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Based on homogeneous system theory, a finite-time proportional-integral controller is first constructed for the d-axis current loop system, such that the desired current can be tracked in finite time. To overcome the influence of the unmatched load torque disturbance of the second-order model for the speed regulation system, a nonlinear integral dynamic is introduced. Then, based on an appropriate coordination and homogeneous system theory, a new finite-time proportional-integral-derivative controller is constructed. Strict theoretical analysis based on Lyapunov stability theory is provided to verify the finite-time stability of the corresponding closed-loop system. 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