A composite helicopter stable flight control method

Abstract

The invention discloses a composite helicopter stable flight control method, which belongs to the technical field of calculation, extrapolation or counting. The invention establishes an incremental nonlinear dynamic inverse framework to decouple the nonlinear system, designs an incremental Lagrangian optimal allocation method to solve the control allocation problem, optimizes the global control efficiency by adjusting the incremental control input, and realizes the ideal control of various task requirements by selecting a suitable allocation matrix.

Description

Technical Field

[0001] The invention relates to a compound helicopter control technology, and in particular discloses a compound helicopter stable flight control method, belonging to the technical field of calculation, estimation or counting. Background Art

[0002] In recent years, compound helicopters have become a hot topic in military and civilian research at home and abroad. Compared with traditional helicopters, compound helicopters have advantages such as long range, large payload and wide speed range. However, since the research on compound helicopters is still in its infancy and the technology is not open to the public, there are few publicly reported research results in this area at home and abroad.

[0003] There is mode switching during the flight of a compound helicopter. It mainly uses the helicopter mode when hovering and flying at low speed, and mainly uses the fixed-wing aircraft mode when flying at high speed. The complex and changeable working modes bring great difficulty to the design of the control system of the compound helicopter, and finding a suitable control allocation strategy plays a vital role in achieving full-mode flight. Considering the different working capabilities of each control surface in the entire flight envelope, designing the control allocation strategy of the compound helicopter, effectively dealing with the control surface control limitation and cross-coupling problems, and reducing the difficulty of designing the flight control system are the key issues that need to be solved in the control of the compound helicopter.

[0004] At present, the control allocation problem of aircraft flight process at home and abroad mostly adopts conventional control allocation strategy. When designing the optimal performance index, it is often only possible to design the control input u to make the global optimal. When facing complex control objects and dealing with complex constraints, the control performance is significantly reduced. If it is not improved, the engineering feasibility is poor. Therefore, for compound helicopters, it is very important to design a distribution matrix that meets various tasks according to the conditions, and to develop a global optimal input for each control surface according to the time-varying working ability of each control surface in multi-modal maneuvers. The present invention aims to propose a new incremental allocation method and design the u+Δu global optimal control input, and update the optimal control law by optimizing the increment Δu. Summary of the invention

[0005] The purpose of the present invention is to provide a method for smooth flight control of a compound helicopter in view of the shortcomings of the above-mentioned background technology. The control allocation problem is solved by an incremental Lagrangian optimal allocation method. The method takes into account the different working capabilities of each control surface in the entire flight envelope, expands the traditional optimal control allocation method on the basis of Lagrangian multiplier optimization, optimizes the global control efficiency by adjusting the incremental control input, and realizes ideal control for various task requirements by selecting a suitable allocation matrix. The control limitation, cross-strong coupling and nonlinear characteristics of the control surfaces of the compound helicopter are effectively handled, the technical problem of control redundancy is solved, and the control efficiency of the control surface is improved.

[0006] The present invention adopts the following technical solutions to achieve the above-mentioned invention object:

[0007] A composite helicopter flight control allocation strategy specifically includes the following six steps.

[0008] Step 1: Establish a nonlinear dynamic model of a compound helicopter. For the convenience of calculation, the nonlinear dynamic model of a compound helicopter can be represented by two subsystems:

[0009]

[0010]

[0011] In formula (1) and formula (2), x 1 is the state vector of the nonlinear dynamic system that changes relatively slowly, x 2 is the state vector of the nonlinear dynamic system that changes relatively quickly, x 1 =[u,v,w],x 2 =[p,q,r], (u,v,w) represents the three velocity components in the body coordinate axis system, and (p,q,r) represents the three angular velocity components in the body coordinate axis system. Represents the state vector x of the nonlinear dynamic system 1 ,x 2 The derivative of 1 ,u 2 represents the input signal of the nonlinear dynamic system, f(.), g(.) represent the system function of the nonlinear dynamic system, f 1 (.) is the state function of the speed outer loop, g 1 (.) is the control function of the speed outer loop, f 2 (.) is the state function of the attitude inner loop, g 2 (.) is the control function of the attitude inner loop.

[0012] Step 2: Use sequential quadratic programming (SQP) to optimize the trim of the flight state from hovering to 360 km / h, and obtain the optimal change of control surface deflection under different flight modes. Under the constraint of ensuring force and torque balance, the objective function of trim optimization is designed as J = u T Hu, where u represents the control input and H represents the optimization matrix.

[0013] Step 3: The composite helicopter control system calculates and outputs the virtual control command of the control surface according to the flight control law. The virtual control command of the control surface is the desired control command vector x of the speed outer loop. 1c 、Expected control command x in attitude inner loop 2c , x 1c Including forward speed u c , lifting speed v c , yaw speed w c , x 2c Including the pitch angle θ c , yaw angle and roll angle φ c .

[0014] Step 4: According to the virtual control instruction u c , v c , w c ,θ c , φ c , the incremental Lagrangian optimal allocation method is used to calculate the control signals of the rudder surface allocated by the composite helicopter control system. The control signals of the rudder surface include: lateral periodic pitch A 1s 、Longitudinal periodic pitch variation B 1s , rotor collective pitch Right flap aileron deflection angle θ wr 、Left flap aileron deflection angle θ wl , thrust vector T, angle θ between the thrust vector and the XOY plane in the body coordinate system 1 , the angle θ between the projection of the thrust vector on the horizontal plane of the aircraft coordinate system and the X-axis 2 According to the obtained control signal of the rudder, the control function g of the nonlinear dynamic system is 1 (.), g 2 (.), and then update x 1 、x 2 .

[0015] Step 5, sending the control surface control signal calculated in step 4 to the actuator, which controls the aerodynamic control surface δ of the compound helicopter 1 =[A 1s B 1s θ wr θ wl θ 1 θ2 ]、Throttle opening Realize the control of the flight process of the compound helicopter.

[0016] Step 6: Real-time detection of the position X, Y, Z, speed u, v, w, and attitude angle of the compound helicopter θ, ψ and attitude angular velocities p, q, r, repeat steps 1 to 5.

[0017] Furthermore, in step 3 of a composite helicopter flight control allocation strategy, the flight control law design of the composite helicopter control system includes the following five steps:

[0018] Step 3.1: The desired control command vector x of the speed outer loop 1c =[u c ,v c ,w c ] or the attitude inner loop desired control command vector x 2c =[φ c ,θ c ,ψ c ]Through the command filter module, the command filter module limits the amplitude and frequency of the input quantity to obtain the first-order derivative and second-order derivative of the desired control command; among them, the first-order derivative of the desired control command of the speed outer loop is The second-order derivative of the expected control command in the attitude inner loop is The second-order filter T used by the instruction filtering module is:

[0019]

[0020] In formula (3), the natural frequency w is selected n =3, damping ratio ζ=0.7.

[0021] Step 3.2, according to the first-order derivative of the desired control command of the speed outer loop, the second-order derivative of the desired control command of the attitude inner loop and the flight state of the compound helicopter, the system control law is designed by the incremental dynamic inverse control method. Due to the coupling and change of some uncertain aerodynamic models, it is difficult to obtain the system parameters of the non-affine nonlinear dynamic model through measurement and theoretical calculation. The non-affine nonlinear dynamic model of the compound helicopter shown in equations (1) and (2) is converted into a nominal model for approximating the compound helicopter dynamic model:

[0022]

[0023]

[0024] In formula (4) and formula (5), the superscript ∧ represents the nominal model. represents the nonlinear dynamics model and the nominal model observation x1 The error, represents the nonlinear dynamics model and the nominal model observation x 2 of error.

[0025] Step 3.3: In order to obtain the incremental form of the composite helicopter dynamics model, replace At each sampling interval, the Taylor series is expanded to:

[0026]

[0027] In formula (6), the superscript 0 represents each sampling interval, the symbol Δ represents the increment of the variable relative to its current value, and R 1 ′(Δx 1 ,Δx 2 ,Δu 1 ) is the higher-order remainder of the Taylor series expansion. By introducing the acceleration feedback from the tracking differentiator, represents the speed outer loop control function g 1 (.) in x 1 、x 2 、u 1 The gradient operator in the direction of change, equation (6) can be written as:

[0028]

[0029] Step 3.4: Ignore the system state change x 1 ,x 2 The change in a short period of time, formula (7) is written as:

[0030]

[0031] In formula (8), represents the speed outer loop control function g 1 (.) In the speed virtual control instruction u 1 Gradient in the direction of change, Δ 1 represents the incremental model error, R 1 represents the incremental high-order disturbance term.

[0032] Based on equation (8), the incremental dynamic inverse control law of the speed outer loop is designed using the dynamic inverse control law in each given sampling interval as follows:

[0033]

[0034]

[0035] In formula (9), represents the derivative of the desired control command state vector of the speed outer loop, which is obtained according to the reference model designed according to the performance index requirements; v L1 It means that the speed outer loop incremental dynamic inverse control system is compensated to a pseudo-linear control signal with a linear transfer relationship and complete decoupling; u 1 0 It is the sampling signal of speed virtual control instruction.

[0036] Step 3.5: Same as steps 3.2, 3.3, and 3.4. The incremental dynamic inverse control law of the attitude inner loop is:

[0037]

[0038] u 2 =u 2 0 +Δu 2 (10)

[0039] In formula (10), represents the derivative of the desired control command state vector of the attitude inner loop, which is obtained according to the reference model designed according to the performance index requirements; v L2 It means that the incremental dynamic inverse control system of the attitude inner loop is compensated to a pseudo-linear control signal with a linear transfer relationship and complete decoupling; u 2 0 It is the sampling signal of the angular velocity virtual control instruction.

[0040] Furthermore, an incremental Lagrangian optimal allocation method involved in step 4 of a composite helicopter flight control allocation strategy specifically includes the following three steps:

[0041] Step 4.1: In order to obtain the optimal pseudo-inverse control in equation (9), let the performance index The constraints are To design the actual control input. 1 It represents the first-order derivative of the control input, i.e. the desired control command of the speed outer loop, Γ 1 represents the allocation matrix, represents the speed outer loop control function g in the nominal model 1 (.) In the speed virtual control instruction u 1 0 The total differential at represents the desired control command vector x of the speed outer loop 1c The state vector x is relatively slow to change with nonlinear dynamics. 1 The differential of the error, v L1 Represents the pseudo-linear control signal of the speed outer loop.

[0042] Step 4.2, using the Lagrange multiplier method, define a Lagrange function:

[0043]

[0044] In formula (11), μ 1 is the given Lagrange multiplier.

[0045]

[0046] Substituting equation (12) into the constraint conditions, we get:

[0047]

[0048] From formula (12), we can know Substituting equation (13) into equation (12), the optimal control law can be expressed as:

[0049]

[0050] In formula (14), k represents the control time series.

[0051] Step 4.3 is the same as steps 4.1 and 4.2. The optimal control law of the attitude inner loop can be expressed as:

[0052]

[0053] In formula (15), k represents the control time series.

[0054] The present invention adopts the above technical solution and has the following beneficial effects:

[0055] (1) Aiming at the control redundancy problem of a compound helicopter, the present invention proposes a Lagrangian optimal control allocation strategy based on an incremental dynamic inverse model. The incremental dynamic inverse model is introduced into the control allocation rate. The change of the control input is accurately described by describing the gradient change of the control function of the nonlinear dynamic system of the compound helicopter in the direction of the input quantity. The constraint conditions of the performance index to be optimized are determined according to the control allocation rate. The Lagrangian operator is introduced to balance the optimization problem of the performance index to be optimized, so that the control efficiency of the compound helicopter is high during the flight, the flight state is stable, and the control algorithm of the aircraft is easy to design.

[0056] (2) The present invention takes into account the different working capabilities of each control surface within the entire flight envelope. On the basis of Lagrange multiplier optimization, the traditional optimal control allocation method is expanded to optimize the global control efficiency by adjusting the incremental control input. By selecting the allocation matrix that meets the performance indicators, ideal control for various mission requirements can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1Assign a block diagram for compound helicopter control.

[0058] Figure 2 Flowchart for trimming a compound helicopter.

[0059] Figure 3 to Figure 4 are the trim values ​​of the control surfaces in the two flight modes.

[0060] Figure 5 is the lateral cyclic pitch variation A of the compound helicopter 1s 、Longitudinal periodic pitch variation B 1s , rotor collective pitch Graph of relationship with time.

[0061] Figure 6 is the right flap aileron deflection angle θ of the compound helicopter wr 、Left flap aileron deflection angle θ wl Graph of relationship with time.

[0062] Figure 7 is the angle θ between the thrust vector of the compound helicopter and the XOY plane in the body coordinate system 1 , the angle θ between the projection of the thrust vector on the horizontal plane of the aircraft coordinate system and the X-axis 2 Graph of relationship with time.

[0063] Figure 8 This is a graph showing the relationship between the thrust vector T and time for a compound helicopter.

[0064] Symbols in the figure: deg-degree (angle unit), t-time, s-second (time unit); m-meter (length unit). DETAILED DESCRIPTION

[0065] To facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings.

[0066] The composite helicopter flight control method disclosed by the present invention adopts Figure 1 The composite helicopter control allocation block diagram shown is implemented, specifically including the following 6 steps.

[0067] Step 1: Establish a nonlinear dynamic model of a compound helicopter. For the convenience of calculation, the nonlinear dynamic model of a compound helicopter can be represented by two subsystems:

[0068]

[0069]

[0070] In formula (1) and formula (2), x 1 =[u,v,w],x 2=[p,q,r], (u,v,w) represents the three velocity components in the body coordinate axis system, (p,q,r) represents the three angular velocity components in the body coordinate axis system. 1 ,x 2 represents the state vector of the nonlinear dynamic system, u 1 ,u 2 represents the input signal of the system, f(.), g(.) represent the system functions of the nonlinear dynamic system.

[0071] Step 2: Use sequential quadratic programming (SQP) to optimize the trim of the flight state from hovering to 360 km / h, and obtain the optimal change of control surface deflection under different flight modes. Under the constraint of ensuring force and torque balance, the objective function of trim optimization is designed as J = u T Hu, where u represents the control input and H represents the optimization matrix. The balancing result is as follows Figure 3 and Figure 4 As shown, Figure 3 and Figure 4 The trim values ​​of the control surfaces are shown for the two flight modes defined according to the aircraft's flight speed.

[0072] Step 3: The composite helicopter control system calculates and outputs the virtual control instructions of the control surface according to the flight control law, including the forward flight speed u c , lifting speed v c , yaw speed w c , pitch angle θ c , yaw angle and roll angle φ c ;The flight control law design of the composite helicopter control system includes the following five steps.

[0073] Step 3.1: The desired control command vector x of the speed outer loop 1c =[u c ,v c ,w c ] or the attitude inner loop desired control command vector x 2c =[φ c ,θ c ,ψ c ]Through the command filter module, the command filter module limits the amplitude and frequency of the input quantity to obtain the first-order derivative and second-order derivative of the desired control command; among them, the first-order derivative of the desired control command of the speed outer loop is The second-order derivative of the expected control command in the attitude inner loop is The second-order filter T used by the instruction filtering module is:

[0074]

[0075] In formula (3), the natural frequency w is selected n =3, damping ratio ζ=0.7.

[0076] Step 3.2, according to the first-order derivative of the desired control command of the speed outer loop, the second-order derivative of the desired control command of the attitude inner loop and the flight state of the high-speed helicopter, the system control law is designed by the incremental dynamic inverse control method. Due to the coupling and changes of some uncertain aerodynamic models, it is difficult to obtain system parameters through measurement and theoretical calculation. The actual model of the non-affine nonlinear dynamic system of the high-speed helicopter shown in equations (1) and (2) is converted into a nominal model for approximating the high-speed helicopter dynamic model:

[0077]

[0078]

[0079] In formula (4) and formula (5), the superscript ∧ represents the nominal model. represents the nonlinear dynamics model and the nominal model observation x 1 The error, represents the nonlinear dynamics model and the nominal model observation x 2 of error.

[0080] Step 3.3: In order to obtain the incremental form of the high-speed helicopter dynamics model, replace At each sampling interval, the Taylor series is expanded to:

[0081]

[0082] In formula (6), the superscript 0 represents each sampling interval, the symbol Δ represents the increment of the variable relative to its current value, and R 1 ′(Δx 1 ,Δx 2 ,Δu 1 ) is the higher-order remainder of the Taylor series expansion. By introducing the acceleration feedback from the tracking differentiator, represents the speed outer loop control function g 1 (.) in x 1 、x 2 、u 1 The gradient operator in the direction of change, equation (6) can be written as:

[0083]

[0084] Step 3.4: Ignore the system state change x 1 ,x 2 The change in a short period of time, formula (7) is written as:

[0085]

[0086] In formula (8), represents the speed outer loop control function g 1 (.) In the speed virtual control instruction u 1 Gradient in the direction of change, Δ 1 represents the incremental model error, R 1 represents the incremental high-order disturbance term.

[0087] Based on equation (8), the incremental dynamic inverse control law of the speed outer loop is designed using the dynamic inverse control law in each given sampling interval as follows:

[0088]

[0089]

[0090] In formula (9), represents the derivative of the desired control command state vector of the speed outer loop, which is obtained according to the reference model designed according to the performance index requirements; v L1 It means that the speed outer loop incremental dynamic inverse control system is compensated to a pseudo-linear control signal with a linear transfer relationship and complete decoupling; u 1 0 It is the sampling signal of speed virtual control instruction.

[0091] Step 3.5: Same as steps 3.2, 3.3, and 3.4. The incremental dynamic inverse control law of the attitude inner loop is:

[0092]

[0093] u 2 =u 2 0 +Δu 2 (10)

[0094] In formula (10), It represents the derivative of the desired control command state vector of the attitude inner loop, which is obtained according to the reference model designed according to the performance index requirements. L2 It means that the incremental dynamic inverse control system of the attitude velocity outer loop is compensated to a pseudo-linear control signal with a linear transfer relationship and complete decoupling; u 2 0 It is the sampling signal of the angular velocity virtual control instruction.

[0095] Step 4: According to the virtual control instruction u c , v c , w c ,θ c , φ c, the incremental Lagrangian optimal allocation method is used to calculate the control signals of the rudder surface allocated by the composite helicopter control system. The control signals of the rudder surface include: lateral periodic pitch A 1s 、Longitudinal periodic pitch variation B 1s , rotor collective pitch Right flap aileron deflection angle θ wr 、Left flap aileron deflection angle θ wl , thrust vector T, angle θ between the thrust vector and the XOY plane in the body coordinate system 1 , the angle θ between the projection of the thrust vector and the horizontal plane of the aircraft coordinate system and the X-axis 2 ,like Figure 2 As shown, it includes the following 3 steps.

[0096] Step 4.1: In order to obtain the optimal pseudo-inverse control in equation (3), let the performance index The constraints are To design the actual control input. 1 It represents the first-order derivative of the control input, i.e. the desired control command of the speed outer loop, Γ 1 represents the allocation matrix, represents the speed outer loop control function g in the nominal model 1 (.) In the speed virtual control instruction u 1 0 The total differential at represents the desired control command vector x of the speed outer loop 1c The state vector x is relatively slow to change with nonlinear dynamics. 1 The differential of the error, v L1 Represents the pseudo-linear control signal of the speed outer loop.

[0097] Step 4.2, using the Lagrange multiplier method, define a Lagrange function:

[0098]

[0099] In formula (11), μ 1 is the given Lagrange multiplier.

[0100]

[0101] Substituting equation (12) into the constraint conditions, we get:

[0102]

[0103] From formula (12), we can know Substituting equation (13) into equation (12), the optimal control law can be expressed as:

[0104]

[0105] In formula (14), k represents the control time series.

[0106] Step 4.3, same as steps 4.1 and 4.2, the optimal control law of the attitude inner loop control system can be expressed as:

[0107] In formula (15), k represents the control time series.

[0108] Step 5, sending the control surface control signal calculated in step 4 to the actuator, which controls the aerodynamic control surface δ of the compound helicopter 1 =[A 1s B 1s θ wr θ wl θ 1 θ 2 ]、Throttle opening Realize the control of the flight process of compound helicopter;

[0109] Step 6: Real-time detection of the position X, Y, Z, speed u, v, w, and attitude angle of the compound helicopter θ, ψ and attitude angular velocities p, q, r, repeat steps 1 to 6.

[0110] Figures 5 to 8 The figure shows the flight simulation results of a compound helicopter. The simulation process is carried out in MATLAB, and the actual control variable change curve of each control surface of the compound helicopter is shown. Figures 5 to 8 It can be seen that the control law proposed by the present invention ensures that the multiple redundant control surfaces of the compound helicopter can efficiently complete the maneuvering task during the entire maneuvering process, and ensures the smoothness of the mode conversion. The helicopter control surface mainly works during low-speed flight and maintains the minimum mode during high-speed flight. On the contrary, in high-speed flight, the fixed-wing control surface plays an important role.

Claims

1. A composite helicopter stable flight control method, It is characterized in that A nonlinear dynamic model of a composite helicopter related to a system control function and an actual control signal of a control surface is established, wherein the nonlinear dynamic model includes a velocity outer loop subsystem and an attitude inner loop subsystem, and the nonlinear dynamic model updates a state vector of the nonlinear dynamic system according to the real-time system control function, an input signal of the non-affine nonlinear dynamic system and the real-time flight state of the composite helicopter; According to the desired control command of the speed outer loop, the control allocation efficiency matrix of the speed outer loop subsystem is calculated by using the incremental Lagrangian optimal allocation algorithm; According to the desired control instructions of the attitude inner loop, the control allocation efficiency matrix of the attitude inner loop subsystem is calculated by using the incremental Lagrangian optimal allocation algorithm; The actual control signals of the control surfaces corresponding to the optimal control law of the speed outer loop and the optimal control distribution law of the attitude inner loop are transmitted to the actuator, the system control function is updated in real time and the real-time flight status data of the compound helicopter is collected; wherein, In the composite helicopter nonlinear dynamics model, the velocity outer loop subsystem is The attitude inner loop subsystem is Among them, x 1 is the state vector of the nonlinear dynamic system that changes relatively slowly, x 2 is the state vector of the nonlinear dynamic system that changes relatively quickly, x 1 =[u,v,w], u,v,w are the three velocity components in the body coordinate system, x 2 =[p,q,r], p,q,r are the three angular velocity components in the body coordinate system, is the state vector x of the nonlinear dynamic system 1 ,x 2 The derivative of 1 is the speed virtual control instruction, u 2 is the angular velocity virtual control instruction, f 1 (.) is the state function of the speed outer loop, g 1 (.) is the control function of the speed outer loop, f 2 (.) is the state function of the attitude inner loop, g 2 (.) is the control function of the attitude inner loop; The specific method of using the incremental Lagrangian optimal allocation algorithm to calculate the control allocation efficiency matrix of the speed outer loop subsystem is as follows: introducing an incremental dynamic inverse model of the speed virtual control instruction into the control allocation law of the speed outer loop, determining the constraint conditions of the performance index to be optimized according to the incremental dynamic inverse model of the speed virtual control instruction, introducing Lagrangian multipliers into the optimization problem determined by the performance index to be optimized and the constraint conditions, and performing sequential quadratic programming on the optimization problem after the introduction of Lagrangian multipliers to obtain a balancing result; After introducing the incremental dynamic inverse model of the speed virtual control instruction, the control distribution law of the speed outer loop is: u 1 =u 1 0 +Δu 1 , where u 1 0 is the speed virtual control instruction u 1 The sampling signal at the initial time, Δu 1 for u 1 The increment of is the speed outer loop control function g 1 (.) in u 1 The gradient in the direction of change, is the desired control command state vector of the speed outer loop [u c ,v c ,w c ], u c is the forward flight speed, v c is the lifting speed, w c is the yaw speed, v L1 is the first pseudo linear control signal, It is the derivative of the relatively slow-changing state vector of the nonlinear dynamic system; The constraint conditions of the performance index to be optimized determined by the incremental dynamic inverse model of the speed virtual control instruction are: The performance index J to be optimized is J=u 1 Γ 1 -1 u 1 ,in, is the speed outer loop control function g in the nominal model 1 (.) In the speed virtual control instruction u 1 0 The total differential at is the desired control command vector x of the speed outer loop 1c The state vector x is relatively slow to change with nonlinear dynamics. 1 The differential of the error, Γ 1 Assign efficiency matrix to the control of speed outer loop subsystem; The specific method of performing sequential quadratic programming on the optimization problem after the introduction of Lagrange multipliers to obtain the balancing result is: according to the Lagrangian function established after the introduction of Lagrangian multipliers, let the Lagrangian function be about Δu 1 The partial derivative of is zero to obtain Δu 1 ; The obtained Δu 1 Substitute the constraints to obtain the Lagrange multiplier, and then perform sequential quadratic programming according to the control allocation law of the speed outer loop to obtain the optimal control law of the speed outer loop: u 1 k 、u 1 k+1 is the sampling signal of the speed virtual control command at time k and time k+1, is the speed outer loop control function g in the nominal model 1 (.) In the speed virtual control instruction u 1 k The total differential at ; The specific method of calculating the control allocation efficiency matrix of the attitude inner loop subsystem using the incremental Lagrangian optimal allocation algorithm is the same as that of calculating the control allocation efficiency matrix of the speed outer loop subsystem. The optimal control law of the attitude inner loop is: Among them, u 2 k 、u 2 k +1 is the sampling signal of the angular velocity virtual control command at time k and time k+1, Γ 2 Assign the efficiency matrix to the control of the attitude inner loop subsystem, is the attitude inner loop control function g in the nominal model 2 (.) In the angular velocity virtual control instruction u 2 k The total differential at is the expected control command x in the attitude inner loop 2c With nonlinear dynamics the state vector x changes relatively fast 2 The differential of the error.

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