Isolation of process and sensor faults for a class of nonlinear uncertain systems

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

In this study the tracking problem for a class of non-linear uncertain systems is analyzed. The considered class of non-linear systems are restricted by those verifying the global Lipschitz condition on non-linearities making them linear-like. A new sliding mode neurocontroller is suggested to solve this problem. The controller desing includes the on-line state estimates construction and the corresponding tracking control based on sliding mode approach and the reconstructed dynamics generated by a special non-linear observer. A special sliding mode technique during the “off-line training” to estimate the right-hand side of the given dynamics in finite-time was applied. This procedure allows use of these estimates for the best (in LQ-sense) nominal weights selection in the neuro observer designed. A switching (sign) type term is incorporated in the observer structure to correct the current state estimates using just the on-line measurable output. This observer is supplied with a new learning procedure with switching structure. Two illustrative examples are presented: a benchmark problem related with a nominal linear system and a real chemical procedure dealing with the organic compounds elimination by ozone effect.

A fault detection and isolation (FDI) scheme is proposed for a class of nonlinear systems with unknown faults, system uncertainties and external disturbances. The main feature is that fault isolation and control reconfiguration are integrated via a supervisory switching strategy. By constructing a set of monitoring functions (MFs) to supervise some variables generated in the backstepping procedure, the candidate controllers are switched to detect the occurrence of fault and identify the specific fault type. It is shown that the tracking error can be preserved within a prescribed performance regardless of system faults. Case study of a manipulator system subject to different faults is carried out to validate the effectiveness of this FDI approach.

On Switched Controller Design for Robust Control of Uncertain Polynomial Nonlinear Systems Using Sum of Squares

Adaptive output feedback event-triggered tracking control for nonlinear systems with unknown control coefficient

An approach for model-based fault detection and isolation (FDI) of sensor and process faults for nonlinear processes is presented. The process is decomposed into several sub-processes and for each process a nonlinear model is identified. This model bank consisting of fuzzy models (Takagi-Sugeno type) is used to generate several different estimates for process outputs and states. Comparing these estimates with the actual measured ones leads to residuals which indicate the state of the system and provide information about the source of possible faults. The two ways to implement a model, as a parallel or as a series-parallel model lead to different FDI results. Hence, this different sensitivity is also investigated in this contribution. The practical applicability is illustrated on an industrial scale thermal plant. Here, seven different process faults and eight different sensor faults can be detected.

Sensor fault detection and isolation filter for polytopic LPV systems: A winding machine application

International audience

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.

Diagnosability of fuzzy discrete event systems

In this paper, we address the stabilization problem for nonlinear systems in a critical case. Namely, we study the class of canonical nonlinear systems. Canonical nonlinear systems or chain of power integrators is an important subject of research. Studying such systems is complicated by the fact that they cannot be mapped onto linear systems. Moreover, they have the uncontrollable first approximation. Previous results on smooth stabilization of such systems were obtained under the assumption that the powers in the right-hand side are strictly decreasing. In this work, we consider a case of non-increasing powers in the right-hand side for a three-dimensional system. A popular approach for studying such systems is the backstepping method, which is a method of step-wise stabilization. This method requires a sequential investigation of lower-dimensional subsystems. Backstepping enables the study of a wide range of nonlinear triangular systems but requires technically complex and cumbersome computations. Therefore, a natural question arises about constructing stabilizing controls of a simple form. Polynomial controls can serve as an example of such controls. In the paper, we demonstrate that linear controls can be considered as stabilizing controls. We derive sufficient conditions for the coefficients of the linear control that ensure the asymptotic stability of the zero equilibrium point of the corresponding closed-loop system. The asymptotic stability is proven using the Lyapunov function method, which is found as the sum of squares. The negative definiteness of the Lyapunov function derivative in a neighborhood of the origin guarantees asymptotic stability. In contrast to the case of strictly decreasing powers, additional conditions on the control coefficients, apart from their negativity, emerge. The obtained result extends to a broader class of nonlinear systems through stabilization by nonlinear approximation. This allows the consideration of systems with higher-order terms in the right-hand side. The effectiveness of the applied approach is illustrated by several model examples. The method used in this work to investigate the case of non-increasing powers can be applied to systems of higher dimensions.

This paper presents a design methodology and some analytical results for distributed sensor fault detection and isolation (SFDI) of a class of nonlinear uncertain systems. During the initial stage of the nonlinear system operation, an adaptive approximation technique is used for learning online the modeling uncertainty. Then, local SFDI modules are designed using a dedicated nonlinear observer scheme. The fault isolation process is enhanced by deriving a combinatorial decision logic that integrates information from local SFDI modules. The performance of the proposed diagnostic scheme is analyzed in terms of its robustness with respect to the modeling uncertainties and conditions for ensuring fault detectability and isolability.

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.

A class of nonlinear systems is considered in IR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> whose system's function is, component-wise, given by the product of real powers of the state's entries. We call it the class of 'Π-algebraic' systems. It is shown that every Π-algebraic nonlinear system undergoes a quadratic embedding into a suitable (non associative) algebra. This means that a product can be defined in the state-space, which makes the latter a non associative algebra, whose associated quadratic differential equation has a subset of entries of its solution equal to the solution of the original nonlinear system. We also study a related control problem, where for a meaningful subclass of the considered systems it is shown that a state-feedback regulator can be build up, having exponential performance, which makes the y-axe in IR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> a globally asymptotically stable equilibrium set of the closed-loop system.

This paper describes a real-time on-line process monitoring and fault isolation approach using PCA (principal component analysis). It also presents the software implementation architecture using an OPC (OLE for process control) compliant framework, which enables a seamless integration with the real plant and DCS. The proposed approach and architecture are implemented to monitor a refinery process simulation that produces cyclohexane using benzene and hydrogen. The result shows that both sensor faults and process faults can be detected on-line and the dominating process variables may be isolated