This paper proposes a model-compensated active disturbance rejection control (MCADRC) method for the structural vibration suppression of an all-clamped plate based on the electromagnetic inertial actuator. The studied system features strong nonlinearity, high-order dynamics, and significant electromechanical coupling effects, which make accurate mathematical modeling challenging. By leveraging the model-independent nature of the extended state observer (ESO), the total disturbance is effectively estimated and compensated in real time. To enhance the disturbance estimation performance without increasing the observer bandwidth, a model-compensated ESO (MCESO) is designed based on a reconstructed vibration system model. The MCESO utilizes available model information which is measured by the experimental device to reduce the estimation burden of the observer. A corresponding state feedback controller is developed to incorporate both system states and total disturbance estimation. The proposed control method is implemented and validated on the vibration experimental platform. Comparative experimental results in both time and frequency domains demonstrate that the proposed MCADRC outperforms the traditional ADRC in terms of vibration suppression. These results confirm the effectiveness and practicality of the proposed method for high-order structural systems with strong coupling effects.