High-precision torque regulation is essential to ensure reaction wheel systems meet the stringent attitude control requirements of modern spacecraft. In three-phase half-bridge brushless DC (BLDC) drives, non-ideal back-electromotive force (back-EMF) waveforms cause pronounced conduction interval torque ripple, leading to inaccurate and unstable output torque. To address this problem, this article proposes a composite torque control strategy integrating an Adaptive Nonsingular Fast Terminal Sliding-Mode Observer (ANFTSMO) with an Adaptive Sliding-Mode Controller (ASMC). The ANFTSMO achieves precise back-EMF estimation and electromagnetic torque reconstruction by eliminating singularities, reducing chattering, and adaptively adjusting observer gains. Meanwhile, the ASMC employs an adaptive switching gain function to achieve asymptotic current convergence with suppressed chattering, thereby ensuring accurate current tracking. System stability is verified via Lyapunov analysis. Simulation and experimental results demonstrate that, compared with conventional constant-current control, the torque smoothness and disturbance rejection of the proposed method are improved, enabling precise and stable reaction wheel torque delivery for high-accuracy spacecraft attitude regulation.