Rolling active load relief technology for launch vehicle bundled with common booster core in face

The aerodynamic interference forces and moments of different windward surfaces of a launch vehicle bundled with a common booster core in the face vary considerably. The servo mechanism is laid out to maximize the control capability of the rocket at a certain angle. The dominant surface of the rocket is determined by aerodynamic interference and control capability. For the problem of large interference and asymmetry during the flight of a nominal rocket, a rolling active load relief control law based on the optimization of the spatial interference vector is proposed. The direction with the largest spatial interference vector is obtained online by visual acceleration information. By adjusting the rolling program angle, the rocket will align the dominant face with the direction of the largest interference when flying through the windy area. And then, the rocket obtains a good control effect. The simulation results show that the control law proposed in this paper can effectively improve the adaptability of the rocket control in the case of sudden changes in wind direction. It achieves the purpose of reducing the static load of the rocket body structure during the flight.


Introduction
Launch vehicles are currently the main means of transporting satellites, manned spacecraft, space probes, space stations, and the like into predetermined orbits.As the quality of the payloads to be transported continues to increase, higher requirements have been placed on the launch vehicle's capacity.Bundled launch vehicles have emerged as a result.At present, the advanced overall design concepts of launch vehicles in the international arena mostly follow the principles of "modularization, generalization, serialization, productization, and commercialization" to achieve rapid design, cost reduction, and rapid implementation of launch vehicles.Against this background, the launch vehicle bundled with a common booster core (CBC) in the face has been rapidly developed and successfully implemented, such as the Delta IV heavy launch vehicle [1], heavy Falcon launch vehicle [2], and so on.
In the atmospheric flight section of the launch vehicle, aerodynamic forces and aerodynamic moments are the main external disturbances in the dense atmosphere.The main reason for their generation is the rocket flight process due to the role of high-altitude wind to make the rocket angle of attack caused by the larger.Especially in the process of reaching the maximum dynamic pressure, the wind angle of attack generated by the wind at high altitudes and the moment formed by the control pendulum angle will bring a large bending moment for the rocket body.A bending moment that is too large will damage the structure of the rocket body.To ensure that the structure of the carrier rocket is not damaged, one way is to increase the strength of the rocket structure.However, this method will reduce the rocket transportation coefficient and affect the rocket transportation performance.Another method is to introduce load reduction technology in the development process of the launch vehicle.The IOP Publishing doi:10.1088/1742-6596/2764/1/012061 2 attitude control technology is used to reduce the static load of the rocket during flight to improve the carrying capacity.There are two main types of launch vehicle load relief techniques: passive load relief and active load relief.
Passive load relief is also known as the ballistic correction compensation method.This method requires the measurement of wind direction and wind speed of steady and shear winds at high altitudes in advance.The information is bound and introduced into the rocket control system before launch.Load reduction is achieved through program angle optimization [3][4].Zhao et al. [5] invented a load relief control method and storage device for non-axisymmetric launch vehicles.The rolling program angle interpolation table and rolling program angle rate interpolation table are bound to the launch vehicle as plurals.However, passive load relief requires high accuracy of wind speed and direction measurement.The wind speed and direction are more stable over a period of time.When the wind field shear is large, the method is difficult to achieve the ideal load relief effect.
Active load relief is also known as real-time wind correction.This method reduces aerodynamic loads by introducing real-time measured feedback of angle of attack, sideslip angle, velocity, and acceleration into the attitude control equations.It can correct the attitude angle in real time to reduce the angle of attack and sideslip angle in flight [6].The Atlas series of launch vehicles can realize load reduction after using feedback from the angle of attack or differential pressure sensors.However, their inability to provide precise angular information affects engineering applications.Saturn V, Titan III, and Long March series launch vehicles introduce accelerometer signals into the control system.This method is the most convenient and accurate in engineering applications [7].The LM-8 launch vehicle [8][9] reduced the load during flight by introducing accelerometers into the attitude control system.Cui et al. [10] realized the launch vehicle flight load reduction effect by designing an adaptive broadening and anti-disturbance load reduction controller with an expansion state for disturbance compensation and an active load reduction control algorithm.Zhang et al. [11] proposed a program for the flight segment of the first stage with a rolling angle.He aligned the direction of maximum control capability to the wind direction at the most dangerous altitude by rolling orientation.This can utilize the maximum control capability while generating the corrected pitch yaw program angle increment for attitude adjustment based on the inertial group acceleration information and reduce the angle between the airflow and the longitudinal axis of the arrow to achieve load reduction.From the related literature research, most of the existing launch vehicle load relief methods realize online load relief only by adjusting the pitch and yaw channels.The method of adopting rolling attitude adjustment for load relief is to perform pre-launch program angle encapsulation with wind field measurement in advance.This requires high accuracy of wind field measurement.If the wind field changes greatly during the rocket flight, it will be difficult to achieve a good load relief effect.The difference in aerodynamic disturbance moments for different windward surfaces of the CBC launch vehicle is very large.It is necessary to utilize the rolling attitude to align the aerodynamic advantageous surface to the direction of the wind field.
Therefore, this paper mainly focuses on the rolling wind active load relief technology for the CBC launch vehicle.A rolling active load relief control law based on the optimization of spatial disturbance vector is proposed.It utilizes a load relief apparent accelerometer to measure the rocket's transverse and normal apparent accelerations to determine the maximum direction of the spatial interference vector online and to correct the flight roll program angle.This enables the nominal general-purpose core stage rocket to align the advantageous face to the maximum direction of the spatial interference vector in case of sudden change of the wind direction at high altitude and reduces the servo pendulum angle and the structural static load during the flight process.

Model attitude dynamics of CBC launch vehicle
The object of this study is CBC launch vehicle with the main characteristics:  One booster on each side of the core stage with the same dimensions, number of engines, and size as the core stage.
 Liquid propellants are used in both the core stage and the booster.The longitudinal axis of symmetry of the propellant tank coincides with the longitudinal axis of the core stage or booster in which it is located.
 Both the core stage and the booster are fitted with rocking engines, which are mainly utilized for joint attitude control.
The process of modelling the six-degree-of-freedom attitude dynamics of the launch vehicle is more complicated.Due to the limited space reason, this paper does not make a detailed derivation.We directly give the six-degree-of-freedom attitude dynamics model of a face-symmetric generalized core-stage bundled rocket rigid body.System of equations for the center of mass advection:  sin sin cos sin cos +sin sin cos sin sin +sin cos cos cos System of equations of rotation around the center of mass: Where V is the relative velocity of the center of mass; θ is the ballistic inclination; σ is the ballistic declination; ω X1 , ω Y1 , ω Z1 are the three-axis components of the arrow's rotational angular velocity of the arrow; Θ is the local ballistic inclination; g is the acceleration of gravity; α is the angle of attack; β is the angle of sideslip; α W is the angle of attack of the wind; β W is the angle of side-slip of the wind; δ φ , δ ψ , and δ γ are the equivalent pendulum angles of the pitching, yawing, and rolling passages; E 1 and so on are acceleration coefficients; C 1 and so on are dynamical coefficients; d 1 , b 2 , and so on are moment coefficients; J cY and J cZ are the inertia of the rotation of the arrow.
The wind angle of attack and wind sideslip angle are modelled as follows: cos sin atan( ) cos cos Where W is the wind speed; A is the angle between the wind direction and the launch plane.1.The reference areas of different windward surfaces are also different when Φ=0° is used as the wide windward surface and Φ=90° is used as the narrow windward surface.It can be seen that the aerodynamic interference force and moment differ greatly between different windward surfaces when encountering high-altitude winds.The aerodynamic interference force and moment of using the narrow side as the windward side is less than that of the wide side as the windward side.Therefore, the narrow face of the CBC launch rocket is called the aerodynamically advantageous face.

Control dominance surface analysis
The core stage of the CBC launch vehicle that is the subject of this study uses an "X" layout to install four engines, with the same boosters as the core stage strapped on both sides, as shown in Figure 2.For a single core stage, the control capability is weakest in the direction around 45° [11].At this point, only two engines can swing in the ability to produce a control moment in that direction.Similarly, the weakest control capability is in the 45° direction for the CBC launch vehicle when only six of the twelve engines can provide a control moment in that direction.Maximum control is obtained in both the y and z directions.
Where 3_ d b  is the single-engine pitching moment coefficient, 3_ d b  is the single-engine yaw moment coefficient, 3_ d d is the single-engine roll moment coefficient.
Similarly, module II and module III control torque for the full arrow are: The way the pendulum angles of the three modules are assigned when each single machine is working normally: When the engine swing angle limitation is small, the CBC launch vehicle is prone to swing angle limitation when flying in a windy area, which will cause a safety hazard to the attitude control of the launch vehicle.To summarize, the narrow side of the CBC launch vehicle is said to be the aerodynamic and control advantageous side.Therefore, when the launch vehicle flies through the windy area, aligning the narrow side to the direction of the wind field can reduce the static load on the body structure.

Design of rolling active load relief controller based on spatial disturbance vector optimization
During the take-off phase of the CBC launch vehicle, the original bound program angle is used for flight.When flying through a windy area, the program angle is corrected based on the pre-launch measurement of the wind field direction so that the narrow side of the rocket is aligned with the direction of the incoming flow.The high-altitude wind field angle A f and the launch plane direction A 0 are shown schematically in Figure 3.The incoming flow azimuth angle in the rocket system is shown schematically in Figure 4.
When flying through a windy area, the corrected program angle γcx for the direction of the wind field will be the narrow side:  In this paper, PD control is used as the rolling channel controller, as shown in Figure 5.The inertia group measurement is utilized to obtain the current rolling angle γ, and the angular rate gyro to obtain the rolling angular velocity ω x .The rolling channel PD control commands the swing angle to be:  Based on the PD controller, the lateral and normal apparent accelerometers in the arrow are utilized to obtain the apparent acceleration during flight.The equation for calculating the apparent acceleration in the coordinate system of the arrow body derived from the attitude dynamics model is: In order to obtain the apparent acceleration deviation due to space disturbances during the flight of a nominal general-purpose core-stage rocket, it is necessary to subtract the current apparent acceleration due to engine thrust and control forces from the apparent accelerometer measurements.The apparent acceleration deviation due to space disturbance is: From this, the optimal direction of the spatial interference vector can be obtained in the arrow system.In fact, this direction is the angular deviation between the current roll angle of the rocket and the theoretical optimal roll angle: At this point, the roll channel control command pendulum angle changes to: The launch vehicle control algorithm with roll control requires roll decoupling.The PD control command swing angle for the decoupled pitch and yaw channels is:

Simulation results and analysis
In this paper, a real measured wind is selected to simulate and verify the effect of the rolling active load relief controller based on spatial disturbance vector optimization proposed in this paper.According to the designed flight program, the change of wind speed and wind angle in the wind field with time is shown in Figure 6.It can be seen that the rocket gradually enters the windy area after 40 s of flight, and the wind speed begins to increase and reaches the maximum wind speed at 88 s.Therefore, 40 s-95 s is selected for verification in this simulation.In order to test the impact of sudden changes in wind direction on the load relief effect of the designed controller, a sudden change in wind angle of 40° is added after 74 s on the basis of the original measured wind field.Under the conventional design state, the equivalent swing angles of the pitch, yaw, and roll channels during the flight of the CBC launch vehicle are shown in Figure 7 (1).The equivalent swing angles of each channel using rolling load relief control based on pre-shot measurement of wind field direction are shown in (2).The equivalent swing angle of each channel using the rolling active load relief controller based on spatial disturbance vector optimization is shown in (3). (1) (2) (3) . Equivalent pendulum angles for pitch, yaw, and roll channels.It can be seen that the rolling load relief control based on the pre-launch measured wind field direction can significantly reduce the equivalent swing angle of the pitch channel when the wind field direction does not change suddenly compared with the pre-shot measured wind direction during the flight.However, when the actual wind field has a sudden change, the maximum required equivalent swing angle of the pitch channel will increase significantly.With the rolling active load relief controller based on spatial disturbance vector optimization proposed in this paper, the required equivalent swing angle of the pitch channel is significantly reduced when the wind field direction changes abruptly.It is reduced by 50.2% compared with the pre-shot wind direction measurement load relief.
The servo swing angles of the core stage and the booster obtained from the simulation are shown in Figure 8.Among them, (1) is the servo swing angle for the conventional design state.( 2) is the servo swing angle with rolling load relief control based on the direction of the wind field measured in front of the shot.(3) is the servo pendulum angle using the rolling active load relief control based on spatial interference vector optimization.The simulation results show that, compared with the conventional design, the maximum servo swing angle of module I with rolling load relief control based on wind field direction is reduced from 3.1° to 1.5°.The maximum servo swing angle of module II is from 2.8° to 1.1°, and the maximum servo swing angle of module III is from 3.1° to 1.5°, when there is no sudden change of wind field direction during the flight.The rolling load relief control based on the pre-launch measurement of the wind field direction reduces the maximum servo swing angle of the CBC launch IOP Publishing doi:10.1088/1742-6596/2764/1/0120619 vehicle by more than 50%.However, when the wind field direction changes abruptly, the servo maximum swing angle increases rapidly to 3.3°.Using the rolling active load relief control based on spatial disturbance vector optimization, the maximum servo swing angle can be reduced to 2.1°, which is 36.4% lower. (1) (2) (3) Figure 8.The pendulum angle of each servo of the core stage and booster.Therefore, the rolling load relief control based on the pre-launch measurement of the wind field direction can effectively reduce the individual servo swing angle during the flight of the CBC launch vehicle.However, the adaptability is poor when the wind direction changes abruptly.The rolling active load relief control based on spatial disturbance vector optimization proposed in this paper can effectively reduce the servo swing angle when the wind direction undergoes a sudden change.It has good adaptability to sudden changes in wind direction.When the servo limit is small, it can prevent flight anomalies from occurring due to insufficient control capability.

Conclusion
In this paper, the rolling active load relief technique for the CBC launch vehicles is investigated.The control advantageous surface and the aerodynamic advantageous surface of the CBC launch vehicle under the engine "X" layout are analyzed.The analysis shows that the narrow side of the rocket is the dominant side in both control and aerodynamics.The active rolling load relief control based on spatial disturbance vector optimization is proposed in this paper.The direction of the spatial interference vector during the rocket flight is obtained by using the onboard visual accelerometer so that the narrow side of the CBC launch vehicle will be oriented in that direction during the flight.In this way, the servo pendulum angle is reduced during flight, and the static load on the rocket body structure is reduced.The effectiveness of the proposed method is verified by numerical simulation.
Unlike axisymmetric launch vehicles, the different windward faces of the CBC launch vehicle are divided into dominant and non-dominant faces.As shown in Figure1, they are the narrow and wide faces of the CBC launch vehicle.q is the dynamic pressure head; S ref is the reference area; n C  is the slope of change of normal force coefficient with the angle of attack; Φ is the azimuthal angle of incoming airflow.

Figure 1 .
Figure 1.Schematic diagram of non-dominant (left) and dominant (right) surfaces.For the CBC launch rocket, different airflow directions are different n C  , as shown in Table1.The

Figure 2 .
Figure 2. Schematic layout of CBC launch vehicle engine.The control torque of module I on the full arrow is: 11 3 3 _ 12 3 3 _ 13 3 3 _ 14 1 1 1 1 2 1 1 1 1 2 1 1 1 1 I I d I I d I I d b b b b d d

Figure 3 .
Figure 3. Schematic diagram of the angle of the wind field at high altitude and the direction of the launch plane.

Figure 5 .
Figure 5. Rolling active load relief controller based on spatial disturbance vector optimization.Based on the PD controller, the lateral and normal apparent accelerometers in the arrow are utilized to obtain the apparent acceleration during flight.The equation for calculating the apparent acceleration in the coordinate system of the arrow body derived from the attitude dynamics model is:

Figure 6 .
Figure 6.Variation of wind speed and wind angle in wind field with time.

Table 1 .
n C  values for different incoming flow directions.