of nonlinear Lipschitz systems subject to unknown inputs. The proposed functional observers can be used to generate residual signals to detect and isolate actuator faults. By using the generalized inverse approach, the effect of the unknown inputs can be decoupled completely from the residual signals. Conditions for the existence and stability of reduced-order unknown input functional observer are derived. A design procedure for the generation of residual signals to detect and isolate actuator faults is presented using the proposed unknown-input observer-based approach. A numerical example is given to illustrate the proposed fault diagnosis scheme in nonlinear systems subject to unknown inputs.     

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.     

Sliding-mode observers for systems with unknown inputs: A high-gain approach

Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.     

Approximation-based disturbance observer approach for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched disturbances

This paper presents an approximation-based nonlinear disturbance observer (NDO) methodology for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched external disturbances. Compared with existing control results using NDO for nonlinear systems in lower-triangular form, the major contribution of this study is to develop an NDO-based control framework in the presence of non-affine nonlinearities and disturbances unmatched in the control input. An approximation-based NDO scheme is designed to attenuate the effect of compounded disturbance terms consisting of external disturbances, approximation errors and control coefficient nonlinearities. The function approximation technique using neural networks is employed to estimate the unknown nonlinearities derived from the recursive design procedure. Based on the designed NDO scheme, an adaptive dynamic surface control system is constructed to ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a neighbourhood of the origin. Simulation examples including a mechanical system are provided to show the effectiveness of the proposed theoretical result.     

Supervisory fault tolerant control for a class of uncertain nonlinear systems

This paper focuses on the design of a unique scheme that simultaneously performs fault isolation and fault tolerant control for a class of uncertain nonlinear systems with faults ranging over a finite cover. The proposed framework relies on a supervisory switching among a family of pre-computed candidate controllers without any additional model or filter. The states are ensured to be bounded during the switching delay, which ends when the correct stabilizing controller has been selected. Simulation results about a flexible joint robotic example illustrate the efficiency of the proposed method.     

Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems

This paper considers observer-based actuator fault detection and reconstruction problems for uncertain nonlinear systems. Based on a kind of full-order observer which is robust to disturbances but sensitive to actuator faults, a single detection observer is constructed to produce a residual which can be used to alarm the occurrence of the actuator faults when at least one actuator fault occurs indeed. The full-order observer is adaptive one because an adaptation law which can adjust the Lipschitz constant of Lipschitz term is introduced. For this reason, the Lipschitz constant can be unknown in our design. After this, a kind of reduced-order observer is developed by choosing a special observer gain matrix. Based on the reduced-order observer, we provide a kind of unknown information estimating method which can be used to not only reconstruct the actuator faults but also estimate the disturbances of the system. In simulation, a real model of the seventh-order aircraft is used to illustrate the effectiveness of the proposed methods.     

Fault diagnosis based on high-gain observer with an update law for a class of nonlinear systems

In this paper, by using the well-known high-gain observer design, an update law for the gain and an adaptive estimation of parameters, a new method of fault diagnosis for a class of nonlinear systems is presented. Without resort to any transformation for the parameters, the estimation errors of the states and the parameters are guaranteed to be globally exponentially convergent by a persistent excitation condition. Compared to the existing results, it can be applied to nonlinear systems with nonlinear terms admitting an incremental rate depending on the measured output. A case study further verifies the validity of the proposed research.     

Actuator fault diagnosis for a class of nonlinear systems and its application to a laboratory 3D crane

In this paper, an actuator fault diagnosis scheme is proposed for a class of affine nonlinear systems with both known and unknown inputs. The scheme is based on a novel input/output relation derived from the considered nonlinear systems and the use of the recently developed high-order sliding-mode robust differentiators. The main advantages of the proposed approach are that it does not require a design of nonlinear observer and applies to systems not necessarily detectable. Conditions are provided to characterize the feasibility of fault detection and isolation using the proposed scheme and the maximum number of isolatable actuator faults. The efficacy of the proposed actuator fault diagnosis approach is tested through experiments on a laboratory 3D Crane, and the experimental results show that the proposed actuator fault diagnosis approach is promising and can achieve fault detection and isolation satisfactorily.     

A sliding mode observer-based strategy for fault detection,isolation, and estimation in a class of Lipschitz nonlinear systems

This article investigates the design and application of a sliding mode observer (SMO) strategy for actuator as well as sensor fault detection, isolation, and estimation (FDIE) problem for a class of uncertain Lipschitz nonlinear systems. Actuator FDIE is addressed by regrouping the system's inputs into a structure suitable for SMO design. Similarly, by filtering the regrouped outputs, a similar system structure can be developed for sensor FDIE problem. Once in the suitable form and under certain assumptions, nonlinear SMOs are proposed for actuator and sensor FDIE. A systematic LMI-based design approach for the proposed SMO is presented. Additionally, the article addresses four problems, namely: (P1) What are the conditions for isolating single and/or multiple faults? (P2) What is the maximum number of faults that can be isolated simultaneously? (P3) How should one design SMO-based FDI approach in order to achieve multiple fault isolation using as few observers as possible? (P4) How can one estimate the shape of the faults? To solve the above problems, a new concept called fault isolation index (FIX) is proposed for actuator and sensor FDIE. It is proved that fault isolation can only be achieved if FIX?≠?0, and also that the maximum number of faults that can be isolated is equal to FIX. Using the proposed fault isolation strategy and by treating some healthy inputs or outputs as unknown inputs, a systematic FDIE design scheme using a bank of nonlinear SMOs, which provides a solution for the four problems is provided. An example is used to illustrate the proposed ideas. The simulation results show that the proposed FDIE scheme can successfully detect and isolate both slowly and fast-changing actuator faults. It is also shown that accurate estimation of actuator faults can be achieved.     

A quadratic boundedness approach to robust DC motor fault estimation

In the paper, a novel methodology of actuator fault estimation for linear discrete-time systems is proposed. To solve such a challenging problem, a quadratic boundedness approach is used to guarantee the convergence of the proposed state and actuator fault estimation method. In the proposed methodology, the robustness is achieved through the unknown input decoupling while an unappealing effect of the undecoupled disturbances is minimized. Moreover, the developed approach enables to obtain a feasible set of joint system state and fault estimation error. Based on this knowledge, a novel methodology of calculating the uncertainty intervals of the system state and actuator fault is proposed. The illustrative part of the paper presents results obtained for the laboratory DC servo-motor and compares the proposed approach with two alternative methods. Based on this real-data example, the efficiency of the developed methodology is clearly exposed.     

A possibilistic clustering approach to novel fault detection and isolation

In this paper, a new approach for fault detection and isolation that is based on the possibilistic clustering algorithm is proposed. Fault detection and isolation (FDI) is shown here to be a pattern classification problem, which can be solved using clustering and classification techniques. A possibilistic clustering based approach is proposed here to address some of the shortcomings of the fuzzy c-means (FCM) algorithm. The probabilistic constraint imposed on the membership value in the FCM algorithm is relaxed in the possibilistic clustering algorithm. Because of this relaxation, the possibilistic approach is shown in this paper to give more consistent results in the context of the FDI tasks. The possibilistic clustering approach has also been used to detect novel fault scenarios, for which the data was not available while training. Fault signatures that change as a function of the fault intensities are represented as fault lines, which have been shown to be useful to classify faults that can manifest with different intensities. The proposed approach has been validated here through simulations involving a benchmark quadruple tank process and also through experimental case studies on the same setup. For large scale systems, it is proposed to use the possibilistic clustering based approach in the lower dimensional approximations generated by algorithms such as PCA. Towards this end, finally, we also demonstrate the key merits of the algorithm for plant wide monitoring study using a simulation of the benchmark Tennessee Eastman problem.     

Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems

In this article, an actuator fault detection and isolation scheme for a class of nonlinear systems with uncertainty is considered. The uncertainty is allowed to have a nonlinear bound which is a general function of the state variables. A sliding mode observer is first established based on a constrained Lyapunov equation. Then, the equivalent output error injection is employed to reconstruct the fault signal using the characteristics of the sliding mode observer and the structure of the uncertainty. The reconstructed signal can approximate the system fault signal to any accuracy even in the presence of a class of uncertainty. Finally, a simulation study on a nonlinear aircraft system is presented to show the effectiveness of the scheme.     

A robust adaptive observer for a class of singular nonlinear uncertain systems

This paper proposes a robust adaptive observer for a class of singular nonlinear non-autonomous uncertain systems with unstructured unknown system and derivative matrices, and unknown bounded nonlinearities. Unlike many existing observers, no strong assumption such as Lipschitz condition is imposed on the recommended system. An augmented system is constructed, and the unknown bounds are calculated online using adaptive bounding technique. Considering the continuous nonlinear gain removes the chattering which may appear in practical applications such as analysis of electrical circuits and estimation of interaction force in beating heart robotic-assisted surgery. Moreover, a simple yet precise structure is attained which is easy to implement in many systems with significant uncertainties. The existence conditions of the standard form observer are obtained in terms of linear matrix inequality and the constrained generalised Sylvester's equations, and global stability is ensured. Finally, simulation results are obtained to evaluate the performance of the proposed estimator and demonstrate the effectiveness of the developed scheme.     

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.     

Nonlinear adaptive speed control of a permanent magnet synchronous motor: A perturbation estimation approach

This paper presents a nonlinear adaptive control (NAC) scheme for the speed regulation of a permanent magnet synchronous motor (PMSM) based on perturbation estimation and feedback linearizing control. All PMSM system’s unknown nonlinearities, parameter uncertainties, and external disturbances including unknown time-varying load torque disturbance, are defined as lumped perturbation terms, which are estimated by designing perturbation observers. The estimates are used to adaptively compensate the real perturbations and achieve adaptive feedback linearizing control of the original nonlinear system. The proposed control scheme does not require accurate system model and full state feedback. Stability of the close-loop system with proposed NAC is investigated via Lyapunov theory, and the effectiveness of proposed NAC scheme is verified through both simulation and experimental studies. Both simulation and experimental results show that the proposed NAC scheme can provide less regulation error in speed tracking, better dynamic performance and robustness against parameter uncertainties and load torque disturbance, compared with conventional vector control and load torque estimated based control.