Method for controlling the speed of a marine vessel power system during the water entry transient
By constructing a dynamic mathematical model of the cross-medium power system and designing a PI speed closed-loop control algorithm, the control instability problem of the vehicle's power system during the water entry transient process was solved, and stable control of combustion chamber pressure and turbine speed was achieved, avoiding the risk of flameout and providing a safety margin.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-02
AI Technical Summary
Existing PID control suffers from control instability due to signal delay during the transient process of a vehicle's power system entering the water, cannot provide a definite safety margin, and cannot effectively cope with the risk of turbine engine shutdown caused by a step change in load.
A dynamic mathematical model of the cross-medium power system is constructed, and a PI-based closed-loop speed control algorithm is designed. The turbine speed is controlled by adjusting the fuel pump displacement. Considering the sensor delay response, hysteresis control is achieved to ensure that the combustion chamber pressure and turbine speed are within a safe range.
It effectively avoids the risk of flameout during the transient process of water entry, quantifies the safety margin of the system, provides key design basis for engineering implementation, and ensures the safe operating time of the system in an uncontrolled state.
Smart Images
Figure CN122133546A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of cross-medium vehicle propulsion system control technology, specifically relating to a method for controlling the rotational speed lag of a vehicle propulsion system during water entry transients. Background Technology
[0002] Submersible vehicles can navigate between air and water, but their entry into the water involves a sudden change in the working medium from air to seawater, causing a sharp increase in the torque required to propel axial-flow pumps. This abrupt change in load can cause a sudden drop in the speed of power systems such as turbine engines, leading to excessively low combustion chamber pressure and engine shutdown, seriously threatening navigation safety.
[0003] Traditional power system speed control often employs proportional-integral-derivative (PID) closed-loop control. However, under extreme transient conditions such as water ingress, existing technologies have the following limitations: First, classical PID control assumes that sensor signals and actuator responses are instantaneous and without delay, while in practical engineering, signal sampling, processing, and servo mechanism actions all have inherent delays. Second, given these inherent delays, if instantaneous control is still performed according to an ideal model, it may lead to a mismatch between the control command and the actual system state, causing overshoot, oscillation, or even instability. Third, existing research has failed to clearly quantify the time window during which the system can operate safely without control, resulting in a lack of definite safety margins in the design of control systems. Summary of the Invention
[0004] The purpose of this invention is to provide a method for controlling the rotational speed lag of a vehicle's propulsion system during water entry, which solves the problems of existing PID control being prone to instability under engineering delays and failing to provide a safety margin for sensors and actuators to determine response time.
[0005] The technical solution adopted in this invention is a method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients, comprising the following steps:
[0006] Step 1: Construct a cross-medium aerial propulsion system, perform aerial and underwater thermodynamic design on the cross-medium propulsion system, and obtain the cross-medium system configuration; Step 2: Based on the configuration of the transmedium system, establish a dynamic mathematical model of the transmedium dynamic system; Step 3: Based on the dynamic mathematical model of the cross-medium dynamic system, design a control algorithm to adjust the fuel pump displacement during the water inlet process, realize closed-loop control of turbine speed, and obtain the optimized dynamic system. Step 4: Simulate the optimized dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry.
[0007] The invention is further characterized by: In step 1, the cross-medium air propulsion system includes an air propulsion system and an underwater propulsion system, which share a set of combustion chambers and turbines. The air propulsion system includes an air intake, compressor, combustion chamber, turbine and its auxiliary engines, combustion chamber and tail nozzle. The process of the air propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of high temperature and high pressure gas. The high temperature and high pressure gas drives the turbine to do work and becomes exhaust gas, which enters the combustion chamber. Air is drawn in and pressurized by the compressor through the air intake. Then, the air and exhaust gas undergo secondary combustion in the combustion chamber. Finally, the gas is ejected from the tail nozzle to propel the aircraft forward. The underwater propulsion system includes a combustion chamber, a turbine and its auxiliary machinery, an axial flow propulsion pump and an internal flow channel. The process of the underwater propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of gas, the gas drives the turbine to do work, the turbine drives the axial flow propulsion pump to rotate through the transmission mechanism, and the axial flow pump pressurizes the water in the internal flow channel and sprays it out to propel the vehicle forward.
[0008] The dynamic mathematical model in step 2 includes the combustion chamber model, turbine output torque model, compressor characteristic model, power system dynamics model, and mixed combustion chamber model.
[0009] The combustion chamber model is as follows: The working gas in the combustion chamber is obtained according to equation (1); (1); in, This refers to the combustion chamber pressure. The volume of the combustion chamber; The quality of the gas inside the combustion chamber; The constant of the fuel gas; This refers to the combustion chamber temperature. Based on equation (1), the derivative is obtained; (2); The characteristics of combustion chamber temperature variation with pressure obtained through simulation are shown in equation (3); (3); In the formula, , , It is a constant; According to equations (2) and (3), we obtain: (4); The combustion chamber model based on variable combustion chamber temperature is obtained according to equation (4), as shown in equation (5); (5); In the formula, This refers to the area of the nozzle throat. This refers to the fuel pump displacement; This refers to the fuel pump speed; This refers to the specific heat ratio of the fuel gas.
[0010] The turbine output torque model is as follows: For underwater turbines, the theoretical output torque is shown in equation (6); (6); In the formula, The theoretical output torque of the turbine; This represents the theoretical output power of the turbine. This refers to the turbine rotational speed; The quality of the gas inside the combustion chamber; The radius of the turbine disk; This refers to the absolute velocity at the turbine blade inlet. The angle between the absolute velocity of the inlet and the plane of the wheel; This is the absolute velocity at the blade exit. The angle between the absolute velocity at the exit and the plane of the wheel; Considering the turbine's disc friction loss, repulsion loss, blade height loss, and sector loss, the final actual output power of the turbine is shown in equation (7). (7); In the formula, This represents the actual output power of the turbine. Power loss due to turbines; Considering the energy loss of the turbine, the actual output torque of the turbine is shown in equation (8); (8); In the formula, This represents the actual output torque of the turbine. Loss due to air leakage; This is the turbine power correction factor; Leaf height loss coefficient; Repulsion loss coefficient; The sector loss coefficient; This is the coefficient of friction loss of the wheel; This refers to the circumferential speed of the turbine impeller; For turbine blade velocity factor; The relative velocity at the blade exit; The angle between the relative velocity at the blade exit and the disk plane.
[0011] The compressor characteristic model is as follows: The characteristic equation of air mass flow rate of the compressor is shown in equation (9); (9); In the formula, This refers to the air mass flow rate of the compressor. The design point air mass flow rate for the compressor; This refers to the compressor speed; The design point speed of the compressor; The compressor efficiency characteristic equation is shown in equation (10); (10); In the formula, For compressor efficiency; Design point efficiency for the compressor; The compressor boost ratio characteristic equation is shown in equation (11); (11); In the formula, The compressor boost ratio; The compressor design point boost ratio; The compressor absorption power is obtained according to equations (9), (10), and (11) as shown in equation (12); (12); In the formula, To absorb power for the compressor; This refers to the compressor inlet temperature. The specific heat ratio of air. The specific heat capacity of air at constant pressure; According to equation (12), the compressor absorption torque is obtained as shown in equation (13); (13); In the formula, This is the torque absorbed by the compressor.
[0012] The dynamic model of the dynamic system is as follows: When the cross-medium power system is running stably, the load of the turbine power system mainly includes the air compressor, underwater axial flow pump, fuel pump, generator, and lubricating oil pump. The dynamic model of the power system is shown in Equation (14). (14); In the formula, The converted moment of inertia of the power system; The turbine's rotational speed acceleration; To provide torque for the turbine output; This is the underwater load absorption torque; Absorbing torque for aerial loads; This is the torque absorbed by the generator; This is to absorb the torque of the lubricating oil pump; For the fuel pump to absorb torque; For axial flow pump torque; Calculate the water entry moment of the vehicle according to equation (15); (15).
[0013] The specific model of the mixed combustion chamber is as follows: For the air power system, both the combustion chamber and the co-combustion chamber undergo exothermic reactions. The heat loss power is calculated according to equation (16). (16); In the formula, This refers to power loss due to heat. This refers to the mass flow rate of exhaust gas. This refers to the calorific value of the fuel. The calorific value of exhaust gas; It is the air-fuel ratio when exhaust gas and air burn together. The air-fuel ratio is the ratio at which exhaust gas and air burn completely. For combustion efficiency; For heat loss efficiency; The entire power system is considered as an isentropic process, and the temperature of the combustion chamber is calculated according to equation (17); (17); In the formula, This refers to the temperature of the combustion chamber. Absorb power for auxiliary equipment; The specific heat capacity of the combustion chamber gas at constant pressure For an isentropic process, the combustion chamber pressure is calculated according to equation (18); (18); In the formula, The pressure in the combustion chamber; This refers to the compressor inlet pressure. This is the total pressure recovery coefficient of the combustion chamber; The exhaust gas and air undergo secondary combustion to produce high-temperature gas, which is then ejected through the tail nozzle to generate thrust. This process is an isentropic process. The tail nozzle outlet temperature is calculated according to equation (19). (19); In the formula, This refers to the tail nozzle exit temperature. This refers to the tail nozzle expansion ratio; The specific heat ratio of the combustion chamber fuel gas; Calculate the tail nozzle exit velocity according to equation (20); (20); In the formula: The tail nozzle exit velocity; This is the tail nozzle velocity factor.
[0014] Step 3 is as follows: The turbine drives the generator at a constant speed ratio. The current turbine speed is obtained by measuring the generator speed through a speed sensor. The turbine speed is used as a feedback signal and sent to the speed closed-loop controller. At the same time, the speed closed-loop controller receives start command, speed command and depth command signals from the host computer. The controller sends control commands to the servo system of the electronically controlled variable displacement fuel pump according to the feedback signal and the received command. The servo motor of the servo system adjusts the pump angle of the fuel pump according to the control command, changes the fuel pump displacement, controls the fuel flow into the combustion chamber, and realizes the control of turbine speed. The closed-loop control system takes the control signal output by the speed controller as the input command and the swashplate position of the fuel pump as the feedback signal, and calculates the pump angle according to formula (21); (twenty one); In the formula, It is a time constant; This refers to the pump angle of the fuel pump; This refers to the pump angle when the input signal voltage is zero. It is a constant; To control pump voltage; The fuel pump displacement is proportional to the swashplate angle, as shown in equation (22); (twenty two); In the formula, It is the gain constant; The navigation depth is relatively small during the water entry process, so the influence of depth on the power system is not considered. The closed-loop control model of the power system is obtained as shown in formula (23). (twenty three); According to equation (23), linearization and Laplace transformation are performed to obtain the transfer function of the dynamic system as shown in equation (24); (twenty four); In the formula, This represents the gain of combustion chamber pressure on rotational speed. This is the gain of fuel pump displacement on combustion chamber pressure; This represents the gain of rotational speed on combustion chamber pressure. The gain of voltage on fuel pump displacement; The time constant of the rotational speed; The time constant of the combustion chamber pressure; The fuel pump displacement and turbine speed jointly control the combustion chamber pressure through an inertial link. The combustion chamber pressure is affected by system disturbances, namely the torque of the axial propulsion pump. The two are affected by the inertial link and jointly control the output of the system, namely the turbine speed. The transfer function of the control system is shown in equation (25). (25); In order to perform closed-loop control of turbine speed, the turbine speed needs to be fed back to the speed control system input. The transfer function of the closed-loop control system is shown in equation (26). (26); The system is subject to interference, so integral control needs to be introduced to eliminate static errors. The PID control algorithm is selected to perform closed-loop speed control of the system, and proportional-integral PI is used to control the pump angle position of the fuel pump.
[0015] Step 4 is as follows: Step 4.1: Obtain the open-loop dynamic characteristics of the power system during the water entry process; Step 4.2: Based on the open-loop dynamic characteristics of the power system, a PID control algorithm is used to perform closed-loop speed control on the power system; Specifically, after the power system is running stably, the torque of the axial flow pump is controlled to change according to the characteristics of formula (15), and the fuel pump is controlled by PID algorithm; Step 4.3: Considering the sensor delay response factor, a simulation study of lag control was conducted on the dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry. Specifically, the optimized power system is simulated, and the simulation process is divided into three stages: stable operation of the power system, continued operation of the power system without control, and operation of the power system under control. The operating status of combustion chamber pressure and turbine speed is analyzed in each of the three stages. When the peak values of combustion chamber pressure and turbine speed reach the safe operating threshold, the operating time at this time is taken as the maximum safe operating time of the power system.
[0016] The beneficial effects of this invention are: The present invention provides a method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients. First, a state-coupled model that better reflects engineering practice was established. By introducing the empirical relationship between combustion chamber temperature and pressure, a dynamic model of a cross-medium dynamic system coupled with "pressure-temperature-speed" was constructed, which can more accurately characterize the transient energy conversion and transfer process during water entry.
[0017] Secondly, the effectiveness of the speed closed-loop control under sudden load changes was verified. The proportional-integral (PI) speed closed-loop controller designed based on the established model can quickly respond to load changes by adjusting the fuel flow rate, stabilizing the combustion chamber pressure and turbine speed within the safe operating range, and avoiding the risk of flameout caused by water ingress.
[0018] Third, the system safety margin was quantified and a lag control strategy was proposed. Simulation results showed that the longest allowable safe operating time for the system under uncontrolled conditions is 0.9 seconds. Based on this, a speed closed-loop lag control method was proposed. The results show that, while retaining the 0.9-second uncontrolled response window, this method, although extending the overall settling time by about 3 seconds compared to conventional closed-loop control, effectively balances the actual delay of the actuator with system stability, providing a crucial design basis for engineering implementation. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the system configuration in Embodiment 6 of the present invention's method for controlling the rotational speed lag during the water entry transient of the vehicle's propulsion system; Figure 2 This is a flowchart of the underwater design working condition propulsion system calculation in Embodiment 6 of the present invention; Figure 3 This is a flowchart of the calculation of the aerial design condition propulsion system in Embodiment 6 of the present invention; Figure 4 This is a schematic diagram of the combustion chamber parameter characteristic curves in Embodiment 6 of the present invention; Figure 5 This is a schematic diagram of the torque characteristics of the axial flow pump in Embodiment 6 of the present invention; Figure 6 This is a schematic diagram of the power system speed closed-loop control system in Embodiment 6 of the present invention; Figure 7 This is a schematic diagram of the open-loop control system structure for the power system speed in Embodiment 6 of the present invention; Figure 8 This is a schematic diagram of the power system speed closed-loop control system structure in Embodiment 6 of the present invention; Figure 9 This is a schematic diagram of the torque variation curve of the axial flow pump in Embodiment 6 of the present invention; Figure 10 This is a schematic diagram of the open-loop response of the power system in Embodiment 6 of the present invention; Figure 11 This is a schematic diagram of the torque variation curve of the power system in the closed-loop control response of the power system in Embodiment 6 of the present invention; Figure 12 This is a schematic diagram of the combustion chamber pressure change curve in the closed-loop control response of the power system in Embodiment 6 of the present invention; Figure 13 This is a schematic diagram of the turbine speed change curve in the closed-loop control response of the power system in Embodiment 6 of the present invention; Figure 14 This is a schematic diagram of the fuel pump displacement change curve in the closed-loop control response of the power system in Embodiment 6 of the present invention; Figure 15This is a schematic diagram of the combustion chamber pressure change curve in the closed-loop lag control response of the power system in Embodiment 6 of the present invention; Figure 16 This is a schematic diagram of the turbine speed change curve in the closed-loop lag control response of the power system in Embodiment 6 of the present invention. Detailed Implementation
[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0021] Example 1 The proposed method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients includes the following steps: Step 1: Construct a cross-medium aerial propulsion system, perform aerial and underwater thermodynamic design on the cross-medium propulsion system, and obtain the cross-medium system configuration; Step 2: Based on the configuration of the transmedium system, establish a dynamic mathematical model of the transmedium dynamic system; Step 3: Based on the dynamic mathematical model of the cross-medium dynamic system, design a control algorithm to adjust the fuel pump displacement during the water inlet process, realize closed-loop control of turbine speed, and obtain the optimized dynamic system. Step 4: Simulate the optimized dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry.
[0022] Example 2 The proposed method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients includes the following steps: Step 1: Construct a cross-medium aerial propulsion system, perform aerial and underwater thermodynamic design on the cross-medium propulsion system, and obtain the cross-medium system configuration; In step 1, the cross-medium air propulsion system includes an air propulsion system and an underwater propulsion system, which share a set of combustion chambers and turbines. The air propulsion system includes an air intake, compressor, combustion chamber, turbine and its auxiliary engines, combustion chamber and tail nozzle. The process of the air propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of high temperature and high pressure gas. The high temperature and high pressure gas drives the turbine to do work and becomes exhaust gas, which enters the combustion chamber. Air is drawn in and pressurized by the compressor through the air intake. Then, the air and exhaust gas undergo secondary combustion in the combustion chamber. Finally, the gas is ejected from the tail nozzle to propel the aircraft forward. The underwater propulsion system includes a combustion chamber, a turbine and its auxiliary machinery, an axial flow propulsion pump and an internal flow channel. The process of the underwater propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of gas, the gas drives the turbine to do work, the turbine drives the axial flow propulsion pump to rotate through the transmission mechanism, and the axial flow pump pressurizes the water in the internal flow channel and sprays it out to propel the vehicle forward. Step 2: Based on the configuration of the transmedium system, establish a dynamic mathematical model of the transmedium dynamic system; Step 3: Based on the dynamic mathematical model of the cross-medium dynamic system, design a control algorithm to adjust the fuel pump displacement during the water inlet process, realize closed-loop control of turbine speed, and obtain the optimized dynamic system. Step 4: Simulate the optimized dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry.
[0023] Example 3 The proposed method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients includes the following steps: Step 1: Construct a cross-medium aerial propulsion system, perform aerial and underwater thermodynamic design on the cross-medium propulsion system, and obtain the cross-medium system configuration; In step 1, the cross-medium air propulsion system includes an air propulsion system and an underwater propulsion system, which share a set of combustion chambers and turbines. The air propulsion system includes an air intake, compressor, combustion chamber, turbine and its auxiliary engines, combustion chamber and tail nozzle. The process of the air propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of high temperature and high pressure gas. The high temperature and high pressure gas drives the turbine to do work and becomes exhaust gas, which enters the combustion chamber. Air is drawn in and pressurized by the compressor through the air intake. Then, the air and exhaust gas undergo secondary combustion in the combustion chamber. Finally, the gas is ejected from the tail nozzle to propel the aircraft forward. The underwater propulsion system includes a combustion chamber, a turbine and its auxiliary machinery, an axial flow propulsion pump and an internal flow channel. The process of the underwater propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of gas, the gas drives the turbine to do work, the turbine drives the axial flow propulsion pump to rotate through the transmission mechanism, and the axial flow pump pressurizes the water in the internal flow channel and sprays it out to propel the vehicle forward. Step 2: Based on the configuration of the transmedium system, establish a dynamic mathematical model of the transmedium dynamic system; The dynamic mathematical model in step 2 includes the combustion chamber model, turbine output torque model, compressor characteristic model, power system dynamics model, and mixed combustion chamber model; The combustion chamber model is as follows: The working gas in the combustion chamber is obtained according to equation (1); (1); in, This refers to the combustion chamber pressure. The volume of the combustion chamber; The quality of the gas inside the combustion chamber; The constant of the fuel gas; This refers to the combustion chamber temperature. Based on equation (1), the derivative is obtained; (2); The characteristics of combustion chamber temperature variation with pressure obtained through simulation are shown in equation (3); (3); In the formula, , , It is a constant; According to equations (2) and (3), we obtain: (4); The combustion chamber model based on variable combustion chamber temperature is obtained according to equation (4), as shown in equation (5); (5); In the formula, This refers to the area of the nozzle throat. This refers to the fuel pump displacement; This refers to the fuel pump speed; Specific heat ratio of fuel gas; The turbine output torque model is as follows: For underwater turbines, the theoretical output torque is shown in equation (6); (6); In the formula, The theoretical output torque of the turbine; This represents the theoretical output power of the turbine. This refers to the turbine rotational speed; The quality of the gas inside the combustion chamber; The radius of the turbine disk; This refers to the absolute velocity at the turbine blade inlet. The angle between the absolute velocity of the inlet and the plane of the wheel; This is the absolute velocity at the blade exit. The angle between the absolute velocity at the exit and the plane of the wheel; Considering the turbine's disc friction loss, repulsion loss, blade height loss, and sector loss, the final actual output power of the turbine is shown in equation (7). (7); In the formula, This represents the actual output power of the turbine. Power loss due to turbines; Considering the energy loss of the turbine, the actual output torque of the turbine is shown in equation (8); (8); In the formula, This represents the actual output torque of the turbine. Loss due to air leakage; This is the turbine power correction factor; Leaf height loss coefficient; Repulsion loss coefficient; The sector loss coefficient; This is the coefficient of friction loss of the wheel; This refers to the circumferential speed of the turbine impeller; This is the turbine blade velocity factor. The relative velocity at the blade exit; The angle between the relative velocity at the blade exit and the disk plane; The compressor characteristic model is as follows: The characteristic equation of air mass flow rate of the compressor is shown in equation (9); (9); In the formula, This refers to the air mass flow rate of the compressor. The design point air mass flow rate for the compressor; This refers to the compressor speed; The design point speed of the compressor; The compressor efficiency characteristic equation is shown in equation (10); (10); In the formula, For compressor efficiency; Design point efficiency for the compressor; The compressor boost ratio characteristic equation is shown in equation (11); (11); In the formula, The compressor boost ratio; The compressor design point boost ratio; The compressor absorption power is obtained according to equations (9), (10), and (11) as shown in equation (12); (12); In the formula, To absorb power for the compressor; This refers to the compressor inlet temperature. The specific heat ratio of air. The specific heat capacity of air at constant pressure; According to equation (12), the compressor absorption torque is obtained as shown in equation (13); (13); In the formula, This is the torque absorbed by the compressor; The dynamic model of the dynamic system is as follows: When the cross-medium power system is running stably, the load of the turbine power system mainly includes the air compressor, underwater axial flow pump, fuel pump, generator, and lubricating oil pump. The dynamic model of the power system is shown in Equation (14). (14); In the formula, The converted moment of inertia of the power system; The turbine's rotational speed acceleration; To provide torque for the turbine output; This is the underwater load absorption torque; Absorbing torque for aerial loads; This is the torque absorbed by the generator; This is to absorb the torque of the lubricating oil pump; For the fuel pump to absorb torque; For axial flow pump torque; Calculate the water entry moment of the vehicle according to equation (15); (15); The specific model of the mixed combustion chamber is as follows: For the air power system, both the combustion chamber and the co-combustion chamber undergo exothermic reactions. The heat loss power is calculated according to equation (16). (16); In the formula, This refers to power loss due to heat. This refers to the mass flow rate of exhaust gas. This refers to the calorific value of the fuel. The calorific value of exhaust gas; It is the air-fuel ratio when exhaust gas and air burn together. The air-fuel ratio is the ratio at which exhaust gas and air burn completely. For combustion efficiency; For heat loss efficiency; The entire power system is considered as an isentropic process, and the temperature of the combustion chamber is calculated according to equation (17); (17); In the formula, This refers to the temperature of the combustion chamber. Absorb power for auxiliary equipment; The specific heat capacity of the combustion chamber gas at constant pressure For an isentropic process, the combustion chamber pressure is calculated according to equation (18); (18); In the formula, The pressure in the combustion chamber; This refers to the compressor inlet pressure. This is the total pressure recovery coefficient of the combustion chamber; The exhaust gas and air undergo secondary combustion to produce high-temperature gas, which is then ejected through the tail nozzle to generate thrust. This process is an isentropic process. The tail nozzle outlet temperature is calculated according to equation (19). (19); In the formula, This refers to the tail nozzle exit temperature. This refers to the tail nozzle expansion ratio; The specific heat ratio of the combustion chamber fuel gas; Calculate the tail nozzle exit velocity according to equation (20); (20); In the formula: The tail nozzle exit velocity; The tail nozzle velocity factor; Step 3: Based on the dynamic mathematical model of the cross-medium dynamic system, design a control algorithm to adjust the fuel pump displacement during the water inlet process, realize closed-loop control of turbine speed, and obtain the optimized dynamic system. Step 4: Simulate the optimized dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry.
[0024] Example 4 The proposed method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients includes the following steps: Based on Example 3; Step 3 is as follows: The turbine drives the generator at a constant speed ratio. The current turbine speed is obtained by measuring the generator speed through a speed sensor. The turbine speed is used as a feedback signal and sent to the speed closed-loop controller. At the same time, the speed closed-loop controller receives start command, speed command and depth command signals from the host computer. The controller sends control commands to the servo system of the electronically controlled variable displacement fuel pump according to the feedback signal and the received command. The servo motor of the servo system adjusts the pump angle of the fuel pump according to the control command, changes the fuel pump displacement, controls the fuel flow into the combustion chamber, and realizes the control of turbine speed. The closed-loop control system takes the control signal output by the speed controller as the input command and the swashplate position of the fuel pump as the feedback signal, and calculates the pump angle according to formula (21); (twenty one); In the formula, It is a time constant; This refers to the pump angle of the fuel pump; This refers to the pump angle when the input signal voltage is zero. It is a constant; To control pump voltage; The fuel pump displacement is proportional to the swashplate angle, as shown in equation (22); (twenty two); In the formula, It is the gain constant; The navigation depth is relatively small during the water entry process, so the influence of depth on the power system is not considered. The closed-loop control model of the power system is obtained as shown in formula (23). (twenty three); According to equation (23), linearization and Laplace transformation are performed to obtain the transfer function of the dynamic system as shown in equation (24); (twenty four); In the formula, This represents the gain of combustion chamber pressure on rotational speed. This is the gain of fuel pump displacement on combustion chamber pressure; This represents the gain of rotational speed on combustion chamber pressure. The gain of voltage on fuel pump displacement; The time constant of the rotational speed; The time constant of the combustion chamber pressure; The fuel pump displacement and turbine speed jointly control the combustion chamber pressure through an inertial link. The combustion chamber pressure is affected by system disturbances, namely the torque of the axial propulsion pump. The two are affected by the inertial link and jointly control the output of the system, namely the turbine speed. The transfer function of the control system is shown in equation (25). (25); In order to perform closed-loop control of turbine speed, the turbine speed needs to be fed back to the speed control system input. The transfer function of the closed-loop control system is shown in equation (26). (26); The system is subject to interference, so integral control needs to be introduced to eliminate static error. PID control algorithm is selected to perform closed-loop speed control of the system, and proportional-integral PI is used to control the pump angle position of the fuel pump. Example 5 The proposed method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients includes the following steps: Based on Example 4; Step 4 is as follows: Step 4.1: Obtain the open-loop dynamic characteristics of the power system during the water entry process; Step 4.2: Based on the open-loop dynamic characteristics of the power system, a PID control algorithm is used to perform closed-loop speed control on the power system; Specifically, after the power system is running stably, the torque of the axial flow pump is controlled to change according to the characteristics of formula (15), and the fuel pump is controlled by PID algorithm; Step 4.3: Considering the sensor delay response factor, a simulation study of lag control was conducted on the dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry. Specifically, the optimized power system is simulated, and the simulation process is divided into three stages: stable operation of the power system, continued operation of the power system without control, and operation of the power system under control. The operating status of combustion chamber pressure and turbine speed is analyzed in each of the three stages. When the peak values of combustion chamber pressure and turbine speed reach the safe operating threshold, the operating time at this time is taken as the maximum safe operating time of the power system.
[0025] Example 6 The proposed method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients includes the following steps: 1. Thermodynamic design of cross-medium dynamic systems; 1.1. Cross-medium dynamic system configuration; The cross-medium propulsion system can be divided into two parts: an airborne propulsion system and an underwater propulsion system. The airborne and underwater propulsion systems share a common combustion chamber and turbine. A schematic diagram of the propulsion system configuration is shown below. Figure 1 As shown.
[0026] The air propulsion system consists of components such as the air intake, compressor, combustion chamber, turbine and its auxiliary engines, mixing chamber, and tail nozzle. The fuel in the Yutu-3 engine burns in the combustion chamber, producing a large amount of high-temperature, high-pressure gas. This gas drives the turbine to perform work, then becomes exhaust gas which enters the mixing chamber. Air is drawn in and pressurized by the compressor through the air intake. The air and exhaust gas then undergo secondary combustion in the mixing chamber. Finally, the gas is ejected from the tail nozzle, propelling the aircraft forward.
[0027] The underwater propulsion system consists of a combustion chamber, a turbine and its auxiliary engines, an axial-flow propulsion pump, and an internal flow channel. Similar to its aerial operation, the fuel in the Yutu-3 combustion chamber burns to produce a large amount of gas, which drives the turbine to do work. However, unlike aerial operation, the turbine drives the axial-flow propulsion pump to rotate via a transmission mechanism. The axial-flow pump pressurizes the water in the internal flow channel and ejects it, propelling the vehicle forward.
[0028] 1.2 Thermodynamic design of the power system; To ensure the stability and high efficiency of the cross-medium propulsion system during underwater operation, the geometry of the turbine and nozzle is determined based on the underwater design conditions. The calculation flow of the underwater design propulsion system is shown in Figure 2.
[0029] In this calculation process, the vehicle's speed and depth are known conditions. The nozzle and turbine blade dimensions are corrected by adjusting the working propellant mass flow rate, thereby improving turbine efficiency and matching turbine power.
[0030] The calculation of the airborne propulsion system takes the aircraft's flight speed as a known condition and adjusts the combustion chamber pressure to meet the power and thrust matching requirements of the airborne design conditions. The flow chart of the airborne design propulsion system is shown in Figure 3.
[0031] 2. Dynamic model of cross-medium dynamic system; Based on the system configuration and operating mode, the dynamic model of the cross-medium power system consists of the combustion chamber model, the compressor characteristic equation, the turbine output torque equation, the power system dynamic equation, and the mixed combustion chamber model.
[0032] 2.1 Combustion chamber model; After being pumped into the combustion chamber by the fuel pump, the fuel is atomized through the nozzle and heated to evaporate within the combustion chamber. The gaseous fuel undergoes a decomposition reaction, producing a large amount of combustible gas and releasing a significant amount of heat. According to the ideal gas law, the working gas in the combustion chamber can be described as follows: (1); in, This refers to the combustion chamber pressure. The volume of the combustion chamber; The quality of the gas inside the combustion chamber; The constant of the fuel gas; This refers to the combustion chamber temperature. During the aircraft's preparation for and entry into the water, the combustion chamber pressure and temperature undergo drastic changes, as shown in Figure 4, which presents the simulation results of two load change processes. After the aircraft stabilizes in flight for 1 second, the compressor and turbine are disconnected. After 5 seconds, the combustion chamber pressure and temperature stabilize. After 10 seconds, the axial propulsion pump is connected to the turbine, and after 12 seconds, the combustion chamber pressure and temperature stabilize. Throughout the entire operation, the combustion chamber pressure decreases from 25 MPa to 4.37 MPa and then increases to 22 MPa, while the combustion chamber temperature decreases from 1510 K to 1354 K and then increases to 1500 K.
[0033] Based on equation (1), the derivative is obtained; (2); The combustion temperature of the propellant is related to the pressure inside the combustion chamber. The characteristics of the combustion chamber temperature changing with pressure are obtained through simulation as follows: (3); In the formula, , , It is a constant; Substituting equation (3) into equation (2), we get: (4); After simplification, we obtain a combustion chamber model based on variable combustion chamber temperature: (5); In the formula, This refers to the area of the nozzle throat. This refers to the fuel pump displacement; This refers to the fuel pump speed; Specific heat ratio of fuel gas; 2.2 Turbine Output Torque Model; For underwater turbines, the theoretical output torque is shown in equation (6); (6); In the formula, The theoretical output torque of the turbine; This represents the theoretical output power of the turbine. This refers to the turbine rotational speed; The quality of the gas inside the combustion chamber; The radius of the turbine disk; This refers to the absolute velocity at the turbine blade inlet. The angle between the absolute velocity of the inlet and the plane of the wheel; This is the absolute velocity at the blade exit. The angle between the absolute velocity at the exit and the plane of the wheel; Considering the turbine's disc friction loss, repulsion loss, blade height loss, and sector loss, the final actual output power of the turbine is shown in equation (7). (7); In the formula, This represents the actual output power of the turbine. Power loss due to turbines; Considering the energy loss of the turbine, the actual output torque of the turbine is shown in equation (8); (8); In the formula, This represents the actual output torque of the turbine. Loss due to air leakage; This is the turbine power correction factor; Leaf height loss coefficient; Repulsion loss coefficient; The sector loss coefficient; This is the coefficient of friction loss of the wheel; This refers to the circumferential speed of the turbine impeller; This is the turbine blade velocity factor. The relative velocity at the blade exit; The angle between the relative velocity at the blade exit and the disk plane; 2.3 Compressor characteristic model; During operation, compressors often deviate from their design point conditions, with air mass flow rate, efficiency, and pressure ratio all deviating from the design parameters. Currently, there is no accurate equation describing the dynamic characteristics of compressors; therefore, experimental methods are often used to measure the dynamic characteristics of various compressor parameters and fit characteristic equations.
[0034] The characteristic equation of air mass flow rate of the compressor is shown in equation (9); (9); In the formula, This refers to the air mass flow rate of the compressor. The design point air mass flow rate for the compressor; This refers to the compressor speed; The design point speed of the compressor; The compressor efficiency characteristic equation is shown in equation (10); (10); In the formula, For compressor efficiency; Design point efficiency for the compressor; The compressor boost ratio characteristic equation is shown in equation (11); (11); In the formula, The compressor boost ratio; The compressor design point boost ratio; The compressor absorption power is obtained according to equations (9), (10), and (11) as shown in equation (12); (12); In the formula, To absorb power for the compressor; This refers to the compressor inlet temperature. The specific heat ratio of air. The specific heat capacity of air at constant pressure; According to equation (12), the compressor absorption torque is obtained as shown in equation (13); (13); In the formula, This is the torque absorbed by the compressor; 2.4 Dynamic model of the dynamic system; During stable operation of a cross-medium power system, the load of the turbine power system mainly includes the compressor (in the air), axial flow pump (underwater), fuel pump, generator, and lubricating oil pump. The dynamic model of the power system is established as follows: (14); In the formula, The converted moment of inertia of the power system; The turbine's rotational speed acceleration; To provide torque for the turbine output; This is the underwater load absorption torque; Absorbing torque for aerial loads; This is the torque absorbed by the generator; This is to absorb the torque of the lubricating oil pump; For the fuel pump to absorb torque; For axial flow pump torque; During the water entry process, the internal flow channel of the submersible vehicle is gradually filled with water. The rotational speed of the axial flow pump remains constant, while the torque gradually increases. To obtain the dynamic characteristics of the axial flow pump torque, CFD simulation calculations were performed on the water entry process of the vehicle. The torque characteristics of the axial flow pump are shown in Figure 5, and the water entry torque equation of the vehicle is shown in Equation (15). (15); 2.5. Combustion Chamber Model; When a submarine-launched vehicle is in flight, the fuel decomposes to produce high-temperature, high-pressure combustion gases that drive a turbine to perform work, eventually turning into exhaust gas. This exhaust gas mainly consists of… , , Despite its composition, it still possesses high energy. To improve propellant energy utilization and engine thrust, a combustion chamber is installed to mix exhaust gas with compressed air from the compressor for secondary combustion.
[0035] For the air propulsion system, both the combustion chamber and the co-combustion chamber undergo exothermic reactions, and their heat loss power is: (16); In the formula, This refers to power loss due to heat. This refers to the mass flow rate of exhaust gas. This refers to the calorific value of the fuel. The calorific value of exhaust gas; It is the air-fuel ratio when exhaust gas and air burn together. The air-fuel ratio is the ratio at which exhaust gas and air burn completely. For combustion efficiency; For heat loss efficiency; If the entire power system is considered as an isentropic process, then the temperature of the combustion chamber is: (17); In the formula, This refers to the temperature of the combustion chamber. Absorb power for auxiliary equipment; The specific heat capacity of the combustion chamber fuel under constant pressure; For an isentropic process, the pressure in the combustion chamber is: (18); In the formula, The pressure in the combustion chamber; This refers to the compressor inlet pressure. This is the total pressure recovery coefficient of the combustion chamber; The exhaust gas undergoes secondary combustion with air to produce high-temperature combustion gas, which is then ejected through the tailpipe to generate thrust. This process is isentropic, and the tailpipe exit temperature is: (19); In the formula, This refers to the tail nozzle exit temperature. This refers to the tail nozzle expansion ratio; The specific heat ratio of the combustion chamber fuel gas; Calculate the tail nozzle exit velocity according to equation (20); (20); In the formula: The tail nozzle exit velocity; The tail nozzle velocity factor; 3. Closed-loop speed control scheme for the power system; The cross-medium propulsion system shown in Figure 1 experiences drastic load changes during water entry. Specifically, during water entry, the axial propulsion pump, connected to the turbine, becomes the primary load on the propulsion system, significantly increasing its load compared to the air-entry preparation phase. If the fuel pump displacement is not adjusted, the increased load leads to a decrease in combustion chamber pressure, which in turn causes a reduction in turbine speed. When the combustion chamber pressure falls below the critical combustion pressure of 3 MPa required for the propulsion fuel, combustion chamber flameout occurs.
[0036] To prevent combustion chamber shutdown due to increased power system load during water entry, effective regulation of the fuel pump displacement is necessary. Based on the established mathematical model of the cross-medium power system, a control algorithm is designed to adjust the fuel pump displacement during water entry, achieving closed-loop control of the turbine speed.
[0037] The principle of the speed closed-loop control system is shown in Figure 6. The turbine drives the generator at a constant speed ratio, and the current turbine speed can be obtained by measuring the generator speed using a speed sensor. The turbine speed is sent as a feedback signal to the speed closed-loop controller, which simultaneously receives start commands, speed commands, and depth commands from the host computer. Based on the feedback signal and received commands, the controller sends control commands to the servo system of the electronically controlled variable displacement fuel pump. The servo motor, the actuator of the servo system, adjusts the pump angle of the fuel pump according to the control commands, changes the fuel pump displacement, controls the fuel flow rate into the combustion chamber, and thus controls the turbine speed.
[0038] The pump angle of the variable displacement fuel pump, acting as the actuator, is itself a closed-loop control system. This closed-loop control system uses the control signal output from the speed controller as the input command and the swashplate angle position of the fuel pump as the feedback signal. Therefore, the relationship between the input electrical signal and the pump angle is: (twenty one); In the formula, It is a time constant; This refers to the pump angle of the fuel pump; This refers to the pump angle when the input signal voltage is zero. It is a constant; To control pump voltage; The fuel pump displacement is proportional to the swashplate angle, as shown in equation (22); (twenty two); In the formula, It is the gain constant; The navigation depth is relatively small during the water entry process, so the influence of depth on the power system is not considered. The closed-loop control model of the power system is obtained as shown in formula (23). (twenty three); Linearizing the four equations in equation (23) and performing a Laplace transform, we obtain the transfer function of the dynamical system as follows: (twenty four); In the formula, This represents the gain of combustion chamber pressure on rotational speed. This is the gain of fuel pump displacement on combustion chamber pressure; This represents the gain of rotational speed on combustion chamber pressure. The gain of voltage on fuel pump displacement; The time constant of the rotational speed; The time constant of the combustion chamber pressure; The system function structure diagram, drawn based on the transfer function, is shown in Figure 7. It can be seen that the system input is a voltage signal, which outputs the fuel pump swashplate angle through an inertial link. The fuel pump displacement is proportional to the swashplate angle. The fuel pump displacement and turbine speed jointly control the combustion chamber pressure through an inertial link. The combustion chamber pressure is affected by system disturbances, namely the axial propulsion pump torque. The influence of these two factors leads to the system output, namely the turbine speed, being controlled jointly through an inertial element. The transfer function of this system is: (25); To perform closed-loop control of the turbine speed, the turbine speed needs to be fed back to the speed control system input. The structure diagram of the turbine speed closed-loop control system is shown in Figure 8. The control algorithm for the turbine speed closed-loop control system; According to Figure 8, the transfer function of the closed-loop control system is: (26); The PID control algorithm is selected for closed-loop speed control of the system. The system block diagram shows that disturbances exist, necessitating the introduction of integral control to eliminate static errors. Therefore, proportional-integral (PI) control is used to control the fuel pump angle position.
[0039] 4. Simulation analysis of dynamic characteristics of the power system; A simulation study was conducted on the water entry process of the submersible. First, the open-loop dynamic characteristics of the propulsion system during the water entry process were obtained. Then, based on the open-loop dynamic characteristics of the propulsion system, a PID control algorithm was used to perform closed-loop speed control of the propulsion system. Finally, considering factors such as sensor delay response, a simulation study on lag control of the propulsion system was carried out.
[0040] 4.1 Open-loop response of the dynamic system; System step response characteristics such as Figure 9 As shown, a simulation of the underwater vehicle's entry into the water was performed, and the results are as follows. Figure 10 As shown. Analysis Figure 9 and Figure 10 It can be seen that the axial flow pump torque jumps to 22.48 Nm in 1 second, and the turbine speed and combustion chamber pressure begin to decrease. After the system runs uncontrolled for 0.8 seconds, the combustion chamber pressure is already close to the critical pressure of 3 MPa. If the power system is not controlled accordingly, the combustion chamber pressure will be too low, and the combustion chamber will shut down.
[0041] 4.2 Simulation of closed-loop control of the power system; The process of the vehicle entering the water was simulated and the parameters were optimized to ensure that the combustion chamber pressure was not overshooted and the fuel pump displacement and turbine speed changed smoothly during the underwater propulsion system under varying operating conditions.
[0042] After the power system has been running stably for 1 second, the torque of the axial flow pump is controlled to change according to the characteristics of formula (15). The fuel pump is controlled by a PID algorithm. The process of the submersible entering the water is simulated. The changes of various physical quantities of the power system are as follows: Figure 11-14 As shown: analyze Figure 11-14 It can be concluded that during the vehicle's water entry process, the internal flow channel is gradually filled with water, the torque of the axial propulsion pump gradually increases, the turbine load torque increases, leading to a decrease in turbine speed. The speed controller sends a signal to the fuel pump, increasing the fuel pump displacement, which in turn increases the combustion chamber pressure and turbine output torque. After 2 seconds, the turbine output torque exceeds the load torque, and the turbine speed increases, stabilizing after 9 seconds. After 6 seconds, the combustion chamber pressure, fuel pump displacement, and turbine output torque all stabilize.
[0043] 4.3 Simulation of closed-loop lag control of the power system; During water entry, sufficient response time needs to be allowed for components such as sensors and fuel supply lines. Therefore, the uncontrolled operation time of the power system must be considered, and its impact on power system control must be studied to determine the permissible uncontrolled operation time of the system, i.e., the safe operating time. ; To investigate the maximum safe operating time Take respectively = 0.9 seconds and = 1.0 second. The simulation process can be divided into three stages as shown in Figure 15. Stage I is: the power system runs stably for 1 second; Stage II is: the power system continues to run without control. Seconds; Stage III is: the power system operates under control. The curves showing the changes in combustion chamber pressure and turbine speed are as follows: Figure 16 As shown; Depend on Figure 15 , 16 It can be concluded that when At 0.9 seconds, the combustion chamber pressure and turbine speed finally reach a stable state, and the peak combustion chamber pressure is below 30 MPa, indicating that the system can operate safely; when At 1.0 second, the powertrain operated for 1.7 seconds under conditions where the combustion chamber pressure exceeded 30 MPa and for 3.4 seconds under conditions where the turbine speed exceeded 80,000 rpm. Furthermore, the peak values of the combustion chamber pressure and turbine speed far exceeded the safe operating thresholds of the combustion chamber and turbine, rendering the powertrain unsafe to operate. Therefore, the safe operating time of the powertrain is... The maximum is 0.9 seconds.
Claims
1. A method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients, characterized in that, Includes the following steps: Step 1: Construct a cross-medium aerial propulsion system, perform aerial and underwater thermodynamic design on the cross-medium propulsion system, and obtain the cross-medium system configuration; Step 2: Based on the configuration of the transmedium system, establish a dynamic mathematical model of the transmedium dynamic system; Step 3: Based on the dynamic mathematical model of the cross-medium dynamic system, design a control algorithm to adjust the fuel pump displacement during the water inlet process, realize closed-loop control of turbine speed, and obtain the optimized dynamic system. Step 4: Simulate the optimized dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry.
2. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 1, characterized in that, The cross-medium air propulsion system mentioned in step 1 includes an air propulsion system and an underwater propulsion system, which share a set of combustion chambers and turbines. The air propulsion system includes an air intake, compressor, combustion chamber, turbine and its auxiliary machinery, mixing chamber and tail nozzle. The process of the air propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of high temperature and high pressure gas. The high temperature and high pressure gas drives the turbine to do work and becomes exhaust gas, which enters the mixing chamber. Air is drawn in and pressurized by the compressor through the air intake. Then, the air and exhaust gas undergo secondary combustion in the mixing chamber. Finally, the gas is ejected from the tail nozzle to propel the aircraft forward. The underwater propulsion system includes a combustion chamber, a turbine and its auxiliary equipment, an axial flow propulsion pump and an internal flow channel. The process of the underwater propulsion system is as follows: fuel is burned in the combustion chamber to produce a large amount of gas, the gas drives the turbine to do work, the turbine drives the axial flow propulsion pump to rotate through the transmission mechanism, and the axial flow pump pressurizes the water in the internal flow channel and sprays it out to propel the vehicle forward.
3. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 2, characterized in that, The dynamic mathematical model mentioned in step 2 includes the combustion chamber model, the turbine output torque model, the compressor characteristic model, the power system dynamics model, and the mixed combustion chamber model.
4. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, The combustion chamber model is specifically as follows: The working gas in the combustion chamber is obtained according to equation (1); （1）； in, This refers to the combustion chamber pressure. This refers to the combustion chamber volume; The quality of the gas inside the combustion chamber; The constant of the fuel gas; The combustion chamber temperature; Based on equation (1), the derivative is obtained; （2）； The characteristics of combustion chamber temperature variation with pressure obtained through simulation are shown in equation (3); （3）； In the formula, , , It is a constant; According to equations (2) and (3), we obtain: （4）； The combustion chamber model based on variable combustion chamber temperature is obtained according to equation (4), as shown in equation (5); （5）； In the formula, This refers to the area of the nozzle throat. This refers to the fuel pump displacement. This refers to the fuel pump speed; This refers to the specific heat ratio of the fuel gas.
5. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, The turbine output torque model is specifically as follows: For underwater turbines, the theoretical output torque is shown in equation (6); （6）； In the formula, This is the theoretical output torque of the turbine; This represents the theoretical output power of the turbine. This refers to the turbine rotational speed; The quality of the gas inside the combustion chamber; The radius of the turbine disk; This refers to the absolute velocity at the turbine blade inlet. The angle between the absolute velocity of the inlet and the plane of the wheel; This is the absolute velocity at the blade exit. The angle between the absolute velocity at the exit and the plane of the wheel; Considering the turbine's disc friction loss, repulsion loss, blade height loss, and sector loss, the final actual output power of the turbine is shown in equation (7). （7）； In the formula, This represents the actual output power of the turbine. Power loss due to turbines; Considering the energy loss of the turbine, the actual output torque of the turbine is shown in equation (8); （8）； In the formula, This represents the actual output torque of the turbine. Loss due to air leakage; This is the turbine power correction factor; Leaf height loss coefficient; Repulsion loss coefficient; This is the sector loss coefficient; This is the coefficient of friction loss of the wheel; This refers to the circumferential speed of the turbine impeller; For turbine blade velocity factor; The relative velocity at the blade exit; The angle between the relative velocity at the blade exit and the disk plane.
6. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, The compressor characteristic model is specifically as follows: The characteristic equation of air mass flow rate of the compressor is shown in equation (9); （9）； In the formula, This refers to the air mass flow rate of the compressor. The design point air mass flow rate for the compressor; This refers to the compressor speed; The design point speed of the compressor; The compressor efficiency characteristic equation is shown in equation (10); （10）； In the formula, For compressor efficiency; Design point efficiency for the compressor; The compressor boost ratio characteristic equation is shown in equation (11); （11）； In the formula, The compressor boost ratio; The compressor design point boost ratio; The compressor absorption power is obtained according to equations (9), (10), and (11) as shown in equation (12); （12）； In the formula, To absorb power for the compressor; This refers to the compressor inlet temperature. The specific heat ratio of air. The specific heat capacity of air at constant pressure; According to equation (12), the compressor absorption torque is obtained as shown in equation (13); （13）； In the formula, This is the torque absorbed by the compressor.
7. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, The dynamic model of the dynamic system is specifically as follows: When the cross-medium power system is running stably, the load of the turbine power system mainly includes the air compressor, underwater axial flow pump, fuel pump, generator, and lubricating oil pump. The dynamic model of the power system is shown in Equation (14). （14）； In the formula, The converted moment of inertia of the dynamic system; The turbine's rotational speed acceleration; To provide torque for the turbine output; This is the underwater load absorption torque; Absorbing torque for aerial loads; This is the torque absorbed by the generator; This is to absorb the torque of the lubricating oil pump; For the fuel pump to absorb torque; For axial flow pump torque; Calculate the water entry moment of the vehicle according to equation (15); （15）。 8. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, The combustion chamber model is specifically as follows: For the air power system, both the combustion chamber and the co-combustion chamber undergo exothermic reactions. The heat loss power is calculated according to equation (16). （16）； In the formula, This refers to power loss due to heat. This refers to the mass flow rate of exhaust gas. This refers to the calorific value of the fuel. The calorific value of exhaust gas; It is the air-fuel ratio when exhaust gas and air burn together. The air-fuel ratio is the ratio at which exhaust gas and air burn completely. For combustion efficiency; For heat loss efficiency; The entire power system is considered as an isentropic process, and the temperature of the combustion chamber is calculated according to equation (17); （17）； In the formula, This refers to the temperature of the combustion chamber. Absorb power for auxiliary equipment; The specific heat capacity of the combustion chamber gas at constant pressure For an isentropic process, the combustion chamber pressure is calculated according to equation (18); （18）； In the formula, The pressure in the combustion chamber; This refers to the compressor inlet pressure. This is the total pressure recovery coefficient of the combustion chamber; The exhaust gas and air undergo secondary combustion to produce high-temperature gas, which is then ejected through the tail nozzle to generate thrust. This process is an isentropic process. The tail nozzle outlet temperature is calculated according to equation (19). （19）； In the formula, This refers to the tail nozzle exit temperature. The tail nozzle expansion ratio; The specific heat ratio of the combustion chamber fuel gas; Calculate the tail nozzle exit velocity according to equation (20); （20）； In the formula: The tail nozzle exit velocity; This is the tail nozzle velocity factor.
9. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, Step 3 specifically involves: the turbine driving the generator at a constant speed ratio; the current turbine speed is obtained by measuring the generator speed through a speed sensor; the turbine speed is used as a feedback signal and sent to the speed closed-loop controller; at the same time, the speed closed-loop controller receives start command, speed command, and depth command signals from the host computer; the controller sends control commands to the servo system of the electronically controlled variable displacement fuel pump based on the feedback signal and the received commands; the servo motor of the servo system adjusts the pump angle of the fuel pump according to the control commands, changes the fuel pump displacement, controls the fuel flow rate into the combustion chamber, and realizes turbine speed control. The closed-loop control system takes the control signal output by the speed controller as the input command and the swashplate position of the fuel pump as the feedback signal, and calculates the pump angle according to formula (21); （21）； In the formula, It is a time constant; For the fuel pump angle; This refers to the pump angle when the input signal voltage is zero. It is a constant; To control pump voltage; The fuel pump displacement is proportional to the swashplate angle, as shown in equation (22); （22）； In the formula, It is the gain constant; The navigation depth is relatively small during the water entry process, so the influence of depth on the power system is not considered. The closed-loop control model of the power system is obtained as shown in formula (23). （23）； According to equation (23), linearization and Laplace transformation are performed to obtain the transfer function of the dynamic system as shown in equation (24); （24）； In the formula, This represents the gain of combustion chamber pressure on rotational speed. This is the gain of fuel pump displacement on combustion chamber pressure; This represents the gain of rotational speed on combustion chamber pressure. The gain of voltage on fuel pump displacement; The time constant of the rotational speed; The time constant of the combustion chamber pressure; The fuel pump displacement and turbine speed jointly control the combustion chamber pressure through an inertial link. The combustion chamber pressure is affected by system disturbances, namely the torque of the axial propulsion pump. The two are affected by the inertial link and jointly control the output of the system, namely the turbine speed. The transfer function of the control system is shown in equation (25). （25）； In order to perform closed-loop control of turbine speed, the turbine speed needs to be fed back to the speed control system input. The transfer function of the closed-loop control system is shown in equation (26). （26）； The system is subject to interference, so integral control needs to be introduced to eliminate static errors. The PID control algorithm is selected to perform closed-loop speed control of the system, and proportional-integral PI is used to control the pump angle position of the fuel pump.
10. The method for controlling the rotational speed lag of a vehicle's propulsion system during water entry transients according to claim 3, characterized in that, Step 4 specifically involves: Step 4.1: Obtain the open-loop dynamic characteristics of the power system during the water entry process; Step 4.2: Based on the open-loop dynamic characteristics of the power system, a PID control algorithm is used to perform closed-loop speed control on the power system; Specifically, after the power system is running stably, the torque of the axial flow pump is controlled to change according to the characteristics of formula (15), and the fuel pump is controlled by PID algorithm; Step 4.3: Considering the sensor delay response factor, a simulation study of lag control was conducted on the dynamic system to obtain the control response characteristics of the cross-medium dynamic system during water entry. Specifically, the optimized power system is simulated, and the simulation process is divided into three stages: stable operation of the power system, continued operation of the power system without control, and operation of the power system under control. The operating status of combustion chamber pressure and turbine speed is analyzed in each of the three stages. When the peak values of combustion chamber pressure and turbine speed reach the safe operating threshold, the operating time at this time is taken as the maximum safe operating time of the power system.