Vertical position control of the elongated plasma is essential for the stable operation of the tokamak device. The PD controller has been the main control algorithm used for vertical position control in EAST in recent years. However, it is difficult for the controller to adapt to the vertical position response changes caused by plasma variations during discharge. Furthermore, the pure time delay in the EAST vertical position control system causes control instability at high vertical displacement growth rates γ. In this work, we expand on Rui et al (2024 Nucl. Fusion64 066040) and provide a comprehensive introduction to the neural network-based vertical position adaptive control system on EAST. To adapt the controller to vertical displacement response variations and compensate for system delay, we propose a model-based control algorithm. In this algorithm, controller parameters are calculated via the Linear Quadratic Regulator method, while system delay is compensated using a Smith predictor. In order to achieve real-time implementation of the above process, we simplified the vertical displacement model of EAST and trained a neural network model to obtain model parameters in real time during discharge. The new control system has been applied to the EAST in the 2024 campaign experiment and can achieve stable control in multiple configurations without manual parameter tuning when the configuration changes during the discharge process. The control system has achieved stable control with a vertical displacement growth rate of ∼1300/s for the first time, providing important assistance for the future development of the device.