Operator-Based Framework for Fault Diagnosis in Nonlinear Tracking Control Systems

In applying control schemes to real plant, operator failures happen due to various environmental factors. Considering the purpose of engineering safety, the control system of the real plant must have the capability of distinguishing fault signals. For this reason, fault diagnosis or fault detection technology of the plant is studied by many researchers1,2,3,4. Broadly speaking, fault diagnosis technology covers two research ways. One is a mechanical method that uses an increased number of sensors. In this approach, each sensor parameter represents a respective working part and has a static normal value in the normal working state. Therefore it is simple to depict the abnormal signal by detecting whether the present sensory data deviate from the standard value or not. The other one is an analytical method that uses measurable processes information of the plant5. That is, measurable signal analysis schemes and plant analysis by using plant models together with parameter and state estimation methods are considered. Mainly the analytical methods are studied because the mechanical method costs more. The analytical methods6,8 are classified into two categories. One is to use a model of the plant and the other is not to use the model of the plant. In the latter case, there are two methods of using a neural network or a genetic algorithm applied to artificial intelligence. On the other hand, the first method uses a static model or a dynamic model. As the static methods, there are parity vector law, vector slope law, and probability model to a static mode. The most commonly used method that uses a dynamic model is the method that uses estimation methods9,10,11,12. Recently, concerning fault diagnosis methods, inference method is introduced6. This method uses the basic relationships between faults and symptoms which are at least partially known so that this a priori knowledge can be represented in causal relations. However, considering nonlinear elements in real plants and in comparison with the inherently difficult problems of nonlinearity, the increasing demand for a mathematical theory is desired in fault diagnosis. Addressing this problem, in this paper, we introduce a framework of operator-based robust fault detection in nonlinear control systems using robust right coprime factorisation approach. The problem of robust fault detection based on a nonlinear operator framework for nonlinear plants subject to operator failures has received relatively less attention. In this paper, a framework of robust fault detection in nonlinear tracking operator systems is presented by using a robust right coprime factorisation approach. The detailed explanation of the proposed design scheme is given below. Concerning the operator-theoretic approach, a few researches that have related the approach are given12,13,14. The relation between the robustness of the right coprime factorisation and the robust stability of the perturbed nonlinear plant is shown by Chen and Han13. Recently, based on the design scheme, a robust tracking operator system of nonlinear plant is shown by Deng et al.14, and the perturbed signal of the nonlinear plant does not affect the plant output error signal. That is, the nonlinear tracking operator system has no relation with the plant output error signal. Following these developments, using two operators in the Bezout identity, the fault signal in the nonlinear tracking operator system can be analysed. By using two operators which satisfy the Bezout identity, we analyse the fault signal of nonlinear tracking operator system based on robust right coprime factorisation. An example is presented to support the theoretical analysis. The outline of this paper is as follows. First, some definitions of operators, comprime factorisation and internal stability are reviewed12,13,15. Next, an operator-based nonlinear tracking control system is designed by using robust right coprime factorisation approach. Then the framework of robust fault detection by using the obtained robust right coprime factorisation presentation in nonlinear control system is shown. Further, simulation and experimental examples are presented to support the theoretical analysis in the previous section. Finally, we draw brief conclusions on our current and further work.