A general active fault-tolerant control framework is proposed for nonlinear systems with sensor faults. According to their identifiability, all sensor faults are divided into two classes: identifiable faults and non-identifiable faults. In the healthy case, the control objective is such that all outputs converge to their given set-points. A fault detection and isolation module is firstly built, which can produce an alarm when there is a fault in the system and also tell us which sensor has a fault. If the fault is identifiable, the control objective remains the same as in the healthy case; while if the fault is non-identifiable, the control objective degenerates to be such that only the healthy outputs converge to the set-points. A numerical example is given to illustrate the effectiveness and feasibility of the proposed method and encouraging results have been obtained.