Sensor‐fault tolerance using robust MPC with set‐based state estimation and active fault isolation

In this paper, a sensor fault‐tolerant control scheme using robust model predictive control (MPC) and set‐theoretic fault detection and isolation (FDI) is proposed. The robust MPC controller is used to control the plant in the presence of process disturbances and measurement noises while implementing a mechanism to tolerate faults. In the proposed scheme, fault detection (FD) is passive based on interval observers, while fault isolation (FI) is active by means of MPC and set manipulations. The basic idea is that for a healthy or faulty mode, one can construct the corresponding output set. The size and location of the output set can be manipulated by adjusting the size and center of the set of plant inputs. Furthermore, the inputs can be adjusted on‐line by changing the input‐constraint set of the MPC controller. In this way, one can design an input set able to separate all output sets corresponding to all considered healthy and faulty modes from each other. Consequently, all the considered healthy and faulty modes can be isolated after detecting a mode changing while preserving feasibility of MPC controller. As a case study, an electric circuit is used to illustrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

On invariant sets and closed‐loop boundedness of Lure‐type nonlinear systems by LPV‐embedding

We address the problem of achieving trajectory boundedness and computing ultimate bounds and invariant sets for Lure‐type nonlinear systems with a sector‐bounded nonlinearity. Our first contribution is to compare two systematic methods to compute invariant sets for Lure systems. In the first method, a linear‐like bound is considered for the nonlinearity, and this bound is used to compute an invariant set by regarding the nonlinear system as a linear system with a nonlinear perturbation. In the second method, the sector‐bounded nonlinearity is treated as a time‐varying parameterised linear function with bounded parameter variations, and then invariant sets are computed by embedding the nonlinear system into a convex polytopic linear parameter varying (LPV) system. We show that under some conditions on the system matrices, these approaches give identical invariant sets, the LPV‐embedding method being less conservative in the general case. The second contribution of the paper is to characterise a class of Lure systems, for which an appropriately designed linear state feedback achieves bounded trajectories of the closed‐loop nonlinear system and allows for the computation of an invariant set via a simple, closed‐form expression. The third contribution is to show that, for disturbances that are ‘aligned’ with the control input, arbitrarily small ultimate bounds on the system states can be achieved by assigning the eigenvalues of the linear part of the system with ‘large enough’ negative real part. We illustrate the results via examples of a pendulum system, a Josephson junction circuit and the well‐known Chua circuit. Copyright © 2015 John Wiley & Sons, Ltd.     

Active fault detection based on set‐membership approach for uncertain discrete‐time systems

Active fault detection facilitates determination of the fault characteristics by injecting proper auxiliary input signals into the system. This article proposes an observer‐based on‐line active fault detection method for discrete‐time systems with bounded uncertainties. First, the output including disturbances, measurement noise and interval uncertainties at each sample time is enclosed in a zonotope. In order to reduce the conservativeness in the fault detection process, a zonotopic observer is designed to estimate the system states allowing to generate the output zonotopes. Then, a proper auxiliary input signal is designed to separate the output zonotopes of the faulty model from the healthy model that is injected into the system to facilitate the detection of small fault . Since the auxiliary input signal generation leads to a nonconvex optimization problem, it is transformed into a mixed integer quadratic programming problem. Finally, a case study based on a DC motor is used to show the effectiveness of the proposed method.     

An iterative learning observer for fault detection and accommodation in nonlinear time‐delay systems

This article addresses fault detection, estimation, and compensation problem in a class of disturbance driven time delay nonlinear systems. The proposed approach relies on an iterative learning observer (ILO) for fault detection, estimation, and compensation. When there are no faults in the system, the ILO supplies accurate disturbance estimation to the control system where the effect of disturbances on estimation error dynamics is attenuated. At the same time, the proposed ILO can detect sudden changes in the nonlinear system due to faults. As a result upon the detection of a fault, the same ILO is used to excite an adaptive control law in order to offset the effect of faults on the system. Further, the proposed ILO‐based adaptive fault compensation strategy can handle multiple faults. The overall fault detection and compensation strategy proposed in the paper is finally demonstrated in simulation on an automotive engine example to illustrate the effectiveness of this approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Set‐based fault detection and isolation for detectable linear parameter‐varying systems

In the context of fault detection and isolation of linear parameter‐varying systems, a challenging task appears when the dynamics and the available measurements render the model unobservable, which invalidates the use of standard set‐valued observers. Two results are obtained in this paper, namely, using a left‐coprime factorization, one can achieve set‐valued estimates with ultimately bounded hyper‐volume and convergence dependent on the slowest unobservable mode; and by rewriting the set‐valued observer equations and taking advantage of a coprime factorization, it is possible to have a low‐complexity fault detection and isolation method. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults. Copyright © 2017 John Wiley & Sons, Ltd.     

Fault estimation and controller compensation in Lure systems by LPV-embedding

Previous works have considered the use of set invariance theory for fault detection and isolation in nonlinear Lure systems. This paper extends those results and proposes a new actuator fault-tolerant control approach. The fault-tolerant control scheme is designed based on linear parameter-varying (LPV) models of Lure systems. The actuator fault situation is diagnosed by an invariant set-based fault detection and isolation algorithm. Faults are compensated by adapting the controller gain based on estimates of the fault magnitude. Conditions for correct fault detection and isolation, and closed-loop stability are derived. The proposed fault-tolerant control scheme is compared with a linearised model approach and the performance of both, LPV-embedding and linearised, approaches are analysed for scalar and second-order systems. An example of a chaotic Chua circuit is also provided to illustrate the proposed fault-tolerant control scheme in higher-order systems.     

Robust fault estimation of uncertain systems using an LMI‐based approach

General recent techniques in fault detection and isolation (FDI) are based on H_∞ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation‐based design methods. This article presents an LMI formulation to design full‐order and reduced‐order robust H_∞ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full‐order filter, which may be solved via recently developed LMI optimization techniques. For the reduced‐order FDI filter, the inequalities include a non‐convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd.     

Sensor selection for fault diagnosis in uncertain systems

ABSTRACT

Finding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.     

Interval observer versus set‐membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set‐membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two‐tanks system is employed for showing the relationship between both approaches while comparing their performance.     

Robust fault diagnosis of disturbed linear systems via a sliding mode high order differentiator

A fault estimator for linear systems affected by disturbances is proposed. Faults appearing explicitly in the state equation and in the system output (actuator faults and sensor faults) are considered. With this design neither the estimation of the state vector nor the estimation of the disturbances is required, implying that the structural conditions are less restrictive than the ones required to design an unknown input observer. Furthermore, the number of unknown inputs (faults plus disturbances) may be greater than the number of outputs. The faults are written as an algebraic expression of a high-order derivative of a function depending on the output. Thus, the reconstruction of the fault signals is carried out by means of a sliding mode high-order differentiator, which requires the derivative of the faults to have a bounded norm.     

Adaptive fault diagnosis and fault-tolerant control of MIMO nonlinear uncertain systems

This article presents an integrated fault diagnosis and fault-tolerant control (FTC) methodology for a class of nonlinear multi-input–multi-output systems. Based on the fault information obtained during the diagnostic procedure, an FTC component is designed to compensate for the effect of faults. In the presence of a fault, a baseline controller guarantees the boundedness of all the system signals until the fault is detected. After fault detection and then again after isolation, the controller is reconfigured to improve the tracking performance using online fault diagnostic information. Under certain assumptions, the stability and tracking performances of the closed-loop system are rigorously investigated. It is shown that the system signals always remain bounded and the output tracking error converges to a neighbourhood of the origin of the state space.     

Experimental application of nonlinear minimum variance estimation for fault detection systems

The purpose of this paper is to present an experimental design and application of a novel model-based fault detection technique by using a nonlinear minimum variance (NMV) estimator. The NMV estimation technique is used to generate a residual signal which is then used to detect faults in the system. The main advantage of the approach is the simplicity of the nonlinear estimator theory and the straightforward structure of the resulting solution. The proposed method is implemented and validated experimentally on DC servo system. Experimental results demonstrate that the technique can produce acceptable performance in terms of fault detection and false alarm.     

Fault detection and isolation for uncertain closed‐loop systems based on adaptive and switching approaches

This paper deals with the fault detection and isolation (FDI) problem for uncertain closed‐loop systems with external disturbances and nonlinear perturbations. To address the system uncertainties and the nonlinear perturbations in different faulty models, adaptive and switching techniques are introduced to construct a bank of FDI observers, such that one of them can match the current system, and the corresponding observer estimate errors can converge asymptotically to zero. An effective FDI scheme is then presented by introducing some model‐matching indexes. Moreover, the introduced switching laws liberate the equality constraints often used in the existing FDI approaches, which are hard to satisfy if the system matrices include uncertainties. Finally, a simulation example of F/A‐18A automatic carrier landing system is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Control performance‐based fault detection and fault‐tolerant control schemes for a class of nonlinear systems

The objective of this paper is to develop performance‐based fault detection (FD) and fault‐tolerant control (FTC) schemes for a class of nonlinear systems. To this end, the representation forms of nonlinear systems with faults and the controller parameterization forms are studied first with the aid of the nonlinear factorization technique. Then, based on the stable kernel representation and the stable image representation of the faulty nonlinear system, the stability performance of the closed‐loop system is addressed, respectively. The so‐called fault‐tolerant margin is defined to evaluate the system fault‐tolerant ability. On this basis, two performance‐based FD schemes are developed aiming at detecting the system performance degradation caused by system faults. Furthermore, to recover the system stability performance, two performance‐based FTC strategies are proposed based on the information provided by the FD unit. In the end, a numerical example and a case study on the three‐tank system are given to demonstrate the proposed results.     

On-line fault diagnosis of dynamic systems via robust parameter estimation

A procedure simultaneously achieving the detection of faults, their location and their identification is presented. The systems considered are MISO systems represented by ARX models, the parameters of which are estimated on-line by a robust procedure. A priori knowledge of the faults which can occur is used. The faults modelled here are outliers, biases or drifts, and can act upon output, inputs or even noise. The magnitude of a fault is estimated on a moving window from the prediction error sequence by least squares. Statistical tests of the significance of the estimated parameters corresponding to the different faults are performed. An application on the strip drive in the furnace of an annealing line is finally presented.     

Fault‐tolerant fusion‐based MPC with sensor recovery for constrained LPV systems

In this paper, we present a robust fault‐tolerant control scheme for constrained multisensor linear parameter‐varying systems, subject to bounded disturbances, that utilises multiple sensor fusion. The closed‐loop scheme consists of a tube model predictive control‐based feedback tracking controller and sensor‐estimate fusion strategy, which allows for the reintegration of previously faulty sensors. The active fault‐tolerant fusion‐based mechanism tracks the healthy‐faulty transitions of suitable residual variables by means of set separation and precomputed transition times. The sensor‐estimate pairings are then reconfigured based on available healthy sensors. Under the proposed scheme, robust preservation of closed‐loop system boundedness is guaranteed for a wide range of sensor fault situations. An example is presented to illustrate the performance of the fault‐tolerant control strategy.     

Online expert systems for fault diagnosis in technical processes

Abstract: It is generally accepted that there has been an increasing interest in online fault detection and diagnosis techniques for technical processes during the last few years. These techniques come from the artificial intelligence field or are classical numerical methods in combination with artificial intelligence methods. This paper presents a survey of recent research work in online expert systems for fault detection and diagnosis in technical processes. In addition, a short reference to other recent artificial intelligence methods for online fault detection is included and the main advantages and limitations of each method are illustrated.     

Reliability and time‐to‐failure bounds for discrete‐time constrained Markov jump linear systems

This paper presents a methodology to obtain a guaranteed‐reliability controller for constrained linear systems, which switch between different modes according to a Markov chain (Markov jump linear systems). Inside the classical maximal robust controllable set, there is 100% guarantee of never violating constraints at future time. However, outside such set, some sequences might make hitting constraints unavoidable for some disturbance realisations. A guaranteed‐reliability controller based on a greedy heuristic approach was proposed in an earlier work for disturbance‐free, robustly stabilisable Markov jump linear systems. Here, extensions are presented by, first, considering bounded disturbances and, second, presenting an iterative algorithm based on dynamic programming. In non‐stabilisable systems, reliability is zero; therefore, prior results cannot be applied; in this case, optimisation of a mean‐time‐to‐failure bound is proposed, via minor algorithm modifications. Optimality can be proved in the disturbance‐free, finitely generated case. Copyright © 2016 John Wiley & Sons, Ltd.     

Active fault detection and isolation of discrete-time linear time-varying systems: a set-membership approach

Active fault detection and isolation (AFDI) is used for detection and isolation of faults that are hidden in the normal operation because of a low excitation signal or due to the regulatory actions of the controller. In this paper, a new AFDI method based on set-membership approaches is proposed. In set-membership approaches, instead of a point-wise estimation of the states, a set-valued estimation of them is computed. If this set becomes empty the given model of the system is not consistent with the measurements. Therefore, the model is falsified. When more than one model of the system remains un-falsified, the AFDI method is used to generate an auxiliary signal that is injected into the system for detection and isolation of faults that remain otherwise hidden or non-isolated using passive FDI (PFDI) methods. Having the set-valued estimation of the states for each model, the proposed AFDI method finds an optimal input signal that guarantees FDI in a finite time horizon. The input signal is updated at each iteration in a decreasing receding horizon manner based on the set-valued estimation of the current states and un-falsified models at the current sample time. The problem is solved by a number of linear and quadratic programming problems, which result in a computationally efficient algorithm. The method is tested on a numerical example as well as on the pitch actuator of a benchmark wind turbine.