Fault detection and fault-tolerant control of actuators and sensors in distributed parameter systems

doi:10.1016/j.jfranklin.2017.03.004

Journal of the Franklin Institute

Volume 354, Issue 8, May 2017, Pages 3341-3363

https://doi.org/10.1016/j.jfranklin.2017.03.004 Get rights and content

Highlights

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A strategy for actuator and sensor fault detection and FTC of DPSs is developed.
•
Model reduction techniques are used to derive a finite-dimensional approximation.
•
A time-varying threshold is designed to detect time occurrence of each actuator fault.
•
A switching policy is employed to arrange switching from faulty actuator to healthy.

Abstract

This paper proposes the architecture for fault detection and fault-tolerant control for distributed parameter systems with control actuators and measurement sensors. In the development of this architecture, it is assumed that the system contains multiple actuators and sensors with only one actuator and partial sensors are activated while keeping the remaining actuators and sensors dormant. For the approximate finite-dimensional model, a detection observer with a time-varying threshold is proposed to ensure the actuator faults can be detected. An actuator switching policy is used to arrange switching from faulty actuators to healthy ones based on performance enhancement arguments. To facilitate actuator fault diagnosis, an adaptive observer that accommodates actuator fault is designed. Residuals are defined so as to detect the sensor fault. Then, an integrated fault detection and fault-tolerant control architecture of actuators and sensors is taken into account in the implementation of the infinite-dimensional system on the basis of the singular perturbation formulation. Finally, the proposed theoretical results are verified through an example of chemical reaction.

Introduction

In industrial control applications, repeated use of actuators and sensors may result in faults. If not properly handled, actuator and/or sensor faults will lead to the degradation of system performance and even substantial economic loss [1]. Therefore, it is necessary to detect and isolate faults quickly in order to ensure the stable system performance.

In the past decades, many approaches have been used in fault detection and fault-tolerant control (FTC) [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Miao et al. [1] exploited the analytical redundancy method to isolate actuator and sensor faults in nonlinear process systems. Based on the adaptive observer method, Dimitrios [2] presented a complete scheme for detection, isolation and identification of multiple actuator and sensor faults in a class of nonlinear dynamic systems. Elkhatib [3] put forth a new robust fuzzy scheduler FTC for managing multivariable nonlinear systems subjected to sensor and actuator faults. Du [4] utilized the augmented descriptor observer method and the switched Lyapunov function technique to tackle sensor FTC for discrete-time switched linear systems. Yin et al. [5], [6] proposed data-driven fault-detection and isolation methods for vehicle suspension systems. Xiao [7] addressed a scheme of velocity-free uncertain attenuation control for a class of nonlinear systems with multiple actuator faults and external disturbance. Therefore, the fault detection and FTC technique can be used in many systems.

Modeling and control of distributed parameter systems (DPSs) with the infinite-dimensional state space are required in engineering fields [11], [12], [13], [14]. Control problems of DPSs often involve the regulation of spatially distributed variables, such as pressure, concentration and temperature, by using spatially distributed measurement sensors and control actuators. Especially in biological engineering and chemical engineering, DPSs, such as tubular reactors, heat exchangers, crystallizers and fluidized beds [15], [16], are widely used. Due to the prevalence of DPSs in engineering fields, the fault detection and FTC problems of sensors and actuators in DPSs are widely concerned.

To date, the most relevant works on this subject have been presented by EI-Farra, Armaou and Demetriou et al. [17], [18], [19], [20], [21], [22]. An integrated fault detection and FTC architecture was established for spatially distributed processes described by DPSs with control constraints and control actuator faults in [17]. A class of DPSs with actuator and component faults were considered in [18]. Through an adaptive detection observer with a time-varying threshold, component and actuator faults could be detected and fault detection time could be minimized. Additionally, an adaptive diagnostic observer could diagnose component faults by using online estimates of fault parameters. However, the adaptive detection observer was designed only to detect occurrence time of the faults, but it could not determine the position where the actuator fault has occurred. Therefore, a supervisor was required to adjust all the actuators, including possibly healthy actuators. In order to avoid the unnecessary shut down of healthy actuators, a fault isolation and reconfiguration scheme was developed for DPSs with control constraints and actuator faults to identify the faulty actuators within an active actuator set, fault detection thresholds and controller design criteria were derived in [19]. However, the fixed thresholds extended the fault detection time, and sensor faults in DPSs were not considered. DPSs are often subjected to the faults caused by sensors, actuators or the system itself [23].

In this paper, we consider a class of DPSs that can be divided into a finite dimensional slow subsystem and an infinite-dimensional fast subsystem. It is assumed that the DPS contains multiple actuators and sensors with only one actuator and partial sensors are activated within a certain time interval while the remaining actuators and sensors are kept dormant as required. In the slow subsystem, each detection observer utilizes a time-varying threshold to identify faulty actuator, thus reducing fault detection time more quickly. A set of switching laws that minimize the cost function while maintaining closed-loop stability are employed to arrange switching from a faulty actuator to a healthy one. In addition, once an actuator fault is detected, an adaptive diagnosis observer will provide an online estimate of the fault parameter. For the sensors fault, a fault detection observer is designed for each sensor, whereas sensor switching strategy considers the position of the faulty actuator. Based on the singular perturbation formulation, the fault detection and FTC architecture of actuators and sensors is adjusted in the infinite-dimensional system. The theoretical results will be applied in a typical DPS for fault detection and FTC architecture of actuators and sensors.

The rest of this paper is organized as follows. The mathematical preliminaries and the dominant dynamics of the distributed process on the basis of appropriate reduced-order model are given in Section 2. The fault detection and FTC architecture of actuators in the finite-dimensional approximate system is discussed in Section 3. Section 4 shows the sensor fault detection and FTC architecture in the finite-dimensional approximate system. The fault detection and FTC architecture of actuators and sensors in the infinite-dimensional system is addressed in Section 5. The simulation example is presented in Section 6. Finally, conclusions are drawn in Section 7.

Section snippets

Problem formulation

Considering a DPS that takes the form: $\frac{\partial z (t, x)}{\partial t} = \frac{\partial^{2} z}{\partial x^{2}} (t, x) + \sum_{i = 1}^{n} b_{i} (x) [u_{i} (t) + H (t - T_{a_{i}}) f_{a_{i}} (t)] + ω (z (t, x)),$ $y (t) = [\begin{matrix} y_{1} (t) \\ ⋮ \\ y_{n} (t) \end{matrix}] = [\begin{matrix} \int_{0}^{h} c_{1} (x) [z (t, x) + H (t - T_{c_{1}}) f_{c_{1}} (t)] d x \\ ⋮ \\ \int_{0}^{h} c_{n} (x) [z (t, x) + H (t - T_{c_{n}}) f_{c_{n}} (t)] d x \end{matrix}]$ subject to the boundary conditions

$\frac{\partial z}{\partial x} (t, 0) = \frac{\partial z}{\partial x} (t, h) = 0$ and the initial condition $z (0, x) = z_{0} (x)$ , where z(t, x) denotes the state variable; $x \in [0, h] \in R^{+}$ is the spatial coordinate; t ∈ [0, ∞) is the time; b_i(x) denotes the spatial distribution of the ith actuating device; u_i(t) denotes the associated control

Fault detection and FTC architecture for actuators

In order to illustrate the specific structure of this system, similar to Ref. [19], we will decompose the approximate slow system ${\tilde{x}}_{s} (t)$ as ${\tilde{z}}_{s} (t) = {\tilde{z}}_{s_{1}} (t) + {\tilde{z}}_{s_{2}} (t) + \dots + {\tilde{z}}_{s_{m}} (t),$ where ${\tilde{z}}_{s_{i}} (t) = P_{s_{i}} {\tilde{z}}_{s} (t) \in H_{s_{i}}$ is the state of a one-dimensional system, describing the evolution of the ith transformed slow mode, where $i = 1, \dots, m$ . $P_{s_{i}}$ is the orthogonal projection operator that projects ${\tilde{z}}_{s} (t)$ onto ${\tilde{z}}_{s_{i}} (t),$ and $P_{s_{i}}$ is invertible.

Based on this decomposition, the evolution equation for the ith transformed

Fault detection and FTC architecture for sensors

As the k(k ≤ n) sensors are activated, the remaining $n - k$ sensors are kept dormant. When the jth sensor fault occurs, we have $y_{j} (t) = C (x_{j}^{s}) [z (t) + H (t - T_{c_{j}}) f_{c_{j}} (t)]$ for $j = 1, \dots, n .$ As only the ith actuator is activated, we have $y_{j} (t) = C (x_{j}^{s}) [{\tilde{z}}_{s_{i}} (t) + H (t - T_{c_{j}}) f_{c_{j}} (t)] .$ For sensor fault detection, the observer can be constructed as follows: ${\hat{y}}_{j} (t) = C (x_{j}^{s}) \hat{z} (t) = C (x_{j}^{s}) \hat{z_{i}} (t) .$ The residual signal between the actual output and estimated output is given by $\begin{matrix} ɛ_{j} (t)) & = & y_{j} (t) - {\hat{y}}_{j} (t) = C (x_{j}^{s}) [{\tilde{z}}_{s_{i}} (t) - \hat{z} (t) + H (t - T_{c_{j}}) f_{c_{j}} (t)] \\ = & C (x_{j}^{s} \end{matrix}$

Fault detection and FTC in the infinite-dimensional system

In the last section, we designed a strategy for the fault detection and FTC of actuators and sensors based on the approximate reduced-order model of $ɛ = 0$ . In this section, we consider how the fault detection and FTC architecture of actuators and sensors is implemented in the infinite-dimensional system of ε > 0.

Numerical results

In this section, we illustrate how the proposed method can be used to deal with the fault detection and FTC problems of actuators and sensors in a DPS through computer simulations. Here, we consider a long and thin catalytic rod in a reactor (Fig. 1). The reactor is being fed with pure species A and a zeroth-order exothermic catalytic reaction of the form A → B takes place on the rod. As the reaction is exothermic, a cooling medium is in contact with the rod [20]. Under standard assumptions,

Conclusion

In this paper, a complete strategy for fault detection, diagnosis and reconfiguration of actuators and sensors for a class of DPS was developed. Model reduction techniques were initially employed to derive a finite-dimensional approximation of the DPS, which was then analyzed. A detection observer utilizing a time-varying threshold was developed to detect the occurrence of each actuator fault and an adaptive diagnosis observer was developed to estimate actuator faults under the condition of

Acknowledgment

This paper was supported by the National Natural Science Foundation of China (No. 41401384, No. 41201368) and Scientific Research Foundation of Binzhou University (No. 2016Y04).

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View full text

Fault detection and fault-tolerant control of actuators and sensors in distributed parameter systems

Highlights

Abstract

Introduction

Section snippets

Problem formulation

Fault detection and FTC architecture for actuators

Fault detection and FTC architecture for sensors

Fault detection and FTC in the infinite-dimensional system

Numerical results

Conclusion

Acknowledgment

J. Franklin Inst.

Chem. Eng. Sci.

Comput. Chem. Eng.

Chem. Eng. Sci.

Ind. Eng. Chem. Res.

AIChE J.

Actuator and sensor fault isolation of nonlinear process systems

Chem. Eng. Sci.

Detection, isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: application to a waste water treatment process

Appl. Math. Model.

Robust fuzzy scheduler fault tolerant control of wind energy systems subject to sensor and actuator faults

Electr. Power Energy Syst.

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IET Control Theory Appl.

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