Research into a Marine Helicopter Traction System and Its Dynamic Energy Consumption Characteristics

: As countries attach great importance to the ocean-going navigation capability of ships, the energy consumption of shipborne equipment has attracted much attention. Although energy consumption analysis is a guiding method to improve energy efﬁciency, it often ignores the dynamic characteristics of the system. However, the traditional dynamic analysis method hardly considers the energy consumption characteristics of the system. In this paper, a new type of electric-driven helicopter traction system is designed based on the ASIST system. Combined with power bond graph theory, a system dynamic modeling method that considers both dynamic and energy consumption characteristics is proposed, and simulation analysis is carried out. The results indicate that the designed traction system in this study displays high responsiveness, robust, steady-state characteristics, and superior energy efﬁciency. When it engages with helicopter-borne aircraft, it swiftly transitions to a stable state within 0.2 s while preserving an efﬁcient speed tracking effect under substantial load force, and no signiﬁcant ﬂuctuations are detected in the motor rotation rate or the helicopter movement velocity. Moreover, it presents a high energy utilization rate, achieving an impressive energy utilization rate of 84% per single working cycle. Simultaneously, the proposed modeling methodology is validated as sound and effective, particularly apt for the dynamic and power consumption analysis of marine complex machinery systems, guiding the high-efﬁciency design of the transmission system.


Introduction
Since modern times, the ability of ships to navigate long distances and engage in long-term combat has become crucial [1][2][3].At the same time, an increasing amount of equipment needs to be carried on ships, especially high-energy auxiliary power equipment represented by helicopter traction systems [4,5], resulting in increased additional energy consumption of ships.However, ships are often unable to carry too much fuel due to their own volume, which puts higher demands on the energy consumption of onboard equipment [6][7][8].The high-energy-consumption problem of shipborne equipment is often caused by the use of hydraulic transmission systems [9,10] and is affected by the operating environment of ships.Complex and bent hydraulic pipelines further exacerbate the energy loss of the system [11,12].In recent years, with the development of power electronics technology, pure electric equipment has attracted the attention and favor of researchers because of its superior dynamic, energy consumption characteristics and simple power transmission characteristics [13,14].Concurrently, in recent years, numerous scholars have undertaken research into the diverse shipborne equipment of helicopter traction systems, encompassing aspects such as aerodynamics [15][16][17][18], multibody dynamics [19][20][21], system reliability [22], and path planning [23,24].However, presently, the issue of [25] high-energy consumption by the current helicopter traction systems when transporting shipborne helicopters [10,26], presenting substantial stress to the vessel's energy supply system, and the intricate entanglement of traction steps during task execution are underrated.Essentially, both issues are attributed to the utilization of hydraulic components for the power source within the helicopter traction system, resulting in uncontrollable traction movement speed.Therefore, an effective solution is to design an electric drive transmission system to replace the original hydraulic transmission system while ensuring the performance indicators of the original shipborne equipment.
Driven by the aggressive advancement of power electronics, rare earth materials, and new energy technologies, the permanent magnet synchronous motor (PMSM), with its inherent benefits of a simple structure, compact size, low moment of inertia, high efficiency, and easy heat dissipation and maintenance, has been adopted in a vast array of industries, including rail transportation, electric vehicles, wind power generation, aerospace, and marine vessels [27][28][29], rendering it exceptionally suited for the operating conditions of helicopter traction systems.If coupled with a consistently reliable speed regulation algorithm, PMSM could replace conventional hydraulic power units as the primary source of propulsion for marine equipment, thus tackling these issues.In view of the high control precision and dynamic response characteristics, vector control technology has emerged as the preferred method of regulating PMSM speed [28,30].However, when marine equipment is operational, the axial load of the motor often fluctuates, causing considerable changes in several parameters such as the resistance and inductance in PMSM [31].Vector control algorithms and traditional PID controllers that work alongside them heavily rely on the mathematical model of the motor, which hinders their efficiency in tracking speed in real-world applications [32].As early as 1988, researchers from the United States, like Mario [33], developed an initial design for a power-assisted descent device, achieving a maximum transverse capture time of 1.5 s, but due to the technological limitations of the era, this device lacked speed regulation functionality and was incapable of adequately addressing the aforementioned concerns.As the AC PMSM servo system advances toward higher power, efficiency, and intelligence, a growing number of smart control algorithms are being designed and implemented for the control of motor speed, with fuzzy control algorithms standing out due to their independence from precise models and being the focus of ongoing research.This control algorithm has already been applied to PMSM and achieved favorable control effects [34,35].By incorporating fuzzy control algorithms with vector control algorithms and designing an appropriate control system for marine equipment, the issue of speed control for propulsion systems driven by electricity can be effectively addressed.
However, another important issue lies in the existing research field of system dynamics modeling, where the dynamic characteristics and energy consumption characteristics of systems are often studied separately [36].On the one hand, existing mechanical system dynamics models excessively focus on studying the transmission characteristics of the system [37][38][39].On the other hand, research into energy consumption characteristics often focuses more on energy consumption monitoring and management during system operation [40][41][42].This issue is mainly due to the diversity and complexity of the energy consumption of the actual system.Power bond graph theory provides a feasible solution to this problem, which was first proposed by Professor H.M. Paynter in the United States.With years of evolution and refinement, it has gained practical application across numerous research fields, particularly in mechatronics systems, unveiling considerable prospects for application.This methodology allows for the extraction of pivotal system parameters based on system attributes, which facilitates a more intuitive derivation of the system state equation [43][44][45], making this theory an instrumental tool for resolving dynamic analysis of complex systems [46][47][48].
In response to the prevalent issues in the hydraulic helicopter traction system, a novel electromotive helicopter traction system has been devised.The system employs a synchronous motor as its power source and integrates the vector control algorithm with the fuzzy adaptive PID control algorithm to function as a velocity-tracking controller, thereby allowing for the regulation of the speed of the helicopter traction system.This strategy ensures efficiency while minimizing force during traction.Furthermore, this article integrates power bond graph theory to establish a dynamics model and dynamic energy consumption model for the helicopter traction system, then conducts systematic simulation.The simulation results demonstrate that the newly designed system effectively elevates energy efficiency, ensuring pre-existing operational requirements while also exhibiting superb speed control efficacy.Simultaneously, this modeling approach is intuitive, efficient, and capable of accurately reflecting the dynamic and energy consumption characteristics of the system, enhancing the preliminary design analysis or postoperative energy optimization of marine equipment.

Working Principle
Among the various helicopter landing assistance systems currently in service, the most widely used is the 'Aircraft Ship Integrated Secure and Traverse System (ASIST)' proposed by Canada, which has the advantages of high automation, short landing assistance time, and high adaptability to sea conditions [4,5,49].As shown in Figure 1, the ASIST system consists mainly of landing indicator lights, laser sources, probe rod, track, correction device, camera, control console, and hydraulic traction system.As shown in Figure 2, the process of a marine helicopter landing on a ship with the aid of ASIST can be segmented into the following stages: helicopter approaches the ship, helicopter hovers above the deck, helicopter lands on the deck, and finally, ASIST guides the helicopter to its predetermined location.Upon approaching a vessel, the marine helicopter is initially identified and tracked by a camera installed on the deck.This camera retrieves the target laser source information of the helicopter, calculates the helicopter's location in real time, and transmits it to the control console.The control console provides illuminated guidance information to the pilot via light indicators, routes the helicopter under the guidance of landing indicator lights, and navigates it to the designated landing area.Simultaneously, the control console apparatus controls the hydraulic traction system to drive the correction device to track the helicopter's position but always maintains a suitable safety distance from the helicopter.When the helicopter is positioned appropriately and the external environment permits, the helicopter initiates its descent; the instant the helicopter lands on the deck, the hydraulic traction system drives the correction device to capture the probe rod on the belly of the helicopter and secures the helicopter in the landing area.Upon completion of the capture and tethering process, the operator controls the hydraulic traction system to maneuver the helicopter along the track to the hangar.
Appl.Sci.2023, 13, x FOR PEER REVIEW 3 of 16 synchronous motor as its power source and integrates the vector control algorithm with the fuzzy adaptive PID control algorithm to function as a velocity-tracking controller, thereby allowing for the regulation of the speed of the helicopter traction system.This strategy ensures efficiency while minimizing force during traction.Furthermore, this article integrates power bond graph theory to establish a dynamics model and dynamic energy consumption model for the helicopter traction system, then conducts systematic simulation.The simulation results demonstrate that the newly designed system effectively elevates energy efficiency, ensuring pre-existing operational requirements while also exhibiting superb speed control efficacy.Simultaneously, this modeling approach is intuitive, efficient, and capable of accurately reflecting the dynamic and energy consumption characteristics of the system, enhancing the preliminary design analysis or postoperative energy optimization of marine equipment.

Working Principle
Among the various helicopter landing assistance systems currently in service, the most widely used is the 'Aircraft Ship Integrated Secure and Traverse System (ASIST)' proposed by Canada, which has the advantages of high automation, short landing assistance time, and high adaptability to sea conditions [4,5,49].As shown in Figure 1, the ASIST system consists mainly of landing indicator lights, laser sources, probe rod, track, correction device, camera, control console, and hydraulic traction system.As shown in Figure 2, the process of a marine helicopter landing on a ship with the aid of ASIST can be segmented into the following stages: helicopter approaches the ship, helicopter hovers above the deck, helicopter lands on the deck, and finally, ASIST guides the helicopter to its predetermined location.Upon approaching a vessel, the marine helicopter is initially identified and tracked by a camera installed on the deck.This camera retrieves the target laser source information of the helicopter, calculates the helicopter's location in real time, and transmits it to the control console.The control console provides illuminated guidance information to the pilot via light indicators, routes the helicopter under the guidance of landing indicator lights, and navigates it to the designated landing area.Simultaneously, the control console apparatus controls the hydraulic traction system to drive the correction device to track the helicopter's position but always maintains a suitable safety distance from the helicopter.When the helicopter is positioned appropriately and the external environment permits, the helicopter initiates its descent; the instant the helicopter lands on the deck, the hydraulic traction system drives the correction device to capture the probe rod on the belly of the helicopter and secures the helicopter in the landing area.Upon completion of the capture and tethering process, the operator controls the hydraulic traction system to maneuver the helicopter along the track to the hangar.The hydraulic traction system, which is the main power equipment of the system, is mainly used to track and tow correction devices and helicopters.However, this system has shortcomings, such as slow response speed and poor steady-state characteristics during operation.It is also affected by complex pipelines in the hydraulic system and oil leakage under high loads, resulting in high-energy consumption of the hydraulic traction system.In response to the problems existing in the hydraulic traction system, this article designs a new type of electric-driven helicopter traction system, whose composition and transmission scheme are shown in Figure 3.The working principle of this system is as follows: the control system directly controls the output speed of the motor and drives the steel cable drum to rotate through a reducer.The steel cable wrapped on the steel cable drum moves along the deck track and pulls the helicopter through the pulley block traction correction device.The red circle in the figure represents the probe rod mentioned earlier.At the same time, the steel cable drum drives the cable drum to rotate through chain transmission, allowing the cable to follow the movement of the correction device.
Because of the complex and unpredictable marine environment that affects the recovery of helicopters on ships, especially the rapid and significant shaking of the ship deck, the system load has the characteristics of high frequency and high amplitude.Using a controller with static PID parameters can greatly reduce control accuracy and amplify noise in the differential process.This study combines fuzzy PI control and permanent magnet The hydraulic traction system, which is the main power equipment of the system, is mainly used to track and tow correction devices and helicopters.However, this system has shortcomings, such as slow response speed and poor steady-state characteristics during operation.It is also affected by complex pipelines in the hydraulic system and oil leakage under high loads, resulting in high-energy consumption of the hydraulic traction system.In response to the problems existing in the hydraulic traction system, this article designs a new type of electric-driven helicopter traction system, whose composition and transmission scheme are shown in Figure 3.The hydraulic traction system, which is the main power equipment of the system, is mainly used to track and tow correction devices and helicopters.However, this system has shortcomings, such as slow response speed and poor steady-state characteristics during operation.It is also affected by complex pipelines in the hydraulic system and oil leakage under high loads, resulting in high-energy consumption of the hydraulic traction system.In response to the problems existing in the hydraulic traction system, this article designs a new type of electric-driven helicopter traction system, whose composition and transmission scheme are shown in Figure 3.The working principle of this system is as follows: the control system directly controls the output speed of the motor and drives the steel cable drum to rotate through a reducer.The steel cable wrapped on the steel cable drum moves along the deck track and pulls the helicopter through the pulley block traction correction device.The red circle in the figure represents the probe rod mentioned earlier.At the same time, the steel cable drum drives the cable drum to rotate through chain transmission, allowing the cable to follow the movement of the correction device.
Because of the complex and unpredictable marine environment that affects the recovery of helicopters on ships, especially the rapid and significant shaking of the ship deck, the system load has the characteristics of high frequency and high amplitude.Using a controller with static PID parameters can greatly reduce control accuracy and amplify noise in the differential process.This study combines fuzzy PI control and permanent magnet The working principle of this system is as follows: the control system directly controls the output speed of the motor and drives the steel cable drum to rotate through a reducer.The steel cable wrapped on the steel cable drum moves along the deck track and pulls the helicopter through the pulley block traction correction device.The red circle in the figure represents the probe rod mentioned earlier.At the same time, the steel cable drum drives the cable drum to rotate through chain transmission, allowing the cable to follow the movement of the correction device.
Because of the complex and unpredictable marine environment that affects the recovery of helicopters on ships, especially the rapid and significant shaking of the ship deck, the system load has the characteristics of high frequency and high amplitude.Using a controller with static PID parameters can greatly reduce control accuracy and amplify noise in the differential process.This study combines fuzzy PI control and permanent magnet synchronous motor vector control technology to design a motor controller, dynamically adjusting the PI parameters of the speed loop and maintaining a stable control effect and high control accuracy of the system.The control system flow chart is illustrated in Figure 4.The permanent magnet synchronous motor engaged in the helicopter traction system, subject to the transmission system and the helicopter's load torque, extracting a designated speed from the aforementioned traction transmission dynamics module.This speed is simultaneously input into the control system with the anticipated speed provided by the manipulation console for the helicopter traction system.Graduated feedback control of the speed of the motor is then executed via a fuzzy PI controller.Moreover, the input current of the synchronous motor is regulated through the vector control module, thereby altering its drive torque and subsequently adjusting the motor speed.
Appl.Sci.2023, 13, x FOR PEER REVIEW 5 of 16 synchronous motor vector control technology to design a motor controller, dynamically adjusting the PI parameters of the speed loop and maintaining a stable control effect and high control accuracy of the system.The control system flow chart is illustrated in Figure 4.The permanent magnet synchronous motor engaged in the helicopter traction system, subject to the transmission system and the helicopter's load torque, extracting a designated speed from the aforementioned traction transmission dynamics module.This speed is simultaneously input into the control system with the anticipated speed provided by the manipulation console for the helicopter traction system.Graduated feedback control of the speed of the motor is then executed via a fuzzy PI controller.Moreover, the input current of the synchronous motor is regulated through the vector control module, thereby altering its drive torque and subsequently adjusting the motor speed.The essence of vector control technology is the equivalent representation of AC motor mathematical models as DC motor models for control.This technique achieves control through regulation of the stator current, thereby controlling motor torque; through coordinate transformation, decoupling control of flux linkage and torque is realized.In this article, the combined space vector pulse width modulation (SVPWM) technology adopts a vector control strategy with id = 0 and constructs a dual closed-loop permanent magnet synchronous motor vector control module with a speed loop and current loop, as shown in Figure 5.The structure of the fuzzy PI controller is shown in Figure 6.The fuzzy PI controller obtains real-time adjustments of parameters P and I through fuzzy inference based on the input speed difference (e) and the rate of change (ec) of the speed difference ΔKp and ΔKi, which are finally substituted into Equation ( 1) to obtain the adjusted PI parameters.In the application of fuzzy control for PMSM control, the majority assumes the transformation of the vector control rotational speed loop's PI control into a fuzzy PI control.This The essence of vector control technology is the equivalent representation of AC motor mathematical models as DC motor models for control.This technique achieves control through regulation of the stator current, thereby controlling motor torque; through coordinate transformation, decoupling control of flux linkage and torque is realized.In this article, the combined space vector pulse width modulation (SVPWM) technology adopts a vector control strategy with i d = 0 and constructs a dual closed-loop permanent magnet synchronous motor vector control module with a speed loop and current loop, as shown in Figure 5.
Appl.Sci.2023, 13, x FOR PEER REVIEW 5 synchronous motor vector control technology to design a motor controller, dynamical justing the PI parameters of the speed loop and maintaining a stable control effect and control accuracy of the system.The control system flow chart is illustrated in Figure 4 permanent magnet synchronous motor engaged in the helicopter traction system, sub the transmission system and the helicopter's load torque, extracting a designated s from the aforementioned traction transmission dynamics module.This speed is simu ously input into the control system with the anticipated speed provided by the mani tion console for the helicopter traction system.Graduated feedback control of the spe the motor is then executed via a fuzzy PI controller.Moreover, the input current of the chronous motor is regulated through the vector control module, thereby altering its torque and subsequently adjusting the motor speed.The essence of vector control technology is the equivalent representation of AC m mathematical models as DC motor models for control.This technique achieves co through regulation of the stator current, thereby controlling motor torque; through coord transformation, decoupling control of flux linkage and torque is realized.In this articl combined space vector pulse width modulation (SVPWM) technology adopts a vector co strategy with id = 0 and constructs a dual closed-loop permanent magnet synchronous m vector control module with a speed loop and current loop, as shown in Figure 5.The structure of the fuzzy PI controller is shown in Figure 6.The fuzzy PI controller obtains real-time adjustments of parameters P and I through fuzzy inference based on the input speed difference (e) and the rate of change (ec) of the speed difference ∆Kp and ∆K i , which are finally substituted into Equation ( 1) to obtain the adjusted PI parameters.In the application of fuzzy control for PMSM control, the majority assumes the transformation of the vector control rotational speed loop's PI control into a fuzzy PI control.This approach dynamically adjusts the PI parameters of the rotational speed loop to arrive at appropriate values for P and I, providing a degree of robustness.
Appl.Sci.2023, 13, x FOR PEER REVIEW 6 of 16 approach dynamically adjusts the PI parameters of the rotational speed loop to arrive at appropriate values for P and I, providing a degree of robustness.

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:

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 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 ).During this period, it is necessary to overcome the motion damping of the correction device on the deck (resistive element, R 18 ) and the external load of the helicopter (potential source, Se).At the same time, the length of the steel cable varies with the force applied (capacitive element, C 15 ); 2 The rotation of the steel cable drum is driven by chain drives (converters, TF3and TF4) to drive the cable drum (inertia element, I 24 ) to rotate.
During this period, it is necessary to overcome the rotational damping of the cable drum (resistive element, R 25 ).The length of the chain changes with the force applied (capacitive element, C 21 ), and the cable does not transmit power to the correction device.
On the basis of the above energy transfer process and the working principle of the traction system, a bond graph model shown in Figure 7 can be drawn.The reference values for each bonding element in the figure are shown in Table 1.
Appl.Sci.2023, 13, x FOR PEER REVIEW 7 of 16 (1) The output speed of the synchronous motor (flow source, Sf) causes the motor spindle (inertia element, I4) to rotate, during which the rotational damping of the motor spindle (resistive element, R5) needs to be overcome, and the torque angle of the motor spindle changes with the torque received (capacitive element, C2); (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, I10) to rotate.During this period, it is necessary to overcome the rotational damping of the gearbox and the steel cable drum (resistive element, R11), and the output shaft torsion angle of the gearbox changes with the torque received (capacitive element, C8); (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, I17).During this period, it is necessary to overcome the motion damping of the correction device on the deck (resistive element, R18) and the external load of the helicopter (potential source, Se).At the same time, the length of the steel cable varies with the force applied (capacitive element, C15); ② The rotation of the steel cable drum is driven by chain drives (converters, TF3and TF4) to drive the cable drum (inertia element, I24) to rotate.During this period, it is necessary to overcome the rotational damping of the cable drum (resistive element, R25).The length of the chain changes with the force applied (capacitive element, C21), and the cable does not transmit power to the correction device.
On the basis of the above energy transfer process and the working principle of the traction system, a bond graph model shown in Figure 7 can be drawn.The reference values for each bonding element in the figure are shown in Table 1.Take the energy storage bonding entities C2, I4, C8, I10, C15, I17, C21, and I24 with integral causality and the corresponding generalized momentum and displacement q2, p4, q8, p10,  with integral causality and the corresponding generalized momentum and displacement q 2 , p 4 , q 8 , p 10 , q 15 , p 17 , q 21 , and p 24 as the state variables of the system.The corresponding bonding entity has the relationship shown in (2).
All resistive components R 5 , R 11 , R 18 , and R 25 have the potential flow relationship shown in the following equation.
e 24 = e 23 − e 25 f 23 = f 24 = f 25 (15) The state equation of the system can be obtained by combining Equations ( 2)-( 15) as follows: Based on the aforementioned equations, one can derive the state equation of the system.The formal expression of such an equation can be represented as Equation (17), where X signifies the state variables of the system, A represents the system matrix, B denotes the control matrix, and U symbolizes the input to the system. .
In accordance with the causal relationship illustrated in Figure 7, it is apparent that the speed of rotation observed by the motor, expressed as sf, serves as an input to the state equation.By selecting q 2 , p 4 , q 8 , p 10 , q 15 , p 17 , q 21 , and p 24 as state variables, we have the potential flow relationship, as shown in Equation ( 18): X = q2 p4 q8 p10 q15 p17 q21 p24 T (18) The system's input is the speed output of the electric motor, yielding Equation (19): The system matrix A can be derived from Equations ( 16) and ( 17): The control matrix B is expressed as Equation ( 21): According to power bond graph theory, a more thorough evaluation of the dynamic energy consumption model reveals that the power transferred across each bond in Figure 6 equates to the scalar product of the potential and flow variables, as follows: The energy transmitted is For electric drive traction systems, the total energy E in (J) transmitted by the motor can be expressed as follows.
Similarly, the useful work of a system is the energy transmitted to the corrective device and helicopter.The effective energy consumption E out (J) of the transmission system can be expressed as follows.

Simulation Analysis 4.1. Dynamic Characteristic Analysis
According to the system usage requirements and actual working conditions, the traction speed is taken as 0.3 m/s.Considering the frequent start and stop characteristics of the helicopter traction system for offshore operations, the simulation time is set to 5 s.According to the data in Table 1, the electromagnetic torque curve of the system motor, motor speed curve, traction force curve of the helicopter, and helicopter motion speed curve are simulated, as shown in Figures 8 and 9  Similarly, the useful work of a system is the energy transmitted to the corrective device and helicopter.The effective energy consumption Eout (J) of the transmission system can be expressed as follows.

Dynamic Characteristic Analysis
According to the system usage requirements and actual working conditions, the traction speed is taken as 0.3 m/s.Considering the frequent start and stop characteristics of the helicopter traction system for offshore operations, the simulation time is set to 5 s.According to the data in Table 1, the electromagnetic torque curve of the system motor, motor speed curve, traction force curve of the helicopter, and helicopter motion speed curve are simulated, as shown in Figures 8 and 9  According to Figure 8, during the acceleration stage of the system (0-0.2s), the torque output by the motor first increases and then decreases.At this time, the output torque is mainly used for the acceleration of the transmission system, which acts on the energy storage components (including inertial and capacitive components) within the system.Finally, the motor's output torque diminishes to approximately 20 N•m and maintains this value for approximately 0.2 s, at which time the majority of the motor's output torque serves to counteract the damping within the system and external resistance, thus remaining constant; the output torque of the motor is reduced to about 20 N•m and remains unchanged.At this time, the torque output by the motor is mainly used to overcome the damping and external resistance in the system to do work, so it remains unchanged.In the acceleration phase, the rotor speed of the electric motor swiftly ascends to its peak under the influence of substantial driving torque.Upon the stagnation of the driving torque, the rotor speed subsequently aligns, which signifies that the system attains steadiness and can execute the function of transporting and pulling a helicopter regularly.According to Figure 8, during the acceleration stage of the system (0-0.2s), the torque output by the motor first increases and then decreases.At this time, the output torque is mainly used for the acceleration of the transmission system, which acts on the energy storage components (including inertial and capacitive components) within the system.Finally, the motor's output torque diminishes to approximately 20 N•m and maintains this value for approximately 0.2 s, at which time the majority of the motor's output torque serves to counteract the damping within the system and external resistance, thus remaining constant; the output torque of the motor is reduced to about 20 N•m and remains unchanged.At this time, the torque output by the motor is mainly used to overcome the damping and external resistance in the system to do work, so it remains unchanged.In the acceleration phase, the rotor speed of the electric motor swiftly ascends to its peak under the influence of substantial driving torque.Upon the stagnation of the driving torque, the rotor speed subsequently aligns, which signifies that the system attains steadiness and can execute the function of transporting and pulling a helicopter regularly.As illustrated in Figure 9, following the initiation of the motor, both its rotational speed and the velocity of the helicopter increase promptly, with approximately 0.2 s required for stabilization, indicating that the system has initiated its normal operation.Utilizing helicopter movement velocity as a control target, it is evident from the simulated diagram that the maximum overshoot of the system is approximately 3.25%.Post the attainment of the steady-state condition, the steady-state error of the system is approximately 0.12%, virtually negligible.This outcome denotes that the system experiences minor overshoot when reaching a steady state, as well as marginal steady-state error post steady state, indicating that the system is capable of securing optimal control effectiveness in steady state, with no significant fluctuations in the speed of the helicopter's motion.

Analysis of Energy Consumption Characteristics
The total energy consumption of the transmission system, the effective energy consumption of the towing helicopter, and the difference between the total energy consumption and the effective energy consumption can be obtained from Equations ( 24) and ( 25), as shown in Figures 10 and 11   As illustrated in Figure 9, following the initiation of the motor, both its rotational speed and the velocity of the helicopter increase promptly, with approximately 0.2 s required for stabilization, indicating that the system has initiated its normal operation.Utilizing helicopter movement velocity as a control target, it is evident from the simulated diagram that the maximum overshoot of the system is approximately 3.25%.Post the attainment of the steady-state condition, the steady-state error of the system is approximately 0.12%, virtually negligible.This outcome denotes that the system experiences minor overshoot when reaching a steady state, as well as marginal steady-state error post steady state, indicating that the system is capable of securing optimal control effectiveness in steady state, with no significant fluctuations in the speed of the helicopter's motion.

Analysis of Energy Consumption Characteristics
The total energy consumption of the transmission system, the effective energy consumption of the towing helicopter, and the difference between the total energy consumption and the effective energy consumption can be obtained from Equations ( 24) and ( 25), as shown in Figures 10 and 11.
During 0~2.2 s, the energy consumption of the traction system sharply increases, which is caused by the combined action of internal energy storage components (inertial and capacitive components) and energy consumption components (resistive components) in the system.At the same time, after about 0.2 s, the system enters a steady state, and the difference between total energy consumption and effective energy consumption begins to grow linearly.At this point, the energy storage element is saturated, and the energy is only consumed by the resistive element.Similarly, the proportion of energy consumption in each part of the system can be obtained from the system's state equation and energy consumption equation, as shown in Figure 10.Within 5 s, the energy consumption of inertial components is about 13.1% of the total energy consumption, far exceeding that of resistive and capacitive components.The total energy utilization rate of the system is approximately 84.1%.cant fluctuations in the speed of the helicopter's motion.

Analysis of Energy Consumption Characteristics
The total energy consumption of the transmission system, the effective energy consumption of the towing helicopter, and the difference between the total energy consumption and the effective energy consumption can be obtained from Equations ( 24) and ( 25), as shown in Figures 10 and 11   During 0~2.2 s, the energy consumption of the traction system sharply increases, which is caused by the combined action of internal energy storage components (inertial and capacitive components) and energy consumption components (resistive components) in the system.At the same time, after about 0.2 s, the system enters a steady state, and the difference between total energy consumption and effective energy consumption begins to grow linearly.At this point, the energy storage element is saturated, and the energy is only consumed by the resistive element.Similarly, the proportion of energy consumption in each part of the system can be obtained from the system's state equation and energy consumption equation, as shown in Figure 10.Within 5 s, the energy consumption of inertial components is about 13.1% of the total energy consumption, far exceeding that of resistive and capacitive components.The total energy utilization rate of the system is approximately 84.1%.

Conclusions
This article is based on the main functions of the ASIST system and designs a new type of electric-driven offshore helicopter traction system.Combining bond graph theory, a complex mechanical system dynamics modeling method that takes into account the dynamic characteristics and energy consumption characteristics of the system is proposed, and simulation analysis is conducted.Simultaneously, the control system design was achieved by integrating the vector control algorithm with the fuzzy PI control algorithm.On this foundation, a new dynamics model of the transmission system was constructed using bond graph theory for a novel helicopter traction system.The dynamic characteris-

Conclusions
This article is based on the main functions of the ASIST system and designs a new type of electric-driven offshore helicopter traction system.Combining bond graph theory, a complex mechanical system dynamics modeling method that takes into account the dynamic characteristics and energy consumption characteristics of the system is proposed, and simulation analysis is conducted.Simultaneously, the control system design was achieved by integrating the vector control algorithm with the fuzzy PI control algorithm.On this foundation, a new dynamics model of the transmission system was constructed using bond graph theory for a novel helicopter traction system.The dynamic characteristics and energy consumption characteristics of the system were scrutinized and simulated in Matlab/Simulink.From the simulation results, it is evident that the innovative helicopter traction system proposed in this article exhibits marked attributes: (1) The developed electric helicopter traction system coupled with a fuzzy adaptive controller demonstrates rapid response and well-defined steady-state characteristics, meeting the demand of helicopter traction diversion whilst offering superior rapid reaction speed and steady-state performance.Specifically, the maximum overshoot of the system is approximately 3.25%, and the steady-state error approximates to 0.12%, which virtually approaches zero.Simultaneously, it presents a high energy utilization ratio with an impressive energy efficiency reaching 84% within a single working cycle.(2) The energy loss in the large inertia dynamic system, exemplified by a helicopter traction system, predominantly stems from the inertial losses during the initiation phase of the system.Consequently, in the realm of optimal design, the rotational inertia of components such as the decelerator input should be reduced while ensuring strength to positively impact system energetic efficiency.(3) The dynamic modeling method proposed in this study, based on the acquisition of the system's dynamic characteristics, vividly reflects the dynamic energy consumption characteristics of the system.This addresses the deficiency in transmission dynamics analysis methods, which rarely consider energy consumption.It provides a reference for the dynamic energy consumption analysis of other complex mechanical systems.
This research effectively amplifies the application domain of shipborne equipment, lessens energy consumption during translocation, and provides a crucial theoretical foundation and data references for the development of an electric propulsion system for carrier helicopters.

Figure 2 .
Figure 2. Schematic diagram of helicopter recycling process.

Figure 3 .
Figure 3. Transmission scheme of the electric drive traction system.

Figure 2 .
Figure 2. Schematic diagram of helicopter recycling process.

Figure 2 .
Figure 2. Schematic diagram of helicopter recycling process.

Figure 3 .
Figure 3. Transmission scheme of the electric drive traction system.

Figure 3 .
Figure 3. Transmission scheme of the electric drive traction system.

Figure 4 .
Figure 4. Flow chart of the traction control system.

Figure 4 .
Figure 4. Flow chart of the traction control system.

Figure 4 .
Figure 4. Flow chart of the traction control system.

Figure 5 .
Figure 5. Vector control system structure.The structure of the fuzzy PI controller is shown in Figure6.The fuzzy PI cont obtains real-time adjustments of parameters P and I through fuzzy inference based o input speed difference (e) and the rate of change (ec) of the speed difference ΔKp and which are finally substituted into Equation (1) to obtain the adjusted PI parameters.I application of fuzzy control for PMSM control, the majority assumes the transform of the vector control rotational speed loop's PI control into a fuzzy PI control.

Figure 7 .
Figure 7. Bonding diagram of the electric drive traction system.

Figure 7 .
Figure 7. Bonding diagram of the electric drive traction system. .

Figure 8 .
Figure 8. Motor dynamic characteristic curve during traction: (a) electromagnetic torque of the motor; (b) rotational speed of motor.

Figure 8 .
Figure 8. Motor dynamic characteristic curve during traction: (a) electromagnetic torque of the motor; (b) rotational speed of motor.

Figure 9 .
Figure 9.The dynamic characteristic curve of a helicopter and its force profile: (a) the traction force on the helicopter; (b) helicopter movement speed. .

Figure 9 .
Figure 9.The dynamic characteristic curve of a helicopter and its force profile: (a) the traction force on the helicopter; (b) helicopter movement speed. .

Figure 10 . 16 Figure 10 .
Figure 10.The correlation chart of total energy consumption and effective energy consumption: (a) total energy consumption and effective energy consumption of the system; (b) total energy consumption and effective energy consumption of the system.

Figure 11 .
Figure 11.Difference between total energy consumption and effective energy consumption.

Figure 11 .
Figure 11.Difference between total energy consumption and effective energy consumption.

Funding:
This research was funded by Hebei Provincial Key Research and Development Program, grant number 22357601D.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.