CN114036628A - Method for collaborative design of wingspan and control strategy of morphing aircraft - Google Patents

Method for collaborative design of wingspan and control strategy of morphing aircraft Download PDF

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CN114036628A
CN114036628A CN202110186059.4A CN202110186059A CN114036628A CN 114036628 A CN114036628 A CN 114036628A CN 202110186059 A CN202110186059 A CN 202110186059A CN 114036628 A CN114036628 A CN 114036628A
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wingspan
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CN114036628B (en
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范泉涌
许斌
王冬生
任宏全
韩渭辛
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Northwestern Polytechnical University
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Abstract

The invention discloses a wing span and control strategy collaborative design method of a variant aircraft, which is mainly used for optimizing the control performance of an aircraft system based on a strategy iteration thought and belongs to the field of intelligent control. The design steps are as follows: establishing a variant aircraft model; determining a solution objective based on the performance function; determining key solving conditions; and designing a strategy iteration algorithm. Aiming at a type of variant aircraft, the method focuses on the influence of span parameters, constructs a longitudinal nonlinear dynamics model, defines a performance function related to disturbance, designs an iterative algorithm based on Sum-of-Squares technology by converting a Hamilton-Jacobi equation into an optimization problem of nonlinear inequality constraint, and solves the problem that the Hamilton-Jacobi equation is difficult to solveAnd (5) problems are solved. To optimize H∞The wingspan parameter and H are given for the purpose of controlling performance∞The control strategy is used for designing the algorithm cooperatively, so that the system has better robustness, and the defect that the existing algorithm cannot process system parameters and control and cannot be designed jointly is overcome.

Description

Method for collaborative design of wingspan and control strategy of morphing aircraft
Technical Field
The invention relates to a wing span and control strategy collaborative design method of a variant aircraft, which is mainly used for optimizing the control performance of an aircraft system based on a strategy iteration thought and belongs to the field of intelligent control.
Background
The variant aircraft can adapt to various flight environments and flight tasks by changing the structural shape, thereby realizing better flight performance and meeting the multi-task requirement in the complex flight environment. The peculiarities of the variant aircraft have given rise to a great deal of interest, especially in the deformation mechanisms of this type of aircraft. For a general aircraft, system structure parameters are usually designed first, and then design work of a control strategy is developed, however, how to coordinate parameters of a deformation mechanism and a control mechanism of the aircraft is a problem to be solved by a variant aircraft, and the coordinated design of the aircraft deformation structure parameters and a controller is bound to have a greater degree of freedom than the design of the control strategy alone, so that the aircraft has the potential of obtaining better flight performance. In addition, the complex flight environment will certainly cause interference to the normal operation of the aircraft, how to ensure that the flight control system has better robustness and reliability through the cooperative design of system parameters and control strategies has very important practical application value, and because such cooperative optimization problems are usually non-convex, no effective method is available at present for processing the cooperative design problem of nonlinear system parameters and control strategies.
Paper "Sum-of-Squares based optimal polynomial system H∞Control (Liushaoping, university of northeast, 2009 graduate) and article Policy evaluation for H∞The approximate H of a nonlinear system was studied based on Sum-of-squares (SOS) and a strategy iteration method∞Control problems, achieve good results, but such methods are only suitableThe robust control strategy for solving the nonlinear system cannot be used for solving the problem of collaborative design of system parameters and the robust control strategy.
Disclosure of Invention
The robust control design method based on strategy iteration is designed for joint optimization of the wingspan and the control of the variant aircraft, the wingspan deformation rate parameters and the robust control strategy of the variant aircraft can be simultaneously optimized and designed, the system stability is ensured, and the control performance of the aircraft under the condition of external disturbance is improved.
The method for cooperatively designing the wingspan and the control strategy of the morphing aircraft comprises the following steps:
(a) building a morphing aircraft model
Defining the wingspan deformation rate of the variant aircraft:
Figure BDA0002943099910000021
wherein b is the wingspan, bminAnd bmaxRespectively, the shortest span and the longest span, and clearly xi ∈ [0,1 ]]。
And (3) establishing a longitudinal nonlinear dynamics model of the variant aircraft by combining a conventional aircraft dynamics modeling process:
Figure BDA0002943099910000022
wherein VsIs the flying speed, alpha is the angle of attack, theta is the pitch angle, q is the pitch angle speed, h is the altitude, m is the variant aircraft mass, and T is TδδtAs a thrust, TδIs the coefficient of thrust, δtIs the throttle opening, g is the acceleration of gravity is a constant value, IyThe pitch moment of inertia, D (xi), L (xi) and M (xi) are respectively resistance, lift force and pitch moment related to the span deformation rate, and the specific form is expressed as follows:
Figure BDA0002943099910000023
in the formula, Qd＝0.5ρV2Is dynamic pressure, ρ is air density, SwIs a wing reference area, cAIs the average geometric chord length of the wing, deltaeFor elevator declination, CL、CD、CmThe lift coefficient, the drag coefficient and the pitching moment coefficient are respectively obtained as follows:
Figure BDA0002943099910000024
wherein the content of the first and second substances,
Figure BDA0002943099910000025
is the drag coefficient at zero angle of attack,
Figure BDA0002943099910000026
is the aerodynamic derivative of the resistance with respect to the angle of attack,
Figure BDA0002943099910000027
the second aerodynamic derivative of the resistance with respect to the angle of attack,
Figure BDA0002943099910000028
is the lift coefficient at zero angle of attack,
Figure BDA0002943099910000029
is the aerodynamic derivative of the lift force with respect to the angle of attack,
Figure BDA00029430999100000210
the aerodynamic derivative of the lift force with respect to the rudder deflection angle,
Figure BDA00029430999100000211
is the aerodynamic derivative of lift with respect to pitch angle velocity,
Figure BDA00029430999100000212
the coefficient of the pitching moment at the zero attack angle,
Figure BDA0002943099910000031
is the aerodynamic derivative of the pitching moment with respect to the angle of attack,
Figure BDA0002943099910000032
the aerodynamic derivative of the pitching moment with respect to the rudder deflection angle,
Figure BDA0002943099910000033
is the aerodynamic derivative of the pitch moment with respect to pitch angle velocity.
Figure BDA0002943099910000034
Figure BDA0002943099910000035
The method is characterized in that the method is a result obtained by performing least square fitting on the flying height h, the Mach number Ma and the wingspan deformation rate xi on longitudinal aerodynamic parameters obtained by simulation and calculation at each working point, and the coefficients and derivatives have linear relation with the wingspan deformation rate xi.
For the convenience of understanding and subsequent analysis, the longitudinal nonlinear dynamics model of the variant aircraft is re-described in the form of an affine nonlinear system
Figure BDA0002943099910000036
Wherein x (t) ═ Vs α θ q h]TIs a state vector; u (t) ═ δeδt]TInputting a vector for control; system function f0(x(t),ξ),g0(x (t), ξ) is a function that is linearly related to ξ.
Figure BDA0002943099910000037
Figure BDA0002943099910000038
Will f is0(x(t),ξ)，g0(x (t), xi) carrying out Taylor expansion on non-polynomial non-linear terms at the working point of the aircraft, and eliminating high-order terms with small influence or considering as system disturbance d (t), and considering that the actual aircraft is influenced by the disturbance, obtaining the following approximate model of the longitudinal dynamics of the variant aircraft:
Figure BDA0002943099910000039
where f (x (t), ξ) and g (x (t), ξ) are f0(x (t), ξ) and g0(x (t), ξ) are Taylor expanded and the approximation of the higher order terms are truncated. It can be seen that f (x (t), ξ) and g (x (t), ξ) are polynomial matrices about the state of the system.
(b) Determining a solution objective based on a performance function
The following performance functions are defined:
Figure RE-GDA0003237369550000041
where Q (x (t)) is a non-negative function, R is a symmetric positive definite matrix, γ0Is the noise attenuation level, also known as the performance indicator. The smaller the γ can be seen0The system can be ensured to have better anti-disturbance effect, and the effective collaborative design algorithm for solving H is provided∞The control strategy u and the span deformation rate xi are such that L2The gain is as small as possible. For a system (3) with a performance function (4), based on zero-sum game theory, for determining a value γ0And fixed span deformation ratio xi, H of the system (1)∞The solution to the control problem can be obtained by solving the following HJB equation:
Figure BDA0002943099910000042
wherein, V*Is a positive definite value function related to the performance function J, is a key function to be solved,
Figure BDA0002943099910000043
is V*For the partial derivatives of x (t), f, g, and k are abbreviated forms of f (x (t), ξ), g (x (t), ξ), k (x (t), and ξ), respectively, and for the convenience of description, similar abbreviated forms of function arguments are used hereinafter, such as x ═ x (t), d ═ d (t), u ═ u (x), and the like.
Obtained H∞The control strategy is as follows:
Figure BDA0002943099910000044
as can be seen from the prior art, H for a nonlinear system with a fixed span deformation ratio ξ∞The control problem can be solved by combining a strategy iteration method and a neural network learning technology, but the control problem cannot be directly solved by the method for solving the collaborative design problem of the adjustable wingspan deformation rate and the robust control strategy, so a value-to-value function V is provided below*And a specific solving algorithm of the span deformation rate xi to determine the control strategy u*(x) And reasonable span deformation rate.
(c) Determining key solution conditions
Define the following function
Figure BDA0002943099910000045
Considering V (x) as the Lyapunov function of the system, and taking its derivative, when there is no disturbance, it can be obtained
Figure BDA0002943099910000051
If L (V, u, γ)0Xi) is not less than 0, then
Figure BDA0002943099910000052
The system is therefore stable when there is no disturbance.
When the system is affected by disturbance, the derivative of the Lyapunov function can be obtained
Figure BDA0002943099910000053
Integrating both sides of the above formula at [0, ∞ ]
Figure BDA0002943099910000054
It can be seen that L (V, u, γ)0Xi) is more than or equal to 0, so that the system has certain suppression capability on disturbance. Thus, the following will be based on L (V, u, γ)0And xi) is more than or equal to 0, constructing a strategy iterative algorithm, and solving the wingspan deformation rate and the robust control strategy.
(d) Design strategy iterative algorithm
For L (V, u, gamma)0Xi) is more than or equal to 0 to ensure that the obtained inequality condition can be solved based on the SOS tool, and a parameter gamma capable of solving the robust performance is given on the basis0And (4) performing an optimized wingspan deformation rate and control strategy collaborative calculation method.
Compared with the prior art, the method has the beneficial effects that:
(1) aiming at a type of variant aircraft, the influence of span parameters is focused, a longitudinal nonlinear dynamics model is constructed, a disturbance-related performance function is defined, an optimization problem of nonlinear inequality constraint is solved by converting a Hamilton-Jacobi equation, and an iterative algorithm based on a Sum-of-Squares technology is designed, so that the problem that the Hamilton-Jacobi equation is difficult to solve is solved.
(2) To optimize H∞The wingspan parameter and H are given for the purpose of controlling performance∞The control strategy is used for designing the algorithm cooperatively, so that the system has better robustness, and the defect that the existing algorithm cannot process system parameters and control and cannot be designed jointly is overcome.
Drawings
FIG. 1 is a flow chart of a method for implementing the collaborative design of the wingspan and control strategy of the variant aircraft.
Detailed Description
The implementation process of the wingspan and control strategy collaborative design method of the variant aircraft in the embodiment comprises the following steps:
(a) building a morphing aircraft model
Defining the wingspan deformation rate of the variant aircraft:
Figure BDA0002943099910000061
wherein b is the wingspan, bminAnd bmaxRespectively, the shortest span and the longest span.
Longitudinal nonlinear dynamical models (1) and (2) of the variant aircraft containing the span deformation ratio are established in combination with a conventional aircraft dynamics modeling process. Will f is0(x(t),ξ)，g0And (x (t) and xi) carrying out Taylor expansion on non-polynomial non-linear terms at the working point of the aircraft, and eliminating high-order terms with small influence or considering system disturbance, wherein the influence of disturbance d on the actual aircraft is considered, so that the following variant aircraft longitudinal dynamics approximate model (3) can be obtained.
(b) Determining a solution objective based on a performance function
The following performance functions are defined:
Figure BDA0002943099910000062
where Q (x) is a non-negative function, R is a symmetric positive definite matrix, γ0Is the noise attenuation level. The smaller the γ can be seen0The system can be ensured to have better anti-disturbance effect, and the effective collaborative design algorithm is provided to obtain H∞The control strategy u and the span deformation rate xi are such that L2The gain is as small as possible.
For a system (3) with a performance function (4), based on zero and game theory, for determining a value γ0And fixed wing spread deformation ratio xi, H of system (1)∞The solution to the control problem can be obtained by solving the following HJB equation:
Figure BDA0002943099910000063
wherein, V*Is a positive definite value function related to the performance function J and is a key function to be solved
H∞The analytic form of the control strategy is as follows:
Figure BDA0002943099910000064
(c) determining key solution conditions
Define the following function
Figure BDA0002943099910000065
Figure BDA0002943099910000071
Figure BDA0002943099910000072
Figure BDA0002943099910000073
Figure BDA0002943099910000074
Based on the Schur complement theorem, the conclusion can be drawn: l (V, u, γ) as long as the following matrix inequality holds0Xi) is always equal to or greater than 0.
Figure BDA0002943099910000075
(d) Design strategy iterative algorithm
First, for a fixed performance parameter γ0Algorithm 1 is designed.
Algorithm 1. selecting an initial wingspan deformation rate xi0Control strategy u0(x) And a scalar ε > 0, solving the following optimization problem to obtain V0(x)：
Figure BDA0002943099910000076
Updated to obtain control strategy u1(x) Comprises the following steps:
Figure BDA0002943099910000077
1): using a control strategy ui(x) Solving the following SOS problem to obtain Vi(x) And xii：
Figure BDA0002943099910000078
2): according to the obtained Vi(x) And xiiThe update control strategy is:
Figure BDA0002943099910000079
3): setting i to i +1 up to Vi(x) And (6) converging.
In Algorithm 1, the performance index γ0Is a constant value, and it is necessary to optimize the performance index γ for better anti-interference performance of the system0Algorithm 2 is given below.
Algorithm 2. selection of an initial System spandeformation Rate
Figure BDA0002943099910000081
Stability control strategy u(1)Scalar epsilon > 0, gamma0＞0，κz＞0。
1) Using determined spandeformation ratio
Figure BDA0002943099910000082
Solving the following SOS problem to obtain V(k)And gammak。
Figure BDA0002943099910000083
Updated to obtain control strategy u(k+1)Comprises the following steps:
Figure RE-GDA0003237369550000084
selecting gamma0＝γk，
Figure BDA0002943099910000085
V0＝V(k)，u0＝u(k+1)。
a) Using a control strategy ui(x) Solving the following SOS problem to obtain Vi(x) And xii
Figure BDA0002943099910000086
b) According to the obtained Vi(x) And xiiThe update control strategy is:
Figure BDA0002943099910000087
if Vi(x) Converge, return to step a) and set i ═ i +1, otherwise stop the inner layer iteration and go to step 2).
2) If | | | γ(k)-γ(k-1)||≥κzSetting k to k +1, returning to step 1) and setting u(k)＝ui+1，
Figure BDA0002943099910000088
Otherwise the algorithm ends.
According to the algorithm 2, the wingspan deformation rate xi and the robust control strategy can be solved in a collaborative optimization mode, and the obtained change rate and the control strategy can ensure that the variant aircraft has better control performance.
The invention is not described in detail and is part of the common general knowledge of a person skilled in the art.

Claims (1)

1. The method for cooperatively designing the wingspan and the control strategy of the morphing aircraft comprises the following steps:
(a) building a morphing aircraft model
Defining the wingspan deformation rate of the variant aircraft:
Figure RE-FDA0003237369540000011
wherein b is the wingspan, bminAnd bmaxRespectively, the shortest span and the longest span, and clearly xi ∈ [0,1 ]]；
And (3) establishing a longitudinal nonlinear dynamics model of the variant aircraft by combining a conventional aircraft dynamics modeling process:
Figure RE-FDA0003237369540000012
wherein VsIs the flying speed, alpha is the angle of attack, theta is the pitch angle, q is the pitch angle speed, h is the altitude, m is the morphing aircraft mass, and T is TδδtAs a thrust, TδIs the coefficient of thrust, δtIs the throttle opening, g is the acceleration of gravity is a constant value, IyThe pitch moment of inertia, D (xi), L (xi) and M (xi) are respectively resistance, lift force and pitch moment related to the span deformation rate, and the specific form is expressed as follows:
Figure RE-FDA0003237369540000013
in the formula, Qd＝0.5ρV2Is dynamic pressure, ρ is air density, SwIs a wing reference area, cAIs the average geometric chord length of the wing, deltaeFor elevator declination, CL、CD、CmThe lift coefficient, the drag coefficient and the pitching moment coefficient are respectively obtained as follows:
Figure RE-FDA0003237369540000014
wherein the content of the first and second substances,
Figure RE-FDA0003237369540000015
is the drag coefficient at zero angle of attack,
Figure RE-FDA0003237369540000016
is the aerodynamic derivative of the resistance with respect to the angle of attack,
Figure RE-FDA0003237369540000017
the second aerodynamic derivative of the resistance with respect to the angle of attack,
Figure RE-FDA0003237369540000021
is the lift coefficient at zero angle of attack,
Figure RE-FDA0003237369540000022
is the aerodynamic derivative of the lift force with respect to the angle of attack,
Figure RE-FDA0003237369540000023
the aerodynamic derivative of the lift force with respect to the rudder deflection angle,
Figure RE-FDA0003237369540000024
is the aerodynamic derivative of lift with respect to pitch angle velocity,
Figure RE-FDA0003237369540000025
the coefficient of the pitching moment at the zero attack angle,
Figure RE-FDA0003237369540000026
is the aerodynamic derivative of the pitching moment with respect to the angle of attack,
Figure RE-FDA0003237369540000027
the pneumatic derivative of the pitching moment with respect to the rudder deflection angle,
Figure RE-FDA0003237369540000028
is the aerodynamic derivative of the pitch moment with respect to pitch angle velocity;
Figure RE-FDA0003237369540000029
Figure RE-FDA00032373695400000210
performing least square fitting on the flight height h, the Mach number Ma and the wingspan deformation rate xi for longitudinal aerodynamic parameters obtained by simulation and calculation at each working point to obtain a result, wherein the coefficients and derivatives have a linear relation with the wingspan deformation rate xi;
for the convenience of understanding and subsequent analysis, the longitudinal nonlinear dynamics model of the variant aircraft is re-described in the form of an affine nonlinear system
Figure RE-FDA00032373695400000211
Wherein x (t) ═ Vs α θ q h]TIs a state vector; u (t) ═ δe δt]TInputting a vector for control; system function f0(x(t),ξ),g0(x (t), ξ) is a function that is linearly related to ξ;
Figure RE-FDA00032373695400000212
Figure RE-FDA00032373695400000213
will f is0(x(t),ξ)，g0(x (t), xi) carrying out Taylor expansion on non-polynomial non-linear terms at the working point of the aircraft, and eliminating high-order terms with small influence or considering as system disturbance d (t), and considering that the actual aircraft is influenced by the disturbance, obtaining the following approximate model of the longitudinal dynamics of the variant aircraft:
Figure RE-FDA0003237369540000031
where f (x (t), ξ) and g (x (t), ξ) are f0(x (t), ξ) and g0(x (t), ξ) are Taylor expanded and the approximation of higher order terms are truncated; it can be seen that f (x (t), ξ) and g (x (t), ξ) are polynomial matrices about the system state;
(b) determining a solution objective based on a performance function
The following performance functions are defined:
Figure RE-FDA0003237369540000032
where Q (x (t)) is a non-negative function, R is a symmetric positive definite matrix, γ0Is the noise attenuation level, also known as the performance indicator; the smaller the γ can be seen0The system can be ensured to have better anti-disturbance effect, and the effective collaborative design algorithm for solving H is provided∞The control strategy u and the span deformation rate xi are such that L2The gain is as small as possible; for a system (3) with a performance function (4), based on zero and game theory, for determining a value γ0And fixed span deformation ratio xi, H of the system (1)∞The solution to the control problem can be obtained by solving the following HJB equation:
Figure RE-FDA0003237369540000033
wherein, V*Is a positive definite value function related to the performance function J, is a key function to be solved,
Figure RE-FDA0003237369540000034
is V*For the sake of description, similar abbreviations with function arguments hidden are used hereinafter, such as x ═ x (t), d ═ d (t), u ═ u (x), and the like;
obtained H∞The control strategy is as follows:
Figure RE-FDA0003237369540000035
as can be seen from the prior art, H for a nonlinear system with a fixed span deformation ratio ξ∞The control problem can be solved by combining a strategy iteration method and a neural network learning technology, but the control problem cannot be directly solved by the method for solving the collaborative design problem of the adjustable wingspan deformation rate and the robust control strategy, so a value-to-value function V is provided below*And a specific solving algorithm of the wingspan deformation rate xi to determine the control strategy u*(x) And reasonable wingspan deformation rate;
(c) determining key solution conditions
Define the following function
Figure RE-FDA0003237369540000041
Considering V (x) as the Lyapunov function of the system, and taking its derivative, when there is no disturbance, it can be obtained
Figure RE-FDA0003237369540000042
If L (V, u, γ)0Xi) is not less than 0, then
Figure RE-FDA0003237369540000043
Thus when there is no disturbance, the system is stable;
when the system is affected by disturbance, the derivative of the Lyapunov function can be obtained
Figure RE-FDA0003237369540000044
Integrating both sides of the above formula at [0, ∞ ]
Figure RE-FDA0003237369540000045
It can be seen that L (V, u, γ)0Xi) is more than or equal to 0, so that the system has certain suppression capability on disturbance; therefore, the following will be based on L (V, u, γ)0Xi) is more than or equal to 0, a strategy iterative algorithm is constructed, and the wingspan deformation rate and the robust control strategy are solved;
(d) design strategy iterative algorithm
For L (V, u, gamma)0Xi) is more than or equal to 0 to ensure that the obtained inequality condition can be solved based on the SOS tool, and a parameter gamma capable of solving the robust performance is given on the basis0And (5) carrying out an optimized wingspan deformation rate and control strategy collaborative design algorithm.
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