Reliability analysis of aging control system via stability margins

Abstract

Automatic control systems are critical sub-systems that ensure the reliable and efficient operation of a modern manufacturing system collaborating with other sub-systems. Critical to the performance of control systems are aging actuators that will ultimately result in an unstable control process and consequently failure of the supported manufacturing system. In this paper, by using the Nyquist stability criterion we prove the stability margin of a first-order control process with dead time, which is the fundamental failure threshold of the corresponding control system. The impact of aging actuators on the control system is modelled by errors in the dead time, which is the key parameter in the transfer function of a control process. By linking the stability margin with the physical degradation process of the actuator, we further derive explicitly the maximum allowable degradation level of the actuator and use the information to compute the failure probability of a control system. The proposed framework is demonstrated on a solar energy platform which can serve as a significant illustration for sustainable manufacturing. This platform is equipped with an aging valve controlling its temperature and the degradation process is modelled by an inverse Gaussian process with a curved hitting boundary to address the varying working conditions of the valve. Our case study shows that our method approximates the exact failure probability well with much lower computational cost compared to the traditional Monte Carlo simulation. Show more