This paper is to develop a general form for Total Measurable Fault Information-based Residual (ToMFIR) approach to fault detection in dynamic systems. The ToMFIR is initially established for systems with a constant control input signal and a fault approaching to a constant. Practical systems satisfying the aforementioned conditions is few. That is why a generalized form is developed in this work. The definition of the ToMFIR is first introduced and the special case is also presented for the continuity of the statement. Based on a stable and linear time-invariant system, the general form of the ToMFIR is derived, and a practical DC motor example, with a PID controller, is used to demonstrate the effectiveness and robustness of the ToMFIR-based fault detection.

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