Isolation and handling of sensor faults in nonlinear systems

This work considers the problem of sensor fault isolation and fault-tolerant control for nonlinear systems subject to input constraints. The key idea is to design fault detection residuals and fault isolation logic by exploiting model-based sensor redundancy through a state observer. To this end, a high-gain observer is first presented, for which the convergence property is rigorously established, forming the basis of the residual design. A bank of residuals are then designed using a bank of observers, with each driven by a subset of measured outputs. A fault is isolated by checking which residuals breach their thresholds according to a logic rule. After the fault is isolated, the state estimate generated using measurements from the healthy sensors is used in closed-loop to maintain nominal operation. The implementation of the fault isolation and handling framework subject to uncertainty and measurement noise is illustrated using a chemical reactor example.     

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints, for cases where the state constraints need to be enforced at all times (hard constraints) and where they can be relaxed for some time (soft constraints). We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time during which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.     

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

Fault-tolerant control of a polyethylene reactor

This work focuses on fault-tolerant control of a gas phase polyethylene reactor. Initially, a family of candidate control configurations, characterized by different manipulated inputs, is identified. For each control configuration, a bounded nonlinear feedback controller, that enforces asymptotic closed-loop stability in the presence of constraints, is designed, and the constrained stability region associated with it is explicitly characterized using Lyapunov-based tools. Next, a fault-detection filter is designed to detect the occurrence of a fault in the control actuator by observing the deviation of the process states from the expected closed-loop behavior. A switching policy is then derived, on the basis of the stability regions, to orchestrate the activation/deactivation of the constituent control configurations in a way that guarantees closed-loop stability in the event of control system faults. Closed-loop system simulations demonstrate the effectiveness of the fault-tolerant control strategy.     

Feature-based handling of surface faults in compact disc players

In this paper a novel method called feature-based control is presented. The method is designed to improve compact disc players’ handling of surface faults on the discs. The method is based on a fault-tolerant control scheme, which uses extracted features of the surface faults to remove those from the detector signals used for control during the occurrence of surface faults. The extracted features are coefficients of Karhunen–Loève approximations of the surface faults. The performance of the feature-based control scheme controlling compact disc players playing discs with surface faults has been validated experimentally. The proposed scheme reduces the control errors due to the surface faults, and in some cases where the standard fault handling scheme fails, our scheme keeps the CD-player playing.     

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.     

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.     

Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems

This paper presents a methodology for the design of an integrated robust fault detection and isolation (FDI) and fault-tolerant control (FTC) architecture for distributed parameter systems modeled by nonlinear parabolic Partial Differential Equations (PDEs) with time-varying uncertain variables, actuator constraints and faults. The design is based on an approximate finite-dimensional system that captures the dominant dynamics of the PDE system. Initially, an invertible coordinate transformation-obtained through judicious actuator placement-is used to transform the approximate system into a form where the evolution of each state is excited directly by only one actuator. For each state, a robustly stabilizing bounded feedback controller that achieves an arbitrary degree of asymptotic attenuation of the effect of uncertainty is then synthesized and its constrained stability region is explicitly characterized in terms of the constraints, the actuator locations and the size of the uncertainty. A key idea in the controller synthesis is to shape the fault-free closed-loop response of each state in a prescribed fashion that facilitates the derivation of (1) dedicated FDI residuals and thresholds for each actuator, and (2) an explicit characterization of the state-space regions where FDI can be performed under uncertainty and constraints. A switching law is then derived to orchestrate actuator reconfiguration in a way that preserves robust closed-loop stability following FDI. Precise FDI rules and control reconfiguration criteria that account for model reduction errors are derived for the implementation of the FDI-FTC structure on the distributed parameter system. Finally, the results are demonstrated using a tubular reactor example.     

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.     

LPV model-based robust diagnosis of flight actuator faults

A linear parameter-varying (LPV) model-based synthesis, tuning and assessment methodology is developed and applied for the design of a robust fault detection and diagnosis (FDD) system for several types of flight actuator faults such as jamming, runaway, oscillatory failure, or loss of efficiency. The robust fault detection is achieved by using a synthesis approach based on an accurate approximation of the nonlinear actuator–control surface dynamics via an LPV model and an optimal tuning of the free parameters of the FDD system using multi-objective optimization techniques. Real-time signal processing is employed for identification of different fault types. The assessment of the FDD system robustness has been performed using both standard Monte-Carlo methods as well as advanced worst-case search based optimization-driven robustness analysis. A supplementary industrial validation performed on the AIRBUS actuator test bench for the monitoring of jamming, confirmed the satisfactory performance of the FDD system in a true industrial setting.     

Sensor and actuator fault isolation by structured partial PCA with nonlinear extensions

Partial PCA based on principal component analysis (PCA) with ideas borrowed from parity relations is a useful method in fault isolation (J. Gertler, W. Li, Y. Huang, T.J. McAvoy, Isolation enhanced principal component analysis, AIChE Journal 45(2) (1999) 323–334). By performing PCA on subsets of variables, a set of structured residuals can be obtained in the same way as structured parity relations. The structured residuals are utilized in composing an isolation scheme for sensor and actuator faults, according to a properly designed incidence matrix. To overcome the limitations of PCA, nonlinear approaches based on generalized PCA (GPCA) and nonlinear PCA (NPCA) are proposed. The nonlinear methods are demonstrated on an artificial 2×2 system while simulation studies on the Tennessee Eastman process illustrate the linear method and some extensions.     

Distributed adaptive fault-tolerant control against actuator faults and lossy interconnection links

This paper presents an adaptive method to solve the robust fault-tolerant control （FTC） problem for a class of large scale systems against actuator failures and lossy interconnection links. In terms of the special distributed architectures, the adaptation laws are proposed to estimate the unknown eventual faults of actuators and interconnections, constant external disturbances, and controller parameters on-line. Then a class of distributed state feedback controllers are constructed for automatically compensating the fault and disturbance effects on systems based on the information from adaptive schemes. On the basis of Lyapunov stability theory, it shows that the resulting adaptive closed-loop large-scale system can be guaranteed to be asymptotically stable in the presence of uncertain faults of actuators and interconnections, and constant disturbances. The proposed design technique is finally evaluated in the light of a simulation example.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

On observer-based fault detection for nonlinear systems

This paper addresses analysis and integrated design of observer-based fault detection (FD) for nonlinear systems. To gain a deeper insight into the observer-based FD framework, definitions and existence conditions for nonlinear observer-based FD systems are studied first. Then, a scheme for an integrated design of observer-based FD systems for affine nonlinear systems is proposed. Our work is considerably inspired by the study on input–output stability and stabilization of nonlinear systems. Examples are given at the end of the paper to illustrate the theoretical results.     

Generalized PI control design for a class of unknown nonaffine systems with sensor and actuator faults

This work deals with the tracking control problem of a class of unknown nonaffine dynamic systems that involve unpredictable sensor and actuation failures. As the control inputs enter into and influence the dynamic behavior of the nonaffine system through a nonlinear and implicit way, control design for such system becomes quite challenging. The underlying problem becomes even more complex if the system dynamics are unavailable for control design yet involving unanticipated sensor and/or actuator faults. In this work, a structurally simple and computationally inexpensive control scheme is proposed to achieve uniformly ultimately bounded (UUB) stable tracking control of a class of nonaffine systems. The proposed control is of a generalized PI form and is able to accommodate both sensor and actuator faults. The effectiveness of the proposed control strategy is confirmed by theoretical analysis and numerical simulations.     

Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking

A reconfigurable control approach for continuous-time piecewise affine (PWA) systems subject to actuator and sensor faults is presented. The approach extends the concept of virtual actuators and virtual sensors from linear to PWA systems on the basis of the fault-hiding principle that provides the underlying conceptual idea: the fault is hidden from the nominal controller and the fault effects are compensated. Sufficient linear matrix inequality (LMI) conditions for the existence of virtual actuators and virtual sensors are given that guarantee the recovery of closed-loop stability and the tracking of constant reference inputs. Since LMIs are efficiently solvable, this solution leads to a tractable computational algorithm that solves the reconfiguration problem. The approach is proven to be robust against model uncertainties and inaccurate fault diagnosis, and is evaluated using an example system of interconnected tanks.     

Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults

A class of unknown nonlinear systems subject to uncertain actuator faults and external disturbances will be studied in this paper with the help of fuzzy approximation theory. Using backstepping technique, a novel adaptive fuzzy control approach is proposed to accommodate the uncertain actuator faults during operation and deal with the external disturbances though the systems cannot be linearized by feedback. The considered faults are modeled as both loss of effectiveness and lock-in-place （stuck at some unknown place）. It is proved that the proposed control scheme can guarantee all signals of the closed-loop system to be semi-globally uniformly ultimately bounded and the tracking error between the system output and the reference signal converge to a small neighborhood of zero, though the nonlinear functions of the controlled system as well as the actuator faults and the external disturbances are all unknown. Simulation results demonstrate the effectiveness of the control approach.     

Fault-tolerant control for a class of nonlinear sampled-data systems via a Euler approximate observer

In this paper, a fault-tolerant control (FTC) scheme is developed for a class of nonlinear sampled-data systems. First, a Euler approximate discrete model is used to describe the plant under the sampling. Under this model, an observer-based fault estimation method is proposed. To guarantee the accuracy of both the state and fault estimation values, the conditions to make the approximate model consistent with the exact model are presented. Then, an active fault-tolerant controller, which has a constraint condition for the sampling time, is designed to make the faulty system stable. Finally, an inverted pendulum is used to show the efficiency of the proposed method.     

Simultaneous fault detection and control for switched systems with actuator faults

This paper is concerned with the fault detection and control problem for discrete-time switched systems. The actuator faults, especially ‘outage cases’, are considered. The detector/controller is designed simultaneously such that the closed-loop system switches under an average dwell time, and when a fault is detected, an alarm is generated and then the controller is switched to allow the norm of the states of the subsystem to increase within the acceptable limits. Thus, a switching strategy which combines average dwell time switching with event-driven switching is proposed. Under this switching strategy, the attention is focused on designing the detector/controller such that estimation errors between residual signals and faults are minimised for the fulfillment of fault detection objectives; simultaneously, the closed-loop system becomes asymptotically stable for the fulfillment of control objectives. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. An example comprising of three cases is considered. Through these cases, it is demonstrated that the fault detection and control for switched systems using a two-stage switching strategy and asynchronous switching are feasible.     

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.