The centrosome plays a crucial role in regulating the flow field of a continuous wind tunnel, and its positioning precision directly impacts the control accuracy of the Mach number. A high‐precision positioning control algorithm for the wind tunnel centrosome is proposed based on a model predictive control framework. Since that the centrosome is a typical non‐linear system with a Hammerstein structure comprising an input backlash and a linear dynamic block in series, a parameterized least‐squares identification method is constructed based on an adaptive forgetting factor strategy and a centrosome position prediction model with input backlash is established. To counteract the weakening effect of the backlash non‐linear block on the control signal, a compensator is constructed to compensate for the non‐linear input block. Considering that the input undetectable disturbance signal in the actuator may lead to unpredictable responses, an intermediate state observer is designed and the stable convergence of the observer algorithm is also proved. Finally, the closed‐loop stability of the proposed control algorithm is analyzed by constructing a Lyapunov function. Experimental testing verifies the superiority and applicability of the proposed algorithm.