A method for synchronous separation control between stages of a launch vehicle

Abstract

This invention discloses a synchronous separation control method for interstage rockets, comprising the following steps: designing an interstage separation system based on high-speed switching valve control and establishing a mathematical model of the rocket interstage separation system; adjusting the relative position of the rockets through a synchronization control method based on control allocation; and finally, performing simulation verification of the synchronous separation of the rocket interstage separation system. This invention addresses the problems of overdrive, strong aerodynamic nonlinearity, and uncertainty in rocket interstage separation systems based on aerodynamic technology by proposing a synchronization separation control method based on control allocation. First, a virtual layer backstepping virtual controller based on a disturbance observer is established. Then, through dynamic control allocation, the virtual control law is distributed to the inner loop to form the control objective of the actuator layer controller. Finally, an inner loop actuator control law based on backstepping control is designed to achieve synchronous separation control, fully considering various disturbances during the separation process and achieving the goal of synchronous movement of the separation actuators.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical system dynamics and control, and specifically relates to a method for interstage synchronous separation control of a launch vehicle. Background Technology

[0002] Stage separation is a crucial step in the successful launch of a launch vehicle, involving the jettisoning of the lower stage while the upper stage continues its flight. As human exploration of outer space becomes increasingly frequent, new demands are placed on launch vehicles. Reusable launch vehicles are currently a research hotspot in the aerospace field worldwide. Reusable rockets can significantly reduce launch costs, but they also present new challenges to the rocket's stage separation system.

[0003] SpaceX's Falcon 9 series rockets have successfully recovered a first stage using an aerodynamic-based interstage separation method. This novel cold separation method offers advantages such as rapid separation, minimal damage to the first stage, and reusability. Therefore, researching this interstage separation method and applying it to small, medium, and large rockets is highly significant for achieving reusability.

[0004] Currently, research on rocket stage separation systems based on aerodynamic technology is limited both domestically and internationally. LandSpace has invented a separation system based on single and multi-cylinder systems, but has not yet conducted modeling and analysis of these systems. Especially for multi-cylinder separation systems, the synchronization of each cylinder affects the relative attitude angle between the separated stages. If the relative attitude angle between the two stages is too large, it may cause a collision between the stages, leading to launch failure. Therefore, researching the synchronous separation of cylinders in multi-cylinder separation systems is of great significance.

[0005] Research on synchronous separation methods for multi-cylinder systems mainly focuses on master-slave control based on deviation coupling, and its application areas are limited. Multi-cylinder inter-stage separation systems are typical overdriven systems, and aerodynamic systems exhibit strong nonlinearity and uncertainty. To achieve synchronous control of multi-cylinder systems, a new control algorithm is urgently needed. Control problems in overdriven systems are mainly addressed using control assignment methods, currently primarily applied in aircraft attitude control and multi-cylinder leveling control of large forging presses. Research on synchronous control of multi-cylinder inter-stage separation systems is still in its early stages. Existing technology (Zhao Shuhao. Research on Nonlinear Control Method for Overdriven Systems Based on Control Assignment [D]. Tianjin University of Technology, 2023.) studies the application of control assignment methods in leveling of multi-cylinder hydraulic presses, but does not provide a control method for aerodynamic synchronous separation systems. Therefore, designing and developing an effective aerodynamic synchronous control system, drawing on the research results of control assignment algorithms in satellites and spacecraft, and then using appropriate control methods to achieve synchronous separation control of multi-cylinder launch vehicle inter-stage separation systems, thereby improving the reliability of rocket inter-stage separation, is a promising new academic topic worthy of research. Summary of the Invention

[0006] This invention proposes a synchronous separation control method based on control allocation. First, a virtual backstepping virtual controller based on a disturbance observer is established. Then, through dynamic control allocation, the virtual control law is allocated to the inner loop to form the control target of the actuator layer controller. Finally, an inner loop actuator control law based on backstepping control is designed to achieve synchronous separation control. This invention aims to solve the problem of asynchronous separation actuators caused by external disturbances and uncertainties in their own parameters during interstage separation of rockets. It explores an effective synchronous control technology for multi-cylinder separation systems, weakens the influence of disturbances, and thus improves the reliability of interstage separation.

[0007] The present invention is achieved by at least one of the following technical solutions.

[0008] A method for synchronous separation control between stages of a launch vehicle includes the following steps:

[0009] Step 1: Construct an interstage pneumatic separation system controlled by a high-speed switching valve;

[0010] Step 2: Establish a mathematical model of the four-cylinder interstage separation system;

[0011] Step 3: Construct a hierarchical controller based on control allocation;

[0012] Step 4: Conduct synchronous separation simulation verification of the rocket stage separation system.

[0013] Furthermore, the interstage separation system includes four or more cylinders and corresponding push rods. The cylinders are evenly distributed on the inner wall of the interstage section. The connection surface between the push rod and the upper stage is on the separation surface between the upper stage and the interstage section. The push rod separates the first and second stage rocket bodies.

[0014] Each cylinder's intake and exhaust are controlled by two high-speed switching valves, one for intake and one for exhaust.

[0015] The pneumatic separation system includes a gas cylinder, a pressure reducing valve, a gas container, and pipelines, which provide high-pressure gas to the cylinder.

[0016] Furthermore, in step 2, a mathematical model of the four-cylinder interstage separation system is established based on the rocket's dynamics, including the following steps:

[0017] Step 2-1: Based on the forces acting on the rocket body during separation, the dynamic model of the separated body using the six-degree-of-freedom Euler equations is as follows:

[0018]

[0019] In equation (1), m1 is the mass of the lower stage separation body; m2 is the mass of the upper stage separation body; v1 and v2 are the velocity vectors of the lower and upper stage separation sub-stages; ω1 and ω2 are the angular velocity vectors of the lower and upper stages; J1 and J2 are the moment of inertia matrices of the lower and upper stage separation sub-stages; and F... i Let be the thrust vector of cylinder i; ψ1,θ1,γ1 and ψ2,θ2,γ2 are the pitch, yaw, and roll angles of the upper and lower separation stages, respectively; G1 and G2 are the gravity of the separated body in the ground coordinate system; F f For the residual thrust of the lower stage engine; M i F is the thrust torque of cylinder i; d1 F d2 External interference; M d1 M d2 External disturbance torque;

[0020] Due to the constraints of the separation system, there are only three controllable degrees of freedom in actual separation: displacement along the rocket body axis, relative pitch angle, and relative yaw angle. Therefore, the six-degree-of-freedom model can be further simplified to a three-degree-of-freedom model, by taking the sub-stage motion state variables respectively. in, For the acceleration of the lower and upper sub-stages, For the yaw angle acceleration of the lower and upper stages, The pitch angle acceleration of the lower and upper levels;

[0021] Three-degree-of-freedom dynamic model of the separated body:

[0022]

[0023]

[0024] In the formula, E1 = E N1 +ΔE1, E2=E N2 +ΔE2;E N1 =diag(m1,J y1 J z1 ) and E N2 =diag(m2,J y2 J z2 ) represents the normal part of the system, m1 and m2 are the masses of the separated parts, and J y1 J z1 J y2 J z2 These are the moments of inertia of the upper and lower separated sub-stages about the y-axis and z-axis, respectively; ΔE1=diag(Δm1,ΔJ y1 ,ΔJ z1 ), ΔE2=diag(Δm2,ΔJ y2 ,ΔJ z2 ) represents the uncertainty of the system, Δm1 and Δm2 represent the mass uncertainty of the separated sub-stages, and ΔJ represents the uncertainty of the system. y1 ,ΔJ y2 ,ΔJ z1 ,ΔJ z2 To separate the uncertainty of the rotational inertia of the sub-stage, d n1 d n2 ∈R 3×1 For external disturbances to the system, η = [F1 F2 F3 F4] T R1 is the cylinder separation force, R1 is the distance from the cylinder mounting position to the arrow body axis, and B1 and B2 are the mounting matrices.

[0025] Selecting relative motion state variables in, The axial velocities of the lower and upper sub-stages, The yaw angular velocities of the lower and upper separation stages are given. Given the pitch angular velocities of the lower and upper separate substages, the system is converted into a state-space model:

[0026]

[0027] in To control the efficiency matrix, For aggregated disturbances, Let be the relative velocity vector of the system. Let η be the relative motion acceleration vector of the system. As can be seen from equation (4), the dimension of the input variable η is greater than the dimension of the state variable X2, and the system is a typical overdriven system.

[0028] Because the relative rotation angle is small, the relative displacement of each cylinder is calculated using the following formula:

[0029]

[0030] In the formula, x A x B x C x D x represents the relative displacement of the four cylinders. 21 To separate the axial relative displacement of the sub-stages, when the relative attitude angle of the separated bodies is very small, assume sinψ 21 ≈ψ 21 sinθ 21 ≈θ 21 , where ψ 21 =ψ2-ψ1,θ 21 =θ2-θ1 are the relative yaw angle and relative pitch angle of the separation stage, respectively.

[0031] Furthermore, the aerodynamics of the four-cylinder interstage separation system are established using a mathematical model, as detailed below:

[0032] Establishing a pneumatic system dynamic model: Since the pressure in the intake chamber is much greater than the pressure in the exhaust chamber, and neglecting the frictional force of the cylinder, the pneumatic system dynamic model is as follows:

[0033]

[0034] In the formula, p m Let A be the gas pressure in the intake chamber of cylinder m. m The effective working area of ​​cylinder m is given by m. m For the mass of the push rod, η m The output force of cylinder m. Let η be the acceleration of the push rod relative to the cylinder. Since the mass of the push rod is relatively small compared to the mass of the arrow body, it can be further simplified as: η m =p m A m ;

[0035] The relationship between the intake chamber pressure and the duty cycle signal of the high-speed switching valve can be obtained from the laws of thermodynamics:

[0036]

[0037]

[0038]

[0039] In the formula, k is the adiabatic coefficient of the gas, R is the gas constant, and T is the gas constant. b Let V0 be the gas temperature, V0 be the sum of the volume of the pipeline from the gas cylinder to the inlet chamber and the volume of the dead zone of the inlet chamber, and x be the gas temperature.m For cylinder displacement, For cylinder speed, q is the derivative of the cylinder pressure. m The mass flow rate of the gas entering the intake chamber, μ m For the duty cycle signal of the high-speed switching valve, C d Where Ae is the flow coefficient, p is the equivalent cross-sectional area of ​​the valve orifice, and p is the flow coefficient. um For upstream pressure, p dm For downstream pressure, This represents the gas flow rate.

[0040] Furthermore, a virtual layer disturbance observer is constructed in the hierarchical controller based on control allocation, as follows:

[0041] Take the virtual control quantity v d =L f η, the state-space model (4) can be transformed into:

[0042]

[0043] in, ξ represents the lumped disturbance;

[0044] Design a nonlinear disturbance observer. For system (10), we can obtain:

[0045]

[0046] In the formula, L = diag(l1,l2,l3) is the observer gain matrix, and l1,l2,l3 > 0; This is an estimate of the disturbance; The derivative of the disturbance estimate;

[0047] Define the observation error of the total disturbance observer. for:

[0048]

[0049] The error derivatives of the interference observations can be obtained from equations (10) to (12). for:

[0050]

[0051] Furthermore, a virtual layer controller is constructed in the hierarchical controller based on control allocation, as follows:

[0052] From equation (10), we define Z1 = X 1d -X1 represents the tracking error, where X 1d ∈R 3×1The target value command is a twice-differentiable command, where X1 is a vector relating the system's relative displacement, relative yaw angle, and relative pitch angle; R 3×1 Representing a 3x1 matrix, X2 in equation (10) is selected as the virtual control variable, so that... Tend to a stable state; let X 2eq Let the desired value of the virtual control be defined as the virtual control error Z2 = X. 2eq -X2;

[0053] The desired value of the virtual control design is X. 2eq :

[0054]

[0055] In the formula, K1=diag(k 11 ,k 12 ,k 13 ), is an adjustable gain matrix, and k 11 ,k 12 ,k 13 >0;

[0056] Differentiate the virtual control error Z2 and use the estimate from the disturbance observer. Replacing the system's disturbance ξ with equations (10) and (14), we get:

[0057]

[0058] in, K1 is the derivative of the virtual control error, and K2 is the gain matrix.

[0059] design Substituting equation (15) into the equation yields the virtual control law of the outer loop virtual control layer:

[0060]

[0061] In the formula, K2=diag(k 21 ,k 22 ,k 23 ), is an adjustable gain matrix, and k 21 ,k 22 ,k 23 >0; The derivative of the target being tracked; I is the identity matrix.

[0062] Furthermore, a control allocation layer is constructed in the hierarchical controller based on control allocation, as follows:

[0063] Consider a dynamic control allocation scheme that minimizes both the energy consumption of the control variable and the rate of change of the control variable, and applies this scheme to the virtual control command v. dPerform dynamic allocation:

[0064]

[0065] In the formula, W0, W1, W2 ∈ R 4×4 Here, η is the weight matrix, T is the control period; c η is the cylinder thrust to be allocated. ca The desired steady-state thrust of the cylinder; J is the objective function; st represents the constraints; v d (t) represents the virtual control quantity; t represents the simulation time;

[0066] Assume that the weight matrices W1 and W2 are symmetric, and W4 = (W1... 2 +W2 2 ) 1 / 2 If it is non-singular, then the cylinder thrust η to be allocated is... c The following solutions are available:

[0067] η c (t)=(I-GL f W4 -2 W1 2 η ca (t)+(I-GL f W4 -2 W2 2 η c (tT)+Gv d (t) (18)

[0068] Where G = W4 -1 (L f W4 -1 ) + η ca (t)=L f T (L f L f T ) -1 v d (t), L f I is the control efficiency matrix, and I is the identity matrix.

[0069] Furthermore, the actuator layer controller in the hierarchical controller based on control allocation is specifically as follows:

[0070] The control force command is converted into the target pressure p in the cylinder intake chamber. md Based on backstep control, let ε m =p m -p md For the inner ring pressure tracking error, p m The actual pressure in the cylinder intake chamber:

[0071] Let the Lyapunov function be:

[0072]

[0073] From the dynamic equation of the intake chamber pressure, we can obtain:

[0074]

[0075] In the formula, k is the adiabatic coefficient of the gas, R is the gas constant, and T is the gas constant. b Let V0 be the gas temperature, V0 be the sum of the volume of the pipeline from the gas cylinder to the inlet chamber and the volume of the dead zone of the inlet chamber, and x be the gas temperature. m For cylinder displacement, A m q is the effective working area of ​​the cylinder. m The mass flow rate of the gas entering the intake chamber. V2(ε) m The derivative of ) For pressure tracking error ε m The derivative, Let m be the relative velocity of the cylinder. The derivative of the pressure tracking target;

[0076] As can be seen from Lyapunov stability, when At that time, the pressure tracking error ε m Converging to 0;

[0077] Design the gas mass flow rate q of the inner loop actuator. md Control Law:

[0078]

[0079] In the formula, η cm The cylinder output force is calculated using the formula, A. m Let m be the piston area of ​​the cylinder, and γ be the piston area. m >0 represents the control gain of the inner loop controller.

[0080] Furthermore, the design of the high-speed switching valve duty cycle signal in the hierarchical controller based on control allocation is as follows:

[0081] Design the duty cycle of the PWM signal:

[0082] When the gas mass flow rate q of the inner ring actuator cylinder md When the air pressure is greater than 0, the inflation valve is open and the deflation valve is closed, with a duty cycle of:

[0083]

[0084] In the formula, This refers to the duty cycle of the high-speed intake switching valve. For the duty cycle of the high-speed exhaust switching valve, Aecu p is the effective throttling area of ​​the intake high-speed switching valve. s p is the pressure after the pressure reducing valve. a T is the intake chamber pressure of the cylinder. s K represents the gas temperature. qa Here is the gas flow equation;

[0085] When q md When the pressure is ≤0, the inflation valve is closed and the deflation valve is open, with a duty cycle of:

[0086]

[0087] In the formula, Ae du The effective throttling area of ​​the high-speed exhaust switching valve is given by p0, where p0 is atmospheric pressure and k is the pressure. qb This is the gas flow equation.

[0088] Furthermore, the synchronous separation simulation verification of the rocket stage separation system is carried out as follows:

[0089] Step 4-1: Perform dynamic modeling of the rocket separation system based on four cylinders, including dynamic modeling of the separation stage during the separation process and dynamic modeling of the high-speed switching valves and cylinders in the pneumatic system;

[0090] Step 4-2: Model the synchronous separation control algorithm, including the virtual layer controller, dynamic control allocation solution, and actuator layer controller;

[0091] Step 4-3: In order to compare the effect of synchronous separation control, the simulation results of open-loop and closed-loop control are compared respectively. To facilitate the verification of the controller effect, it is assumed that the pressure at the outlet of the pressure reducing valve remains unchanged during the simulation.

[0092] Compared with the prior art, the present invention has the following significant advantages:

[0093] 1) Based on a novel rocket separation system based on pneumatic technology, this invention introduces closed-loop control technology and designs a four-cylinder interstage separation system controlled by a high-speed switching valve, which can adjust the separation force in real time during the separation process. This is one of the innovative applications of this invention.

[0094] 2) The control allocation method is a control method for overdrive systems, which is currently mostly used in the field of satellite attitude control. The novelty of this invention lies in combining this method with backstepping control and interference observers and applying it to the synchronous control of multi-cylinder separation systems.

[0095] 3) The control method for synchronous separation of a multi-actuator rocket stage separation system provided by the present invention uses a pneumatic separation system instead of a traditional pyrotechnic separation system, which has the advantages of being clean, low cost and reusable. After the introduction of synchronous control, the reliability of stage separation is further improved and the robustness of the system is enhanced. Attached Figure Description

[0096] To further illustrate the technical means of this invention and to present the principles, objectives, and features of this invention in a more accessible and understandable way, the following embodiments will be provided, accompanied by illustrations.

[0097] Figure 1 This is a schematic diagram of the structure of the four-cylinder interstage separation system of the present invention;

[0098] Figure 2 This is a structural diagram of the four-cylinder interstage separation system based on high-speed switching valve control of the present invention;

[0099] Figure 3 This is a structural diagram of a synchronization controller based on control allocation according to the present invention;

[0100] Figure 4 The curve showing the relative motion of the separated body about the Y-axis according to the present invention;

[0101] Figure 5 The relative motion curve of the separated body about the Z-axis in this invention;

[0102] Figure 6 The relative velocity and relative displacement curves of the separation stage of this invention are shown.

[0103] Figure 7 The pressure variation curves of the intake chambers of each cylinder in this invention are shown.

[0104] Figure 8 This is the estimated value of the interference around the Y-axis for the interference observer of this invention;

[0105] Figure 9 This is the Z-axis interference estimate of the interference observer of the present invention;

[0106] Figure 10 The curves showing the displacement changes and synchronization error of each cylinder under the closed-loop control of this invention are shown.

[0107] Figure 11 The curves showing the displacement changes and synchronization error of each cylinder under the open-loop control of this invention are shown.

[0108] In the diagram: 1-Upper stage rocket; 2-Lower stage rocket; 3-Interstage section; 4-First cylinder A; 5-Second cylinder B; 6-Third cylinder C; 7-Fourth cylinder D; 8-Gas pipe; 9-Intake high-speed switch valve; 10-Exhaust high-speed switch valve; 11-First push rod A; 12-First intake chamber A; 13-Pressure reducing valve; 14-High-pressure gas cylinder; 15-Second push rod B; 16-Second intake chamber B; 17-Third intake chamber C; 18-Third push rod C; 19-PWM signal generator; 20-Gas container; 21-Fourth intake chamber D; 22-Fourth push rod D. Detailed Implementation

[0109] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0110] like Figure 1 As shown in the figure, this embodiment of a synchronous separation control method for an interstage rocket separation system includes the following steps:

[0111] Step 1: Design a four-cylinder interstage separation system controlled by a high-speed switching valve, as follows:

[0112] The interstage separation system includes four or more cylinders (4, 5, 6, 7), which are evenly distributed on the inner wall of the interstage section 3. The push rods (11, 15, 18, 22) corresponding to the cylinders are connected to the upper stage on the separation surface between the upper stage rocket 2 and the interstage section 3. The push rods separate the upper stage rocket and the lower stage rocket body (2, 1).

[0113] The air intake of each cylinder consists of two high-speed switching valves (9, 10), one responsible for filling the air intake chamber 12 and the other responsible for exhausting the air intake chamber 12.

[0114] The pneumatic system consists of at least one gas cylinder 14, a pressure reducing valve 13, a gas container 20 of a certain volume, a pipeline 8, and a high-speed switching valve 9, which provide high-pressure gas to the cylinder intake chambers (12, 16, 17, 21).

[0115] In one embodiment, the cylinder body is fixed to the interstage section, and each cylinder is evenly distributed at 90-degree intervals. The high-speed switching valve is installed near the air inlet of the rodless chamber of the cylinder and is switched on and off by a PWM signal. The gas cylinder 14, the pressure reducing valve 13, and the PWM signal generator 19 are installed on the front bottom of the lower separation stage arrow body. The gas cylinder, the pressure reducing valve, the high-speed switching valve, and the cylinder are connected by a gas pipe 8.

[0116] Step 2: Establish the mathematical model of the four-cylinder interstage separation system, as follows:

[0117] Step 2-1: Based on the forces acting on the rocket body during separation, the dynamic model of the separated body using the six-degree-of-freedom Euler equations is as follows:

[0118]

[0119]

[0120] In equation (1), m1 is the mass of the lower stage separated body; m2 is the mass of the upper stage separated body; v1 and v2 are the velocity vectors of the separated sub-stages; ω1 and ω2 are the angular velocity vectors; J1 and J2 are the moment of inertia matrices of the separated sub-stages; and F... i (i = 1, 2, 3, 4) represents the thrust vector of the four cylinders; ψ1, γ1 and ψ2, γ2 represents the pitch, yaw, and roll angles of the lower and upper separation stages, respectively. L gd Here is the coordinate transformation matrix, c = cos, s = sin, and γ is the roll angle. ψ is the yaw angle, and ψ is the pitch angle; G1 and G2 are the gravitational forces of the separated body in the ground coordinate system; F f For the residual thrust of the lower stage engine; M i The thrust torque of 4 cylinders; F d1 F d2 External interference; M d1 M d2 External disturbance torque.

[0121] Due to the constraints of the separation system, there are only three controllable degrees of freedom in actual separation: displacement along the rocket's axis, relative pitch angle, and relative yaw angle. Therefore, the six-degree-of-freedom model can be further simplified to a three-degree-of-freedom model. (Taking state variables...) The three-degree-of-freedom dynamic model of the separated body is as follows:

[0122]

[0123]

[0124] In the formula, E1 = E N1 +ΔE1, E2=E N2 +ΔE2;E N1 =diag(m1,J y1 J z1 ) and E N2 =diag(m2,J y2 J z2 ) represents the normal part of the system, m1 and m2 are the masses of the separated parts, and J y1 J z1 J y2 J z2 Let ΔE1 = diag(Δm1, ΔJ) represent the moments of inertia of the upper and lower separated sub-stages about the y-axis and z-axis, respectively. y1 ,ΔJ z1), ΔE2=di ag (Δm2,ΔJ y2 ,ΔJ z2 ) represents the uncertainty of the system, Δm1 and Δm2 represent the mass uncertainty of the separated sub-stages, and ΔJ represents the uncertainty of the system's mass uncertainty. y1 ΔJ y2 ΔJ z1 ΔJ z2 To separate the uncertainty of the rotational inertia of the sub-stage. d n1 d n2 ∈R 3×1 For external disturbances to the system, η = [F1 F2 F3 F4] T R1 is the cylinder separation force, and R1 is the distance from the cylinder mounting position to the arrow body axis.

[0125] Furthermore, select state variables Convert the system into a state-space model:

[0126]

[0127] in To control the efficiency matrix, This is a lumped disturbance. As can be seen from equation (5), the input quantity is greater than the state quantity, and the system is a typical overdriven system.

[0128] Furthermore, since the relative rotation angle is small, the relative displacement of each cylinder can be calculated using the following formula:

[0129]

[0130] In the formula, x A x B x C x D x represents the relative displacement of the four cylinders. 21 To determine the axial relative displacement of the separated sub-stages, when the relative attitude angle of the separated bodies is very small, we can assume sinψ 21 ≈ψ 21 sinθ 21 ≈θ 21 ψ 21 =ψ2-ψ1,θ 21 =θ2-θ21, which are the relative yaw angle and relative pitch angle of the separation substage, respectively.

[0131] From equation (6), the relative axial displacement x between the cylinder displacement and the separator can be obtained. 21 Relative yaw angle ψ 21 Relative pitch angle θ 21 The relationship between them.

[0132]

[0133] Step 2-2: Establish the pneumatic system dynamic model. Since the pressure in the intake chamber is much greater than the pressure in the exhaust chamber, and neglecting cylinder friction, the pneumatic system dynamic model is as follows:

[0134]

[0135] In the formula, A, B, C, and D are four cylinders, p m The gas pressure in the intake chamber of each cylinder, A m The effective working area of ​​the cylinder is in meters. m For the mass of the push rod, η m The output force of the cylinder, Let η be the acceleration of the push rod relative to the cylinder. Since the mass of the push rod is relatively small compared to the mass of the arrow body, we can further simplify: η m =p m A m

[0136] Furthermore, the relationship between the intake chamber pressure and the duty cycle signal of the high-speed switching valve can be obtained from the laws of thermodynamics:

[0137]

[0138]

[0139]

[0140] In the formula, k is the adiabatic coefficient of the gas, R is the gas constant, and T is the gas constant. b Let V0 be the gas temperature, V0 be the sum of the volume of the pipeline from the gas cylinder to the inlet chamber and the volume of the dead zone of the inlet chamber, and x be the gas temperature. m This represents the cylinder displacement. q m This represents the mass flow rate of the gas entering the intake chamber. (μ) m For the duty cycle signal of the high-speed switching valve, C d Where Ae is the flow coefficient, p is the equivalent cross-sectional area of ​​the valve orifice, and p is the flow coefficient. um For upstream pressure, p dm For downstream pressure, This is the gas flow equation.

[0141] As one embodiment, C d Take 0.72.

[0142] Step 3: Construct a hierarchical controller based on control allocation, as follows:

[0143] Step 3-1: Design a virtual control layer based on an interference observer, and take the virtual control variable v. d =L f η, Equation (5) can be transformed into:

[0144]

[0145] Step 3-1-1: Design a nonlinear interference observation device. For system (12), we can obtain:

[0146]

[0147] In the formula, L = diag(l1,l2,l3) and l1,l2,l3 > 0 are the observer gain matrix coefficients. This is an estimate of the disturbance;

[0148] Define the observation error of the total disturbance observer. for:

[0149]

[0150] From equations (12), (13), and (14), we can obtain:

[0151]

[0152] As can be seen from equation (15), by selecting an appropriate observer gain, the observer error can converge exponentially.

[0153] Step 3-1-2: Design a backstepping controller based on an interference observer, as follows:

[0154] Define Z1 = X 1d -X1 represents the tracking error, where X 1d ∈R 3×1 Given the target value, and the target command being second-order continuously differentiable, according to equation (12), X2 is selected as the virtual control, making... Tend to a stable state; let X 2eq Let the desired value of the virtual control be defined as the virtual control error Z2 = X. 2eq -X2.

[0155] Design control law X 2eq :

[0156]

[0157] Differentiate with respect to Z2 and use the estimate from the disturbance observer. Substituting the system disturbance ξ into equations (12) and (16), we get:

[0158]

[0159] In the formula, K1=diag(k 11 ,k 12 ,k 13 ), and k 11 ,k 12 ,k13 >0 indicates an adjustable gain.

[0160] design Substituting equation (17) into the equation yields the virtual control law of the outer loop virtual control layer:

[0161]

[0162] In the formula, K2=diag(k 21 ,k 22 ,k 23 ), and k 21 ,k 22 ,k 23 >0 indicates an adjustable gain.

[0163] Design a Lyapunov function:

[0164]

[0165] Substituting equations (15), (16), (17), and (18) into the equations, we get:

[0166]

[0167] From equation (20), we can see that The system is uniformly bounded.

[0168] Step 3-2: Design the control allocation layer. Consider a dynamic control allocation scheme that minimizes both the energy consumption of the control variable and the rate of change of the control variable, and applies this scheme to the virtual control command v. d Dynamic allocation will be performed, as follows:

[0169]

[0170] In the formula, W0, W1, W2 ∈ R 4×4 Here is the weight matrix, T is the control period, and η is the weight matrix. c η is the cylinder thrust to be allocated. ca This represents the desired steady-state thrust of the cylinder.

[0171] Assume that the weight matrices W1 and W2 are symmetric, and W4 = (W1... 2 +W2 2 ) 1 / 2 If it is non-singular, then the control allocation η is... c The following solutions are available:

[0172] η c (t)=(I-GL f W4 -2 W1 2 η ca (t)+(I-GLf W4 -2 W2 2 η c (tT)+Gv d (t) (22) where G=W4 -1 (L f W4 -1 ) + η ca (t)=L f T (L f L f T ) -1 v d (t), L f This is for controlling the efficiency matrix.

[0173] Step 3-3: Design the actuator layer controller, and convert the control force command obtained in step 3-2 into the target pressure p in the cylinder intake chamber. md Based on backstep control, let ε m =p m -p md For the inner ring pressure tracking error, p m This represents the actual pressure in the cylinder's intake chamber.

[0174] Let the Lyapunov function be:

[0175]

[0176] Combining equations (9), we get:

[0177]

[0178] Design the gas mass flow rate q of the inner loop actuator. md Control Law:

[0179]

[0180]

[0181] In the formula, η cm The cylinder output force is calculated using the formula, A. m γ is the piston area of ​​the cylinder. m >0 represents the control gain of the inner loop controller.

[0182] Substituting equation (26) into equation (24), we get:

[0183]

[0184] Equation (27) shows that the tracking system is stable in the Lyapunov sense.

[0185] Furthermore, the duty cycle of the PWM signal is designed using equations (11) and (26):

[0186] When q md When the air pressure is greater than 0, the inflation valve is open and the deflation valve is closed, with a duty cycle of:

[0187]

[0188] In the formula, This refers to the duty cycle of the high-speed intake switching valve. Duty cycle of the high-speed exhaust switching valve. Ae cu p represents the effective throttling area of ​​the high-speed intake switching valve. s p is the pressure after the pressure reducing valve. a T is the intake chamber pressure of the cylinder. s The temperature is the gas temperature.

[0189] When q md When the pressure is ≤0, the inflation valve is closed and the deflation valve is open, with a duty cycle of:

[0190]

[0191] In the formula, Ae du p0 represents the effective throttling area of ​​the high-speed exhaust valve, and p0 represents atmospheric pressure.

[0192] The duty cycle of the PWM control signal for each high-speed switching valve can be obtained from equations (28) and (29), thereby controlling the pressure in the cylinder intake chamber.

[0193] Step 4: Conduct synchronous separation simulation verification of the rocket stage separation system, as detailed below:

[0194] First, based on the relevant parameters of a certain heavy-lift rocket, the main parameter is m1 = 45000 kg; J y1 =J z1 =4.19×10 6 m2 = 100000 kg; J y2 =J z2 =1.26×10 6 Pressure reducing valve outlet pressure p s =10Mpa; The main controller parameters are: K1=diag(10,20,20), K2=diag(10,20,20), L=diag(10,20,20), γ=diag(10,10,10,10);

[0195] The specific steps for modeling and simulation in Matlab / Simulink are as follows:

[0196] Step 4-1: Perform dynamic modeling of the rocket separation system based on four cylinders, including dynamic modeling of the separation stage during the separation process and dynamic modeling of the high-speed switching valves and cylinders in the pneumatic system;

[0197] Step 4-2: Model the synchronous separation control algorithm, including the virtual layer controller, dynamic control allocation solution, and actuator layer controller;

[0198] Step 4-3: In order to compare the effect of synchronous separation control, the simulation results of open-loop and closed-loop control are compared respectively. To facilitate the verification of the controller effect, it is assumed that the pressure at the outlet of the pressure reducing valve remains unchanged during the simulation.

[0199] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A method for interstage synchronous separation control of a launch vehicle, characterized in that, Includes the following steps: Step 1: Construct an interstage pneumatic separation system controlled by a high-speed switching valve; Step 2: Establish the mathematical model of the four-cylinder interstage separation system: Based on the rocket body dynamics, establish the mathematical model of the four-cylinder interstage separation system, including the following steps: Step 2-1: Based on the forces acting on the rocket body during separation, the dynamic model of the six-degree-of-freedom Euler equations for the separation stage is as follows: (1) In formula (1) m 1 represents the mass of the lower-level separation sub-stage; m 2 represents the mass of the upper stage separator; v1 and v2 represent the velocity vectors of the lower and upper stage separators, respectively. Let ω be the angular velocity vector of the lower-level separating sub-stage and the upper-level separating sub-stage. The rotational inertia matrices of the lower-level separated sub-stages and the upper-level separated sub-stages are given. F i Let be the thrust vector of cylinder i; and These are the pitch angle, yaw angle, and roll angle for the lower-level and upper-level separation sub-stages, respectively. G 1. G 2 represents the gravity of the lower and upper stage separation sub-stages in the ground coordinate system; F f This is the residual thrust of the lower stage engine; M i The thrust torque of cylinder i; F d1 , F d2 External interference; M d1 , M d2 External disturbance torque; Due to the constraints of the separation system, there are only three controllable degrees of freedom in actual separation: displacement along the rocket body axis, relative pitch angle, and relative yaw angle. Therefore, the six-degree-of-freedom model can be further simplified to a three-degree-of-freedom model, taking the motion state variables of the lower-level separation sub-stage and the upper-level separation sub-stage, respectively. , ,in, , The accelerations of the lower-level separating sub-stages and the upper-level separating sub-stages. , For the yaw angle acceleration of the lower stage separation substage and the upper stage separation substage, , For the pitch angle acceleration of the lower stage separation substage and the upper stage separation substage; Three-degree-of-freedom dynamic model of the separated sub-stage: (2) (3) In the formula, ; and This is part of the normal system. m 1. m 2 represents the mass of the lower-level separation sub-stage and the mass of the upper-level separation sub-stage. J y1 , J z1 , J y2 , J z2 These are the moments of inertia of the lower-level and upper-level separation sub-stages about the y-axis and z-axis, respectively. , This represents the uncertain part of the system. The quality uncertainty of separating lower-level sub-levels and higher-level sub-levels. The uncertainty in the rotational inertia of the lower-level separated sub-stage and the upper-level separated sub-stage is given. External interference to the system For cylinder separation force, R 1 represents the distance from the cylinder mounting position to the arrow body axis. B 1. B 2 represents the installation matrix; Selecting relative motion state variables ,in, , The axial velocities of the lower-level separation sub-stage and the upper-level separation sub-stage are given. , The yaw angular velocities of the lower stage separation substage and the upper stage separation substage are given. , To separate the pitch angular velocities of the lower-level and upper-level sub-stages, the system is converted into a state-space model: (4) in To control the efficiency matrix, For aggregated disturbances, Let be the system's relative velocity vector. Let be the system's relative motion acceleration vector. From equation (4), it can be seen that the input quantity... Dimension is greater than the relative motion state variables X With a dimension of 2, the system is a typical overdriven system; Because the relative rotation angle is small, the relative displacement of each cylinder is calculated using the following formula: (5) In the formula, x A , x B , x C , x D This represents the relative displacement of the four cylinders. x 21 To separate the axial relative displacement of the sub-stages, when the relative attitude angle of the separated sub-stages is very small, assume... ,in These are the relative yaw angle and relative pitch angle of the separation substage, respectively; Step 3: Construct a hierarchical controller based on control allocation, specifically constructing the control allocation layer within the hierarchical controller based on control allocation, as follows: Consider a dynamic control allocation scheme that minimizes both the energy consumption of the control variable and the rate of change of the control variable, and applies this scheme to the virtual control variable. Perform dynamic allocation: (17) In the formula, The weight matrix, T To control the cycle; The cylinder thrust to be allocated; Let J be the desired steady-state thrust of the cylinder; J is the objective function. st Indicates constraints; This is a virtual control variable; t For simulation time; Assuming a weight matrix and It is symmetrical, and = ( 2 + W 2 2 ) 1 / 2 If it is non-singular, then the cylinder thrust to be allocated... The following solutions are available: (18) in, , , To control the efficiency matrix, I It is the identity matrix; Step 4: Conduct synchronous separation simulation verification of the rocket stage separation system.

2. The interstage synchronous separation control method for a launch vehicle according to claim 1, characterized in that, The interstage separation system includes four or more cylinders and corresponding push rods. The cylinders are evenly distributed on the inner wall of the interstage section. The connection surface between the push rod and the upper stage is on the separation surface between the upper stage and the interstage section. The push rod separates the upper stage and the lower stage rocket body. Each cylinder's intake and exhaust are controlled by two high-speed switching valves, one for intake and one for exhaust. The pneumatic separation system includes a gas cylinder, a pressure reducing valve, a gas container, and pipelines, which provide high-pressure gas to the cylinder.

3. The interstage synchronous separation control method for a launch vehicle according to claim 1, characterized in that, The aerodynamics of the four-cylinder interstage separation system are established using a mathematical model, as detailed below: Establishing a pneumatic system dynamic model: Since the pressure in the intake chamber is much greater than the pressure in the exhaust chamber, and neglecting the frictional force of the cylinder, the pneumatic system dynamic model is as follows: (6) In the formula, p m Let be the gas pressure in the intake chamber of cylinder m. A m The effective working area of ​​cylinder m is... m m For the mass of the push rod, The output force of cylinder m. Let's consider the acceleration of the push rod relative to the cylinder. Since the mass of the push rod is relatively small compared to the mass of the arrow body, we can further simplify this: ; The relationship between the intake chamber pressure and the duty cycle signal of the high-speed switching valve can be obtained from the laws of thermodynamics: (7) (8) (9) In the formula, k The adiabatic coefficient of the gas. R The gas constant is T b For gas temperature, V 0 represents the sum of the volume of the pipeline from the gas cylinder to the intake chamber and the volume of the dead zone in the intake chamber. x m For cylinder displacement, For cylinder speed, This is the derivative of the pressure inside the cylinder. q m The mass flow rate of the gas entering the intake chamber. For the duty cycle signal of the high-speed switching valve, C d For flow coefficient, A e is the equivalent cross-sectional area of ​​the valve orifice of the switching valve. p um Due to upstream pressure, p dm For downstream pressure, This represents the gas flow rate.

4. The interstage synchronous separation control method for a launch vehicle according to claim 1, characterized in that, A virtual layer disturbance observer is constructed in a hierarchical controller based on control allocation, as follows: Take virtual control quantity The state-space model (4) can be transformed into: (10) in, , For lumped disturbances; Design a nonlinear disturbance observer. Based on formula (10), we can obtain: (11) In the formula Let be the observer gain matrix, and ; This is an estimate of the disturbance; The derivative of the disturbance estimate; Define the observation error of the total disturbance observer. for: (12) The error derivatives of the interference observations can be obtained from equations (10) to (12). for: (13)。 5. The interstage synchronous separation control method for a launch vehicle according to claim 4, characterized in that, The virtual layer controller in the hierarchical controller based on control allocation is constructed as follows: From equation (10), we define For tracking error, where Let be the target value instruction, and let be a second-order continuously differentiable instruction. X 1 is a vector relating to the system's relative displacement, relative yaw angle, and relative pitch angle; To represent a 3x1 matrix, select from equation (10) X 2 is the relative motion state variable, making The situation is trending towards a stable state. make Define the virtual control error as the expected value of the virtual control. ; The desired value of designing virtual control is : (14) In the formula, , is an adjustable gain matrix, and ; For virtual control error Z 2. Differentiate using the estimated value of the perturbation. Replace lumped disturbance Substituting equations (10) and (14) into the equations, we get: (15) in, The derivative of the virtual control error. K 1 represents the adjustable gain matrix; design Substituting equation (15) into the equation yields the virtual control law of the outer loop virtual control layer: (16) In the formula, , is an adjustable gain matrix, and ; The derivative for tracking the target; I It is an identity matrix.

6. The interstage synchronous separation control method for a launch vehicle according to claim 1, characterized in that, The actuator layer controller in a hierarchical controller based on control allocation is as follows: The control force command is converted into the target pressure of the cylinder intake chamber. Based on backstep control, let For the inner ring pressure tracking error, The gas pressure in the intake chamber of cylinder m: Let the Lyapunov function be: (19) From the dynamic equation of the intake chamber pressure, we can obtain: (20) In the formula, k The adiabatic coefficient of the gas. R The gas constant is T b For gas temperature, V 0 represents the sum of the volume of the pipeline from the gas cylinder to the intake chamber and the volume of the dead zone in the intake chamber. x m For cylinder displacement, A m The effective working area of ​​cylinder m is... q m The mass flow rate of the gas entering the intake chamber. for The derivative, For pressure tracking error The derivative, For cylinder speed, The derivative of the pressure tracking target; As can be seen from Lyapunov stability, when At that time, pressure tracking error Converging to 0; Design the gas mass flow rate of the inner loop actuator. Control Law: (21) In the formula, A m The effective working area of ​​cylinder m is... The gain is controlled by the inner loop controller.

7. The interstage synchronous separation control method for a launch vehicle according to claim 1, characterized in that, The design of the high-speed switching valve duty cycle signal in a hierarchical controller based on control allocation is as follows: Design the duty cycle of the PWM signal: When the gas mass flow rate of the inner ring actuator cylinder At this time, the inflation valve is open and the deflation valve is closed, with a duty cycle of: (22) In the formula, This refers to the duty cycle of the high-speed intake switching valve. The duty cycle of the high-speed exhaust switching valve. The effective throttling area of ​​the high-speed intake switching valve. p s The pressure after the pressure reducing valve. p m Let be the gas pressure in the intake chamber of cylinder m. T s For gas temperature, Here is the gas flow equation; when At this time, the inflation valve is closed and the deflation valve is open, with a duty cycle of: (23) In the formula, The effective throttling area of ​​the high-speed exhaust switching valve, p 0 represents atmospheric pressure. This is the gas flow equation.

8. The interstage synchronous separation control method for a launch vehicle according to claim 1, characterized in that, The simulation verification of synchronous separation of the rocket stage separation system is carried out as follows: Step 4-1: Perform dynamic modeling of the rocket separation system based on four cylinders, including dynamic modeling of the separation stage during the separation process and dynamic modeling of the high-speed switching valves and cylinders in the pneumatic system; Step 4-2: Model the synchronous separation control algorithm, including the virtual layer controller, dynamic control allocation solution, and actuator layer controller; Step 4-3: In order to compare the effect of synchronous separation control, the simulation results of open-loop and closed-loop control are compared respectively. To facilitate the verification of the controller effect, it is assumed that the pressure at the outlet of the pressure reducing valve remains unchanged during the simulation.

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