Abstract: In view of the time-varying bias faults of a wind turbine pitch angle system, we propose an adaptive convex polyhedron observer and an improved fault estimation algorithm on the basis of the traditional fault observer. We design a linear parameter varying (LPV) fault-tolerant controller of the double convex polyhedron on the premise of obtaining the estimated fault signal by combining real-time measurable scheduling variables and the linear matrix inequality technique. This method not only eliminates the linearization error of the traditional model of the single-layer structure but also improves the linearization degree of the system and guarantees the inhibiting effect of the controller on faults. We design the fault diagnosis observer and the output feedback fault-tolerant controller separately and consider their performances simultaneously to simplify design procedures. Simulation results show the effectiveness of the proposed method.