Intermediate Observer-Based Fault-Tolerant Control for Continuous-Time Switched Affine Systems: Application to Power Converters

Abstract

In this paper, the fault estimation and fault-tolerant control problems are addressed for a class of continuous-time switched affine systems with actuator faults and bounded disturbances. Two novel observer-based approaches are developed to address the fault estimation problem for switched affine systems. The first one refers to a dynamic proportional-integral observer design method, where the presented fault estimate constitute proportional and integral terms to enhance the accuracy of the fault estimation, the common assumption that the measurement output derivative needs to be measurable is eliminated. The second one is an intermediate variable observer, which relaxes the observer matching condition. The output estimation error feedback term is added to the intermediate variable observer to improve the estimation performance. Then, by introducing a switching multi-shifted-point-dependent Lyapunov functional, both a fault-tolerant controller and a new robust output-dependent switching law are jointly designed to compensate the fault effects in the closed-loop switched affine systems and to ensure the practical exponential stability of augmented system, where the convergence region consists of multiple regions and the center point is around some shifted points. The traditional switching quadratic Lyapunov function method is generalized by the designed method. A practical study of a DC-DC boost converter and a numerical example are provided to illustrate effectiveness and validity of the developed fault-tolerant control design method. Note to Practitioners—Power electronics are very common in practical systems, which are usually modeled as a class of switched affine systems. In real applications, faults inevitably occur, which may lead to undesirable behavior and damage to the system. Therefore, how to achieve better fault-tolerant control objectives to guarantee the normal operation of the system with faults is a hot topic. It is practically important to address the fault-tolerant control problem for switched affine systems, where actuator faults and bounded disturbances exist simultaneously. In addition, on account of the existence of affine terms, the controller synthesis of switched affine systems is more complicated than switched linear systems. Based on the special structure of switched affine systems, two kinds of novel fault observers are proposed, where the dynamic proportional-integral observer is proposed to improve the estimation accuracy and speed by utilizing the current output information, and the common supposition that the output derivative needs to be measurable is eliminated. Furthermore, to avoid the limitation of observer matching conditions, an improved intermediate variable observer is designed to estimate faults. Different from the conventional method, the intermediate variable parameters can be selected separately for the corresponding fault channel of each subsystem and the error feedback term of output estimation is added to the intermediate variable observer to enhance the estimation performance. In addition, it is challenging to design a fault-tolerant controller and an output-dependent switching law to guarantee that the augmented system is practically stable and robust to bounded disturbances. The results demonstrate that the designed fault-tolerant control scheme has a definitive practical value.