## 3 Dynamic Energy Consumption Model of the System  
The principle of power bond graphs theoretically depicts the energy transfer process in a system utilizing a series of graphical symbols. The flow variables of each energy transmission segment in the system are represented by f, the potential variables by e, the generalized displacement by q, the generalized momentum by p, and the transferred energy by E.  
Within the power bond graph model, resistive elements are utilized to signify the transmission dampening of components, denoted by the symbol R. Capacitive elements depict the elastic losses of components, designated by the letter C. Inertial elements reflect the inertial losses of components, emblazoned with the letter I. Notably, in hydraulic systems, the internal leakage action of oil fluid is often depicted by a resistive element. To more clearly depict the system model, power bond graph theory incorporates energy sources, converters, and interconnections. The rotating speed output by the motor is envisaged as a flow source, signified by the character Sf; the system's exterior load belongs to a potential source and denotes Se; the transformation relationship between potential variables and fluid variables within the system is depicted using the converter, symbolized as TF. Moreover, while detailing the process of energy transmission, the aforementioned components are interconnected via 0 junctions and 1 junctions. The 0 junction serves as a common potential junction, connected to constituents that share identical potential variables for input or output; the 1 junction functions as a common flow junction, connecting components with uniform flow variables for input or output. The utilization of power bond graphs is predicated on its myriad benefits: Power bond graphs can succinctly represent the physical topology structure and a variety of dynamic influencing factors of the system, allowing the modeling of computing structures. It is a precise method to express the mathematical model of the system, facilitating the derivation of sets of relatively simple and straightforward equations for programming implementation, ideal for the application of automated modeling and simulation technologies. It possesses hierarchical structures and object-oriented attributes, augmenting the convenience of model construction and reusability. As an indispensable system model representation method, power bond graphs can be readily transformed into other forms, such as state space representations, transfer functions, block diagrams, and signal flow charts. According to bond graph theory, energy transfer during the operation of a traction system can be described as follows:  
1. The output speed of the synchronous motor (flow source, Sf) causes the motor spindle (inertia element, I\({}_{4}\)) to rotate, during which the rotational damping of the motor  
Figure 6: Structure of fuzzy PI controller. spindle (resistive element, R\({}_{5}\)) needs to be overcome, and the torque angle of the motor spindle changes with the torque received (capacitive element, C\({}_{2}\));
2. The rotation of the motor spindle will amplify the torque and reduce the speed through the gearbox transmission ratio (converter, TF1), thereby driving the gearbox and the steel cable drum (inertia element, I\({}_{10}\)) to rotate. During this period, it is necessary to overcome the rotational damping of the gearbox and the steel cable drum (resistive element, R\({}_{11}\)), and the output shaft torsion angle of the gearbox changes with the torque received (capacitive element, C\({}_{8}\));
3. At the steel cable drum, energy transfer is divided into 1 the rotation of the steel cable drum is converted into the translation of the steel cable (converter, TF2), and the steel cable is fixedly connected to the correction device, thereby pulling the correction device and the captured helicopter (inertia element, I\({}_{17}\)).