# Event-Driven Dynamics Model of Operating State Evolution for Cantilever Roadheader
## 2 Dynamics Model of the State Evolution of Cantilever Roadheader
### Real-Time Data-Driven Dynamics Evolution of the Cutting State
#### 2.3.3 State Transition Mechanism  
After the abnormal state is recognized, a state transition mechanism is employed to ensure that the transition to the normal operating state is both rapid and smooth. To ensure the accuracy of the information feedback from the remote control system, the state transition involves the synchronization of the physical and virtual control environment. This synchronized processing improves the accuracy and reliability of the transition process, enabling an efficient transition from abnormal to normal conditions. By keeping the data of the two environments synchronized in real time, the time delay of information transmission is minimized, which enhances the ability to instantly control the operation status. The leap process involves synchronization work in both spatial and temporal dimensions, including threshold synchronization and periodic synchronization. As shown in Figure 13, at timestamp T1, the physical spatial model executes a control instruction that is scheduled to perform a state change at the same time as the digital twin. However, the moment when the digital spatial model executes this instruction is not synchronized with the physical model due to the inherent time delay. The digital model completes the state change to A1 at timestamp T2, corresponding to the state B1 of the physical model at timestamp T1. At this point, the digital space side is already behind \(\Delta t_{1}\) compared to the time when the instruction was executed in the physical space, and the state of the physical model has transitioned to an intermediate state B1\({}^{\prime}\). Figure 13: State transition schematic. In order to optimize the digital twin hysteresis problem caused by the inherent time delay, the digital model will predict the future state evolution of the physical model when the state change is performed at timestamp T2. The predicted state of the physical model will be changed to B2 at timestamp T3, and the digital model will take the predicted B2 as the goal of the state change, and take timestamp T3 as the endpoint of the change to carry out the state leap of the digital twin model. At this time, the digital model will no longer follow the state evolution route of the physical model via the intermediate state B1\({}^{\prime}\), and the state of the object on one side of the digital space will be changed directly from A1 to A2 via \(\Delta t_{2}\). After completing the leap, the bilateral spatial model state will reach a real sense of spatiotemporal synchronization at timestamp T3. By predicting and adjusting the state change target and time of the digital model, the effect of the inherent time delay on the digital twin lag can be effectively reduced, and more accurate spatiotemporal synchronization can be achieved. Threshold synchronization, based on the state transition principle, identifies the critical state B1\({}^{\prime}\) achieved at timestamp T2 when lateral slippage occurs during physical tunneling. Upon exceeding preset thresholds, cutting arm adjustments alone become insufficient to meet the operational requirements, triggering classification as a new disturbance event. This event state mapping relationship is archived in the database and integrated into the state evolution graph. The physical operation must adjust the body parameters to return to the normal operation state. The state evolution path of the digital twin may deviate from the physical tunneling because the operation state experiencing the sudden perturbation is not in the planned trajectory. To ensure the synchronization between the virtual and physical state after a disturbance event, the corrective control commands of the physical tunneling operation need to be combined with the auxiliary guidance of the digital twin.