Simultaneous Fault Detection and Control Design for Linear Fractional-Order Systems

Abstract

The focus of this paper is the analysis and design scheme of simultaneous fault detection and control (SFDC) for linear continuous-time fractional-order systems assumed to be affected by sensor, actuator and process faults as well as disturbances. In essence, this simultaneous design unifies both the control and the detection modules into a single unit that is called the controller/detector unit. This unit is designed such that it generates two signals, namely the residual and the control signals. The system can be stabilized using the control signal, and the residual signals can detect the fault based on model-based fault detection and isolation algorithms. The SFDC module should be designed so that the effects of faults and disturbances on the residual signals are maximized and minimized, respectively. To this end, the SFDC problem is formulated as the mixed $$H_{ - } /H_{\infty }$$ optimization problem. Stability and fault detection are both considered through certain performance indices, and new sufficient conditions in the form of linear matrix inequalities are obtained. Finally, some simulation examples are given to illustrate the effectiveness of the proposed design method.