A robust fault detection scheme for a class of nonlinear systems with uncertainty is proposed. The proposed approach utilizes robust control theory and parameter optimization algorithm to design the gain matrix of fault tracking approximator (FTA) for fault detection. The gain matrix of FTA is designed to minimize the effects of system uncertainty on residual signals while maximizing the effects of system faults on residual signals. The design of the gain matrix of FTA takes into account the robustness of residual signals to system uncertainty and sensitivity of residual signals to system faults simultaneously, which leads to a multiobjective optimization problem. Then, the detectability of system faults is rigorously analyzed by investigating the threshold of residual signals. Finally, simulation results are provided to show the validity and applicability of the proposed approach.
In recent years, with the development of intelligent control technology and processing ability of microchips, modern dynamic systems are becoming more and more complex. Fault detection and identification (FDI) can be deployed for monitoring and reacting to the faults occurring in these modern dynamic systems, which has a broad range of applications including intelligent power grids, underwater robot, high voltage direct current transmission lines, and long transmission lines in pneumatic, chemical processes. Effective FDI schemes can ensure safety and reliability of complex dynamic systems. The most fundamental problem for FDI is to develop a fault diagnosis observer or fault diagnosis filter. Due to the development of various nonlinear or linear states observers, the model-based analytical redundancy approaches received more and more attention in the last two decades, including observer based method, parity space based method, eigenstructure assignment based method, and parameter identification based method and
Early fault diagnosis approaches often assumed the availability of an accurate dynamic system model. In practice, however, such an assumption can be invalid. The main reason is that unstructured modeling uncertainties are always unavoidable when modeling system mathematical structures. Therefore, there are a growing number of researchers focusing their interests on FDI for nonlinear systems with uncertainty. A novel integrated fault diagnosis and fault tolerant control algorithm for non-Gaussian singular time-delayed stochastic distribution control system was proposed based on iterative learning observer. The iterative learning observer was developed to obtain estimation of system faults. Recently in [
In our previous work [
An outline of this paper is organized as follows. In Section
Consider a class of uncertain nonlinear systems described by
The observability matrix associated with the pair
The function
The nonlinear function
To detect a fault, the FTA is constructed as follows [
The basic idea behind the FTA is to adjust the virtual fault
From (
First, we convert the parameter optimization problem into a performance index optimization problem. Then, the design of gain matrix is given in terms of linear matrix inequality (LMI).
Define the state estimation error
The item
Let
Given a constant
We choose a Lyapunov function of the form:
When the system uncertainty
Given a constant
We choose a Lyapunov function of the form:
When the system faults
Given constants
By combining Theorems
Theorem
In the above sections, we have investigated the optimization of the value of gain matrix
Suppose Assumptions
Without loss of generality, we assume
Subtracting (
Due to
This completes the proof.
In the presence of unstructured modeling uncertainty, we have to determine the upper bounds of the residual signals for fault detection, referred to as the threshold. Theorem
In this section, we use the proposed method to detect faults for a class of uncertain nonlinear systems. Let us consider the uncertain nonlinear system with parameters as follows:
White noise signal.
Generated residual signal.
From Figure
Evolution of residual evaluation function.
This paper has proposed a fault detection scheme for a class of uncertain nonlinear systems. The main contribution of this paper is to utilize robust control theory and multiobjective optimization algorithm to design the gain matrix of FTA. The gain matrix of FTA is designed to minimize the effects of system uncertainty on residual signals while maximizing the effects of system faults on residual signals. The calculation of the gain matrix is given in terms of LMIs formulations. The selection of threshold for fault detection is rigorously investigated as well. In the end, an illustrative example has demonstrated the validity and applicability of the proposed approach.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by National Natural Science Foundation of China (nos. 51407078, 61201124) and Special Fund of East China University of Science and Technology for Basic Scientific Research (WJ1313004-1, WH1114027, H200-4-13192, and WH1414022).