Adaptive rudder distribution method for hypersonic flight vehicle

Abstract

The invention discloses a self-adaptive rudder allocation method for a hypersonic aircraft. The method comprises the following steps: firstly, comprehensively analyzing physical attributes from a channel rudder to single rudders, and combining information such as amplitude limit, speed limit, weight and allocation matrix of each single rudder; secondly, a self-adaptive rudder distribution problem is converted into a quadratic programming problem; and finally, realizing hot start through a pseudo-inverse matrix, converting a quadratic programming problem into an unconstrained programming problem by combining an effective set method, and performing rapid iterative calculation to obtain the optimal rudder distribution of the channel rudder. The method has a very wide military application prospect, and the rudder deflection angle is reasonably utilized in a feasible range.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft, and in particular relates to an adaptive rudder allocation method for a hypersonic aircraft. Background Art

[0002] With the development of modern warfare, the demand for the control performance of hypersonic aircraft is getting higher and higher. If hypersonic aircraft can give full play to the advantages of rudder deflection angle under limited rudder resources and maximize the overload capacity, it will greatly improve the maneuverability and stability of the missile. In extreme cases, by making full use of the rudder resources, the efficient effect of the rudder deflection angle can also be maximized.

[0003] In domestic and foreign research, in order to ensure the rapid allocation of channel rudders within a control cycle, the orthogonal decomposition method is usually used. First, the channel rudder is allocated to each channel in advance, and then the channel rudder is allocated to the single-chip rudder by orthogonal decomposition. Although this allocation can efficiently calculate the rudder allocation and ensure that the allocation calculation is completed within a control cycle, it does not give full play to the advantages of the rudder deflection angle, resulting in a waste of rudder resources. Although some studies have proposed that the use of optimization methods can maximize the use of rudder resources, this type of method is difficult to complete the high-speed solution of optimized allocation within a control cycle, and has no practical engineering application value. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a method for adaptive rudder allocation for hypersonic aircraft. First, the physical properties of the channel rudder to the monolithic rudder are comprehensively analyzed, combined with the information such as the amplitude limit, speed limit, weight, and allocation matrix of each monolithic rudder; secondly, the adaptive rudder allocation problem is converted into a quadratic programming problem; finally, the hot start is realized through the pseudo-inverse matrix, and the quadratic programming problem is converted into an unconstrained programming problem by combining the effective set method to quickly iterate and calculate the optimal rudder allocation of the channel rudder. This method has a very broad prospect for military application, and the reasonable use of the time-limited rudder deflection angle within the feasible range.

[0005] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0006] Step 1: Set the channel rudder to single-chip rudder allocation method;

[0007] Assume that the hypersonic vehicle has m single-piece rudders and the arbitrary rudder deflection angle is , different subscripts represent different single-piece rudders, and the rudder deflection angle is uniformly expressed as ;

[0008] Assume that each rudder deflection angle has upper and lower bounds due to the limitation of the limit mechanism, hinge torque, rudder surface normal force, and rudder deflection angle velocity limit factors, which can be expressed as: ,in The rudder angle limit mechanism, rudder angle speed, maximum normal phase overload and maximum hinge moment are used to jointly limit the intersection;

[0009] set up They are roll channel, yaw channel, and pitch channel. The moment coefficients of the three channels are Expressed as angle of attack , Sideslip Angle ,Mach number , rudder deflection angle Related functions or tables; The moment coefficients of the three channels are linearized at zero rudder deviation using the frozen coefficient method to obtain the distribution matrix :

[0010] (1)

[0011] Therefore, the control allocation problem is to solve the following equation (2):

[0012] (2)

[0013] in Synthetic three-axis channel rudder ;

[0014] Step 2: Establish the rudder allocation optimization problem;

[0015] Assume the desired rudder deflection angle is: , then the rudder allocation index function is selected as:

[0016] (3)

[0017] Set the allocation weight matrix Adjust the priority of each channel and rewrite the indicator function as follows:

[0018] (4)

[0019] Among them, the allocation weight matrix is a diagonal matrix. Each eigenvalue describes the weight priority of the channel rudder. The channel with high priority has a large weight. Therefore, the rudder allocation problem is expressed as the following quadratic programming problem:

[0020] (5)

[0021] in , ;

[0022] Step 3: Fast calculation of rudder allocation optimization problem;

[0023] The quadratic programming problem expressed in formula (5) has the following limitations:

[0024] 1) The matrix is ​​positive semidefinite;

[0025] 2) The size of the matrix is ;

[0026] 3) No equality constraints;

[0027] 4) Only the independent variable has an inequality constraint, and the inequality constraint is only triggered when the rudder is fully steered or reaches the limit value;

[0028] Compute the quadratic programming problem through different branches:

[0029] 1) Unconstrained optimization problem;

[0030] (6)

[0031] set up , that is, the matrix Perform singular value decomposition, where is a diagonal matrix, are 3×3 unitary matrices in singular value decomposition, and the rudder deflection angle is expressed as:

[0032] (7)

[0033] 2) Solution when the rudder deflection is limited;

[0034] Direct limiting of the limited control variable:

[0035] (8)

[0036] Record the number of the servos that are limited.

[0037] (9)

[0038] Define the unrestricted Hessian matrix ,gradient and rudder deviation ;

[0039] (10)

[0040] in, express The element in the i-th row and i-th column of the matrix, Representation vector The i-th element of Representation vector The i-th element of ;

[0041] The rudder angle correction value that does not trigger the limit is for:

[0042] (11)

[0043] The new limited rudder deflection angle is iteratively calculated as follows until stop;

[0044] (12)

[0045] in is the step size of gradient descent, determined by the Armijo criterion; is the preset calculation accuracy, , Respectively represent the kth and k+1th rudder deviations The result of the iterative calculation.

[0046] Preferably, the The optimal value is 4 and the maximum is 8.

[0047] The beneficial effects of the present invention are as follows:

[0048] The rudder deflection angle designed by the invention can provide a larger synthetic rudder deflection angle when the channels are coupled. The method has a very broad military application prospect and can reasonably utilize the rudder deflection angle within a feasible range.

[0049] Compared with the traditional orthogonal decomposition rudder allocation method, the method proposed in the present invention uses a special quadratic programming solution to quickly solve the rudder allocation problem, which can not only maximize the rudder control capability, but also complete the solution within one control cycle. The present invention considers hard constraints such as the hinge torque and limit mechanism of the single-piece rudder, and also considers the speed limit constraint of the rudder deflection angle, converts the optimal allocation problem into a special type of quadratic programming problem, and uses pseudo-inverse and effective set methods to efficiently solve it. It can be calculated as efficiently as the orthogonal decomposition method, and can also achieve optimal rudder allocation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The figure is a flow chart of the calculation of the method of the present invention.

[0051] Figure 2 Schematic diagram of torque accessible space according to an embodiment of the present invention.

[0052] Figure 3 Schematic diagram of the comparison of computational efficiency of common algorithms in embodiments of the present invention.

[0053] Figure 4 Schematic diagram of the synthetic channel rudder curve in the first 20 seconds of a typical trajectory according to an embodiment of the present invention.

[0054] Figure 5Schematic diagram of the single-piece rudder distribution curve in the first 20 seconds of a typical trajectory according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0056] In order to solve the problem of fast optimal allocation of existing hypersonic aircraft rudder deflection angle limitation and speed limitation, the present invention provides a hypersonic aircraft adaptive rudder allocation method, which fully utilizes the performance of a single-chip rudder to synthesize a desired channel rudder and maximizes the use of the missile's control performance. The calculation process can be completed within one control cycle.

[0057] The method of the invention can achieve the maximum efficiency allocation of the control rudder deflection under the condition of limited amplitude and speed. Through in-depth analysis of the relationship between the channel rudder and the monolithic rudder of the hypersonic aircraft, the pseudo-inverse hot start combined with the effective set method is innovatively proposed to achieve the maximum approximation of the monolithic rudder to the channel rudder under the condition of limited amplitude and speed, so as to achieve the purpose of maximizing the use of rudder resources.

[0058] A hypersonic vehicle adaptive rudder allocation method, the specific steps are described as follows:

[0059] Step 1: Set the channel rudder to single-chip rudder allocation method;

[0060] Assume that the hypersonic vehicle has m rudders and the arbitrary rudder deflection angle is , different subscripts represent different single-piece rudders, and the rudder deflection angle is uniformly expressed as Assume that each rudder deflection angle has upper and lower bounds due to the limitation of the limit mechanism, hinge torque, rudder surface normal force, rudder deflection angle velocity limit and other factors, which are expressed as: ,in The rudder angle limit mechanism, rudder angle speed, maximum normal phase overload, and maximum hinge torque are used to jointly limit the intersection. Three-channel (roll, yaw, pitch) moment coefficients , usually expressed as the angle of attack , Sideslip Angle ,Mach number , rudder deflection angle The frozen coefficient method is used to linearize the three-axis moment coefficients at zero rudder deviation to obtain the distribution matrix :

[0061] (1)

[0062] Therefore, the control allocation problem is to solve the following equation (2):

[0063] (2)

[0064] in Synthetic three-axis channel rudder .

[0065] Step 2: Establish the rudder allocation optimization problem;

[0066] In order to maximize the use of a single-piece rudder to synthesize a channel rudder, the desired rudder deflection angle is assumed to be: . Then the rudder allocation index function is selected as:

[0067] (3)

[0068] The indicator Describes the L2 norm of the difference between the assigned channel rudder and the expected channel rudder. Its physical meaning is that the synthesized rudder angle is close to the expected rudder angle. When this indicator is zero, the expected channel rudder can be accurately achieved. Depending on the actual task, the priority of the rudder angle of each channel can be different, and the allocation weight coefficient can be set. Adjust the priority of each channel and rewrite the indicator function as follows:

[0069] (4)

[0070] Assigned weight matrix It is usually selected as a diagonal matrix, and each eigenvalue describes the weight priority of the channel rudder, and the channel with a high priority has a large weight. Therefore, the rudder allocation problem can be expressed as the following quadratic programming problem:

[0071] (5)

[0072] in , .

[0073] Step 3: Rapid calculation of rudder allocation optimization problem;

[0074] The quadratic programming problem expressed in the optimization problem (5) has the following special features:

[0075] 1) Among them The matrix is ​​positive semidefinite;

[0076] 2) The size of the matrix is ;

[0077] 3) There are no equality constraints in the optimization;

[0078] 4) Only the independent variable has an inequality constraint, and the probability of triggering the inequality constraint is not high (it is only triggered when the rudder is fully turned or the limit value is reached).

[0079] Based on the above particularities, the optimization process can be accelerated to complete the optimization calculation of rudder allocation within one control cycle. Therefore, the calculation is performed through different branches:

[0080] 1) Unconstrained optimization problem;

[0081] (6)

[0082] Since the servo will not reach the limit in most flight situations, this optimization problem is an unconstrained optimization problem in most cases. , that is, the matrix Perform singular value decomposition, where is a diagonal matrix, the rudder deflection angle can be directly expressed as:

[0083] (7)

[0084] 2) Solution when the rudder deflection is limited;

[0085] The initial solution given by the above formula has a certain probability of triggering the rudder angle constraint . Direct limiting of the limited control variable:

[0086] (8)

[0087] Record the number of the servos that are limited.

[0088] (9)

[0089] Assume the unrestricted Hessian matrix ,gradient and rudder deviation :

[0090] (10)

[0091] The rudder angle correction value that does not trigger the limit is for:

[0092] (11)

[0093] The new limited rudder deflection angle is iteratively calculated as follows until stop.

[0094] (12)

[0095] in is the step size of gradient descent, determined by the Armijo criterion; is the preset calculation accuracy. The final solution of the rudder deflection angle usually only needs 1~2 iterations to meet the requirements, so the calculation complexity of the algorithm is only ,in Iteration coefficient. For missiles Usually 4 is used, and the maximum is 8 (with additional ailerons), so the computational complexity fully meets the requirement of completing the rudder allocation within one control cycle. In summary, the solution process of the rudder allocation problem is as follows Figure 1 shown.

[0096] Example:

[0097] In order to verify the effectiveness of the algorithm, the present invention is further described in combination with a hypersonic aircraft rudder allocation example. Assume that the hypersonic aircraft is an axisymmetric missile, and is controlled by four fork-shaped air rudders, with an air rudder limit of 28° and a speed limit of 100° / s.

[0098] Step 1: Set the channel rudder to single-chip rudder allocation method;

[0099] Assume the distribution matrix of the fork-shaped air rudder At different attack angles, Mach is:

[0100]

[0101] Rudder angle limit for:

[0102]

[0103] Step 2: Establish the rudder allocation optimization problem;

[0104] Assume that the weight matrix :

[0105]

[0106] Assume the desired rudder angle , then the optimization problem can be organized as:

[0107]

[0108] Step 3: Rapid calculation of rudder allocation optimization problem;

[0109] First, a hot start is performed through unconstrained optimization, and the initial solution for:

[0110]

[0111] Obviously, the rudder angle triggers the rudder angle limit, and then the effective set is iterated once to complete the solution;

[0112]

[0113] So far, the calculation of rudder allocation has been completed. In order to verify the effectiveness of the algorithm, the corresponding channel rudder after synthesizing the initial solution and the final result is only the desired rudder deflection angle;

[0114]

[0115] Although Violation of the rudder angle constraint , but the result of an optimization iteration calculation meets the limit requirement and obtains the desired rudder deflection angle.

[0116] In order to verify the superiority and practicality of the algorithm, three typical simulations are performed. 1) Figure 2 As shown in the figure, the torque attainable space (AMS) of the orthogonal decomposition and the method of the present invention is calculated. 2) The speed of solving the rudder allocation optimization problem (5) is compared with that of the existing typical quadratic programming solver, as shown in the figure. Figure 3 3) The method of the present invention and the traditional orthogonal decomposition method are respectively introduced into the standard 6-DOF model to decompose and synthesize the desired rudder deflection angle. The simulation results are shown in Figure 4 and Figure 5 As shown, Figure 4 This is a schematic diagram of the synthetic channel rudder curve in the first 20 seconds of a typical trajectory, which represents the channel rudders in the three directions of x (roll), y (yaw), and z (pitch) from top to bottom. Figure 5 It is a schematic diagram of the single-piece rudder distribution curve in the first 20 seconds of a typical trajectory, which, from top to bottom and from left to right, respectively represent the deviation angles of the X-row layouts of No. 1, 2, 3, and 4.

[0117] From the simulation results, we can see that: 1) the rudder allocation result satisfies the constraints throughout the process and the maximum torque space is 46% larger than that of the orthogonal decomposition method; 2) the calculation efficiency of the method of the present invention is much higher than that of the standard quadratic programming method, and can meet the calculation requirements of completing the rudder allocation within one control cycle; 3) in practical applications, the rudder output is significantly increased compared with the traditional orthogonal decomposition method, especially when the three-channel coupling is serious, the superiority is more obvious, and it does not violate the rudder angle constraint.

Claims

1. A method for adaptive rudder allocation for a hypersonic vehicle, characterized in that: The following steps are involved: Step 1: Set the channel rudder to single-chip rudder allocation method; Assume that the hypersonic vehicle has m single-piece rudders and the arbitrary rudder deflection angle is , different subscripts represent different single-piece rudders, and the rudder deflection angle is uniformly expressed as ; Assume that each rudder deflection angle has upper and lower bounds due to the limitation of the limit mechanism, hinge torque, rudder surface normal force, and rudder deflection angle velocity limit factors, which can be expressed as: ,in The rudder angle limit mechanism, rudder angle speed, maximum normal phase overload and maximum hinge moment are used to jointly limit the intersection; set up They are roll channel, yaw channel, and pitch channel. The moment coefficients of the three channels are Expressed as angle of attack , Sideslip Angle ,Mach number , rudder deflection angle Related functions or tables; The moment coefficients of the three channels are linearized at zero rudder deviation using the frozen coefficient method to obtain the distribution matrix : （1） Therefore, the control allocation problem is to solve the following equation (2): （2） in Synthetic three-axis channel rudder ; Step 2: Establish the rudder allocation optimization problem; Assume the desired rudder deflection angle is: , then the rudder allocation index function is selected as: （3） Set the allocation weight matrix Adjust the priority of each channel and rewrite the indicator function as follows: （4） Among them, the allocation weight matrix is a diagonal matrix. Each eigenvalue describes the weight priority of the channel rudder. The channel with high priority has a large weight. Therefore, the rudder allocation problem is expressed as the following quadratic programming problem: （5） in , ; Step 3: Fast calculation of rudder allocation optimization problem; The quadratic programming problem expressed in formula (5) has the following limitations: 1) The matrix is ​​positive semidefinite; 2) The size of the matrix is ; 3) No equality constraints; 4) Only the independent variable has an inequality constraint, and the inequality constraint is only triggered when the rudder is fully steered or reaches the limit value; Compute the quadratic programming problem through different branches: 1) Unconstrained optimization problem; （6） set up , that is, the matrix Perform singular value decomposition, where is a diagonal matrix, are 3×3 unitary matrices in singular value decomposition, and the rudder deflection angle is expressed as: （7） 2) Solution when the rudder deflection is limited; Direct limiting of the limited control variable: （8） Record the number of the servos that are limited. （9） Define the unrestricted Hessian matrix ,gradient and rudder deviation ; （10） in, express The element in the i-th row and i-th column of the matrix, Representation vector The i-th element of Representation vector The i-th element of ; The rudder angle correction value that does not trigger the limit is for: （11） The new limited rudder deflection angle is iteratively calculated as follows until stop; （12） in is the step size of gradient descent, determined by the Armijo criterion; is the preset calculation accuracy, , Respectively represent the kth and k+1th rudder deviations The result of the iterative calculation.

2. A hypersonic vehicle adaptive rudder allocation method according to claim 1, characterized in that: Said Less than or equal to 8.

3. The method for adaptive rudder allocation for a hypersonic vehicle according to claim 1, characterized in that: Said The value is 4.

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