In this article, we study a new approach to predict failures in feedback control system and particularly in actuators. However, we use two-tank control system with a proportional–integral–derivative controller for controlling a process variable. In practice, the actuator is a dynamic operating component in a random environment. Moreover, its capacity decreases over time and becomes valuable information for reliability analysis. The loss of capacity which is related to degradation, either normally or in an accelerated manner, depends on different operational conditions of the feedback control system and environmental factors. For this reason, to improve its working condition, a service life time analysis is necessary. Obviously, one has to predict the trend of future system characteristics, such as the reliability, which is measured by the estimate value of remaining useful life. In this situation, we use the stochastic gamma process model to describe the degradation behavior of the actuator. Generally, the algorithm of extended Kalman filter is a widely used method to overcome the difficulties of estimating the state vector in a nonlinear model of two-tank control system. This algorithm gives an innovation vector or prediction residual which contains fault information, when the system is failed. The prediction residuals can be recursively computed for diagnosis by the generalized likelihood ratio test. However, we use the generalized likelihood ratio test algorithm to estimate the moment at which the prognostic started. Finally, a practical case study is given to show the effectiveness of the proposed approaches for failure detection. Obviously, the simulation results show that the degradation path of the actuator capacity is estimated and the reliability based on remaining useful life predicted is analyzed.

在本文中，我们研究了一种预测反馈控制系统（尤其是执行器）故障的新方法。但是，我们使用带有比例-积分-微分控制器的两缸控制系统来控制过程变量。在实践中，执行器是随机环境中的动态操作组件。而且，其容量会随着时间的推移而降低，并成为进行可靠性分析的有价值的信息。与退化相关的容量损失，无论是正常情况还是加速情况，都取决于反馈控制系统的不同运行条件和环境因素。因此，为了改善其工作条件，必须进行使用寿命分析。显然，必须预测未来系统特性的趋势，例如可靠性，通过剩余使用寿命的估计值来衡量。在这种情况下，我们使用随机伽马过程模型来描述执行器的退化行为。通常，扩展卡尔曼滤波器算法是克服两罐控制系统非线性模型中估计状态向量的难题的一种广泛使用的方法。当系统出现故障时，该算法会给出包含故障信息的创新矢量或预测残差。可以通过广义似然比检验递归计算预测残差以进行诊断。但是，我们使用广义似然比检验算法来估计预后开始的时刻。最后，通过一个实际案例研究来说明所提出的故障检测方法的有效性。明显地，