Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies
This paper reviews the use of set-membership methods in fault diagnosis (FD) and fault tolerant control (FTC). Setmembership methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between observed and predicted behaviour by using simple sets to approximate the exact set of possible behaviour (in the parameter or the state space). When an inconsistency is detected between the measured and predicted behaviours obtained using a faultless system model, a fault can be indicated. Otherwise, nothing can be stated. The same principle can be used to identify interval models for fault detection and to develop methods for fault tolerance evaluation. Finally, some real applications will be used to illustrate the usefulness and performance of set-membership methods for FD and FTC.
Saúl de Oca, Vicenç Puig, Marcin Witczak and Łukasz Dziekan
Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter
In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used.
Amir Hossein Hassanabadi, Masoud Shafiee and Vicenç Puig
In this paper, the robust fault detection problem for LPV singular delayed systems in the presence of disturbances and actuator faults is considered. For both disturbance decoupling and actuator fault detection, an unknown input observer (UIO) is proposed. The aim is to compute a residual signal which has minimum sensitivity to disturbances while having maximum sensitivity to faults. Robustness to unknown inputs is formulated in the sense of the ℋ∞-norm by means of the bounded real lemma (BRL) for LPV delayed systems. In order to formulate fault sensitivity conditions, a reference model which characterizes the ideal residual behavior in a faulty situation is considered. The residual error with respect to this reference model is computed. Then, the maximization of the residual fault effect is converted to minimization of its effect on the residual error and is addressed by using the BRL. The compromise between the unknown input effect and the fault effect on the residual is translated into a multi-objective optimization problem with some LMI constraints. In order to show the efficiency and applicability of the proposed method, a part of the Barcelona sewer system is considered.
A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H∞ norm bounding constraints. Simulation results are used to compare the different FTC strategies.
Julián Cayero, Damiano Rotondo, Bernardo Morcego and Vicenç Puig
This paper presents the design of a state observer which guarantees quadratic boundedness of the estimation error. By using quadratic Lyapunov stability analysis, the convergence rate and the ultimate (steady-state) error bounding ellipsoid are identified as the parameters that define the behaviour of the estimation. Then, it is shown that these objectives can be merged in a scalarised objective function with one design parameter, making the design problem convex. In the second part of the article, a UAV model is presented which can be made linear by considering a particular state and frame of reference. The UAV model is extended to incorporate a disturbance model of variable size. The joint model matches the structure required to derive an observer, following the lines of the proposed design approach. An observer for disturbances acting on the UAV is derived and the analysis of the performances with respect to the design parameters is presented. The effectiveness and main characteristics of the proposed approach are shown using simulation results.
Juan M. Grosso, Carlos Ocampo-Martinez and Vicenç Puig
This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalised flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamical allocation of safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the case study considered.
Feng Xu, Vicenç Puig, Carlos Ocampo-Martinez, Sorin Olaru and Silviu-Iulian Niculescu
In this paper, a fault-tolerant control (FTC) scheme is proposed for actuator faults, which is built upon tube-based model predictive control (MPC) as well as set-based fault detection and isolation (FDI). In the class of MPC techniques, tubebased MPC can effectively deal with system constraints and uncertainties with relatively low computational complexity compared with other robust MPC techniques such as min-max MPC. Set-based FDI, generally considering the worst case of uncertainties, can robustly detect and isolate actuator faults. In the proposed FTC scheme, fault detection (FD) is passive by using invariant sets, while fault isolation (FI) is active by means of MPC and tubes. The active FI method proposed in this paper is implemented by making use of the constraint-handling ability of MPC to manipulate the bounds of inputs.
After the system has been detected to become faulty, the input-constraint set of the MPC controller is adjusted to actively excite the system for achieving FI guarantees on-line, where an active FI-oriented input set is designed off-line. In this way, the system can be excited in order to obtain more extra system-operating information for FI than passive FI approaches.
Overall, the objective of this paper is to propose an actuator MPC scheme with as little as possible of FI conservatism and computational complexity by combining tube-based MPC and set theory within the framework of MPC, respectively.
Finally, a case study is used to show the effectiveness of the proposed FTC scheme.
Fatemeh Karimi Pour, Vicenç Puig and Carlos Ocampo-Martinez
This paper proposes two different health-aware economic predictive control strategies that aim at minimizing the damage of components in a pasteurization plant. The damage is assessed with a rainflow-counting algorithm that allows estimating the components’ fatigue. By using the results obtained from this algorithm, a simplified model that characterizes the health of the system is developed and integrated into the predictive controller. The overall control objective is modified by adding an extra criterion that takes into account the accumulated damage. The first strategy is a single-layer predictive controller with an integral action to eliminate the steady-state error that appears when adding the extra criterion. In order to achieve the best minimal accumulated damage and operational costs, the single-layer approach is improved with a multi-layer control scheme, where the solution of the dynamic optimization problem is obtained from the model in two different time scales. Finally, to achieve the advisable trade-off between minimal accumulated damage and operational costs, both control strategies are compared in simulation over a utility-scale pasteurization plant.