CN108594653B - Performance limit analysis system designed by large envelope flight control law - Google Patents

Performance limit analysis system designed by large envelope flight control law Download PDF

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CN108594653B
CN108594653B CN201810233122.3A CN201810233122A CN108594653B CN 108594653 B CN108594653 B CN 108594653B CN 201810233122 A CN201810233122 A CN 201810233122A CN 108594653 B CN108594653 B CN 108594653B
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范国梁
刘朝阳
刘振
袁如意
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Abstract

The invention belongs to the technical field of automatic control, and particularly relates to a performance limit analysis system designed by a large envelope flight control law. The problem that the prior art can not carry out analysis to big envelope line aircraft when performance limit is solved. The invention provides a performance limit analysis method and a performance limit analysis device for a large envelope flight control law design, which comprise a first calculation unit, a second calculation unit and a third calculation unit, wherein the first calculation unit is used for converting a pre-constructed aircraft model into a standard model by adopting an extended linearization method; the second calculation unit is used for carrying out nonlinear coordinate transformation on the standard model and calculating the frequency domain performance robustness of the standard model; the third calculation unit is used for calculating the stability criterion of the standard model according to the consistent progressive stability criterion of the linear time-varying system; the fourth calculation unit is used for analyzing the performance limit of the standard model. The method can provide basis for the design verification of the flight control law of the large envelope curve and the overall design of the aircraft.

Description

Performance limit analysis system designed by large envelope flight control law
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to a performance limit analysis system designed by a large envelope flight control law.
Background
With the continuous expansion of mission range of the aircraft, the flight envelope line of the aircraft is larger and larger. Generally, an aircraft flies in the atmosphere (within 2 ten thousand meters) and in an atmosphere edge adjacent space (within 2 to 10 ten thousand meters), the flight speed ranges from high subsonic speed to high supersonic speed above mach 5, the flight speed changes greatly, the dynamic characteristics of the aircraft also change greatly, and therefore in the flying process of the aircraft, performance parameters of the aircraft, such as structural elasticity and the like, cannot be ignored, and the design of a flight control law presents a serious challenge. The control law of the existing large envelope aircraft mainly relates to control stability, performance robustness and robustness stability, and a method for analyzing the performance limit of the control law is lacked. The method for analyzing the performance limit of the control law of the large envelope flight vehicle can reveal the intrinsic mechanism of the performance limit of the nonlinear system, provide more layers of performance limits, and aim to expand the performance limit theory of the linear system into the nonlinear system, enrich the performance limit analysis theory of the nonlinear system, reveal the intrinsic mechanism of the performance limit of the longitudinal trajectory tracking of the aircraft from the engineering perspective, and provide a basis for the design verification of the large envelope flight control law and the overall design of the aircraft.
Therefore, how to provide a solution for internal flight quality calibration meeting the flight control law of the large envelope curve is a problem that needs to be solved by those skilled in the art at present.
Disclosure of Invention
In order to solve the above problems in the prior art, that is, to solve the problem that the prior art cannot analyze the performance limit of a large envelope aircraft, the present invention provides a performance limit analysis system designed by a large envelope flight control law, wherein the system includes:
a first computing unit configured to convert a pre-built aircraft model into a standard model using an extended linearization method;
a second calculation unit configured to perform nonlinear coordinate transformation on the standard model, and calculate frequency domain performance robustness of the standard model;
a third calculation unit configured to calculate a stabilization criterion of the standard model according to a linear time-varying system-consistent progressive stabilization criterion;
a fourth computing unit configured to analyze performance limits of the standard model for frequency domain performance robustness of the second computing unit and a stability criterion of the third computing unit.
In a preferred embodiment of the foregoing method, the first computing unit is further configured to:
linearizing the aircraft model by adopting an extended linearization method, and segmenting unstable zero dynamics of the aircraft model;
calculating a PD characteristic structure of the aircraft model and a time domain performance index of the aircraft model, and judging whether the aircraft model is controllable;
and if the aircraft model is controllable, carrying out nonlinear coordinate transformation on the aircraft model.
In the preferred technical solution of the above method, "judge whether the aircraft model is controllable", the method is:
calculating the PD characteristic structure of the aircraft model and the zero initial value time domain response of the aircraft model, judging whether the aircraft model is equivalent to a standard system, and if the aircraft model is equivalent to the standard system, controlling the aircraft model;
the PD characteristic structure of the aircraft model is calculated, and the method is shown in the following formula:
Figure BDA0001603112190000021
pi(t)、
Figure BDA0001603112190000022
for the PD characteristic value rhoi(t) right and left PD feature vectors, ck(t),bj(t) is the correlation component of the output-input matrix;
wherein, the standard system is as follows:
Figure BDA0001603112190000023
Figure BDA0001603112190000024
in the preferred technical solution of the above method, "calculating the frequency domain performance robustness of the standard model", the method includes:
calculating the PD spectrum of the standard model under the condition of uncertain parameters and the perturbation condition of the line PD characteristic vector through a scalar polynomial differential algorithm;
and analyzing the norm of the perturbation range of the time domain performance parameter vector of the standard model according to the perturbation condition of the PD spectrum and the line PD feature vector and in combination with the time domain response of the standard model, and calculating the frequency domain performance robustness of the standard model.
Compared with the closest prior art, the invention provides a performance limit analysis system for a large envelope flight control law design, which comprises a first computing unit, a second computing unit and a third computing unit, wherein the first computing unit is configured to convert a pre-constructed aircraft model into a standard model by adopting an extended linearization method; a second calculation unit configured to perform nonlinear coordinate transformation on the standard model, and calculate frequency domain performance robustness of the standard model; a third calculation unit configured to calculate a stabilization criterion of the standard model according to a linear time-varying system-consistent progressive stabilization criterion; a fourth computing unit configured to analyze performance limits of the standard model for frequency domain performance robustness of the second computing unit and a stability criterion of the third computing unit.
The technical scheme at least has the following beneficial effects: the technical scheme of the invention can reveal the intrinsic mechanism of the performance limitation of the nonlinear system, provide more layers of performance limits, and aim to expand the performance limit theory of the linear system into the nonlinear system, enrich the performance limit analysis theory of the nonlinear system, reveal the intrinsic mechanism of the performance limitation of the airplane longitudinal trajectory tracking from the engineering perspective, and provide a basis for the design verification of the large envelope flight control law and the overall design of an aircraft.
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Fig. 1 is a schematic structural diagram of a performance limit analysis system designed according to the flight control law of the large envelope curve in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention
Preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention, and are not intended to limit the scope of the present invention.
Referring to fig. 1, fig. 1 schematically shows a flow chart of a performance limit analysis system designed by the large envelope flight control law in this embodiment. As shown in fig. 1, the performance limit analysis system designed by the large envelope flight control law in this embodiment includes the following contents:
the method adopts the conversion from a nonlinear system to a linear system, utilizes the theoretical development of a linear time-varying system, changes the system into a standard form through nonlinear coordinate transformation, and provides a time domain and frequency domain performance limited mechanism and performance limit calculation, limited mechanism calculation of performance robustness, a class of nonlinear non-minimum system consistent progressive stability criterion calculation and a realization method of stability robustness and limited mechanism calculation.
Modeling the dynamics of the elastomer aircraft with the large envelope aircraft, the longitudinal dynamics model can be shown as the following formula:
Figure BDA0001603112190000041
Figure BDA0001603112190000042
Figure BDA0001603112190000043
Figure BDA0001603112190000044
Figure BDA0001603112190000045
Figure BDA0001603112190000046
the model comprises 11 flight states, 5 rigid body states V, gamma, h, α, Q respectively representing speed, track inclination angle, altitude, attack angle and pitch angle rate, and 6 elastomer states
Figure BDA0001603112190000047
Respectively representing the first three elastic modes and their differentials. Wherein, ω isiNatural frequency of elastic mode, ξiM, g, I as damping ratioyyL, D, T, M, N representing mass, gravitational acceleration, and moment of inertia about the Y axis, respectivelyiRespectively representing lift force, resistance force, thrust force, pitching moment and generalized elastic force. The model has a complex nonlinear relationship with the flight state and the control input, and can be represented by a high-precision fitting model, which is specifically shown in the following formula (7):
Figure BDA0001603112190000048
wherein the content of the first and second substances,
Figure BDA0001603112190000049
represents an elastic mode vector of ═ 2 [, ]c,e]TThe vector of the rudder deflection angle is represented,c,erespectively showing the rudder deflection angles of the canard and the elevator,
Figure BDA00016031121900000410
represents the dynamic pressure, ρ is the atmospheric density.
The aerodynamic coefficient of a large envelope aircraft can be shown in equation (8):
Figure BDA0001603112190000051
wherein, CT,φThe thrust coefficient of thrust versus roll angle,
Figure BDA0001603112190000052
are respectively CT,φDerivatives of the angle of attack of order 3, 2, 1 and offset values; cTIs the thrust coefficient of thrust versus angle of attack,
Figure BDA0001603112190000053
are respectively CTDerivatives of the angle of attack of order 3, 2, 1 and offset values;
CLcoefficient of lift, angle of attack
Figure BDA0001603112190000054
(elastic mode vector), andc,e]T(rudder deflection angle vector) of the rudder angle of the vehicle,c,erespectively showing the rudder deflection angles of the canard and the elevator,
Figure BDA0001603112190000055
as the lift coefficient of lift to angle of attack,
Figure BDA0001603112190000056
as a pair of lifting forceseThe coefficient of lift force of (a) is,
Figure BDA0001603112190000057
as a pair of lifting forcescThe coefficient of lift force of (a) is,
Figure BDA0001603112190000058
the lift coefficient is zero, and the lift coefficient is zero,
Figure BDA0001603112190000059
the lift coefficient is the lift force versus elastic modal vector η.
CDIs coefficient of resistance, angle of attack
Figure BDA00016031121900000510
(elastic mode vector), andc,e]T(rudder deflection angle vector) of the rudder angle of the vehicle,c,erespectively showing the rudder deflection angles of the canard and the elevator,
Figure BDA00016031121900000511
the drag coefficient of drag to the square of the angle of attack and the angle of attack,
Figure BDA00016031121900000512
is a resistance paireSum of squareseThe coefficient of resistance of (a) is,
Figure BDA00016031121900000513
is a resistance paircSum of squarescThe coefficient of resistance of (a) is,
Figure BDA00016031121900000514
the resistance coefficient of the material is zero, and the material is,
Figure BDA00016031121900000515
is the drag coefficient of drag versus elastic mode vector η.
CMIs the coefficient of pitching moment and the angle of attack
Figure BDA00016031121900000516
(elastic mode vector), andc,e]T(rudder deflection angle vector) of the rudder angle of the vehicle,c,erespectively showing the rudder deflection angles of the canard and the elevator,
Figure BDA00016031121900000517
the coefficient of the pitching moment coefficient is the square of the pitching moment to the attack angle and the attack angle,
Figure BDA00016031121900000518
as a pitching moment paireThe coefficient of the pitching moment of (a),
Figure BDA00016031121900000519
as a pitching moment paircCoefficient of pitching moment,
Figure BDA00016031121900000520
The pitch moment coefficient is zero, and the pitch moment coefficient is zero,
Figure BDA00016031121900000521
the pitch moment coefficient is the pitch moment coefficient versus the elastic mode vector η.
L,D,T,M,NiRespectively representing lift force, resistance force, thrust force, pitching moment and generalized elastic force.
Figure BDA00016031121900000522
The thrust T, the lift L, the drag D and the pitching moment M are paired
Figure BDA00016031121900000523
Thrust coefficient, lift coefficient, drag coefficient, and pitching moment coefficient of (elastic modal vector).
Figure BDA00016031121900000524
Is a generalized elastic force pair
Figure BDA00016031121900000525
The generalized elastic force coefficient (elastic modal vector).
The canard wing of the large envelope aircraft is connected to the elevator by a hinge to eliminate the non-minimum phase characteristic, so the control input to be designed for the aircraft may be u ═ ce,φ]TAnd phi is the engine fuel equivalence ratio. The control output may be y ═ V, h]TI.e. control speed and altitude.
The aircraft mathematical model is a typical multivariable, strong nonlinear and strong coupling model, and due to the fact that the aircraft is high in flying speed, large in flying envelope, complex in mechanism such as scramjet combustion and the like, and lack of sufficient flight test data support, the control model has serious uncertainty and belongs to a typical system with complex structure uncertainty. While uncertainty has a significant impact on model properties. Taking the case of reentry flight, the reentry process is accompanied by rapid velocity and altitude changes, resulting in dynamic pressure
Figure BDA0001603112190000064
The fast time-varying and uncertain effect of dynamic pressure variations have a significant influence on the flight characteristics.
Specifically, the performance limit analysis method for the large envelope flight control law design comprises the following steps of:
step S1: calculating a time domain and frequency domain performance limit mechanism and a performance limit;
step S11: the nonlinear system is linearized by a differential homomorphic method at a balance point by adopting an extended linearization method and a differential geometric method, and the unstable zero dynamic is divided out, wherein the zero dynamic is a concept in a nonlinear theory and is equivalent to a zero point in a transfer function, and the unstable zero dynamic system is also called as a non-minimum phase system. For an analog signal system, a system in which a system function has one or more zero points on the right half plane of the S plane is a non-minimum phase system, and in the control of the non-minimum phase system, it is necessary to suppress negative modulation caused by an unstable zero point and shorten the adjustment time of the system, so that the original system is converted into a linear time-varying system
Figure BDA0001603112190000063
Wherein, x is a state variable, A (t) is a state equation, B (t) is an input matrix, u is a control input, and t is time, thereby completing the standardization of a system model;
step S12: adopts linear time-varying system differential algebraic spectrum theory and utilizes the essential condition that the system is consistent and completely controllable, i.e. the system is consistent with a standard system
Figure BDA0001603112190000061
Equivalently, z is the state variable of the standard system, the dimension of z is the same as that of the original system, Az(t) is the system matrix for the standard type system, Bz(t) is the input matrix for the standard type system, t is time, u represents the control input, wherein,
Figure BDA0001603112190000062
whether the system is equivalent to a standard system or not is judged, whether the system is consistent and completely controllable is judged, and then a constraint mechanism of unstable zero dynamics on a frequency domain index PD (Parallel D-Eigenvalue) characteristic value and PD characteristic vector configuration is researched, the system is not completely controllable, and PD characteristic structure configuration is limited inevitably. Wherein the PD characteristic values and PD characteristic vectors are concepts in a non-linear system, and are consistent with the concepts of the PD characteristic values and PD characteristic vectors in a linear system. And when the system is judged to be consistent and completely controllable, the next step can be carried out.
Step S13: according to PD characteristic structure and system zero initial value time domain response
Figure BDA0001603112190000071
Wherein p isi(t)、
Figure BDA0001603112190000072
Respectively PD characteristic value rhoi(t) right and left PD feature vectors, ck(t),bj(t) are the k-th row vector of the output matrix c, the j-th vector of the input matrix b, uj(τ) denotes the j row vector of the control variable, K denotes the number of rows of the output matrix c, N denotes the eigenvalue ρ of the eigenvalue PDi(t) the number of columns of the feature vector, m is the number of control inputs, t0Indicating the starting time. Calculating the relation between the time domain performance indexes (rise time, overshoot and undershoot) and the PD characteristic structure, and analyzing the constraint mechanism of the unstable zero dynamics on the time domain performance indexes of the system: and when a single unstable zero z and a single unstable pole p existing in the system are given, the limits of system overshoot and undershoot are respectively as follows:
Figure BDA0001603112190000073
step S14: for a system of flight dynamics, based on a time scale separation thought, an aircraft attitude control system is divided into a slowly-changing attitude angle loop and a rapidly-changing angular velocity loop, a fast loop is generally a minimum phase system, and a corresponding PD characteristic value and a corresponding PD characteristic vector can be set to be constant values
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
Those of skill in the art will appreciate that the method steps of the examples described in connection with the embodiments disclosed herein may be embodied in electronic hardware, computer software, or combinations of both, and that the components and steps of the examples have been described above generally in terms of their functionality in order to clearly illustrate the interchangeability of electronic hardware and software. Whether such functionality is implemented as electronic hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.

Claims (1)

1. A performance limit analysis system for a turnbuckle flight control law design, the system comprising:
a first computing unit configured to convert a pre-built aircraft model into a standard model using an extended linearization method;
a second calculation unit configured to perform nonlinear coordinate transformation on the standard model, and calculate frequency domain performance robustness of the standard model;
a third calculation unit configured to calculate a stabilization criterion of the standard model according to a linear time-varying system-consistent progressive stabilization criterion;
a fourth calculation unit configured to analyze performance limits of the standard model according to the frequency domain performance robustness of the second calculation unit and a stability criterion of the third calculation unit;
the first computing unit is further to:
linearizing the aircraft model by adopting an extended linearization method, and segmenting unstable zero dynamics of the aircraft model;
calculating a PD characteristic structure of the aircraft model and a time domain performance index of the aircraft model, and judging whether the aircraft model is controllable;
if the aircraft model is controllable, carrying out nonlinear coordinate transformation on the aircraft model;
the method for judging whether the aircraft model is controllable comprises the following steps:
calculating the PD characteristic structure of the aircraft model and the zero initial value time domain response of the aircraft model, judging whether the aircraft model is equivalent to a standard system, and if the aircraft model is equivalent to the standard system, controlling the aircraft model;
the PD characteristic structure of the aircraft model is calculated, and the method is shown in the following formula:
Figure FDA0002500490580000011
where k denotes the number of rows of the output matrix c, and N denotes the eigenvalues PD, ρi(t) the number of columns of the feature vector, m is the number of control inputs, t0Denotes the starting time, pi(t)、
Figure FDA0002500490580000012
For the PD characteristic value rhoi(t) right and left PD feature vectors, ck(t),bj(τ) is the k-th row vector of the output matrix c, the j-th vector of the input matrix b, uj(τ) represents the j th row vector of the control variable;
wherein, the standard system is as follows:
Figure FDA0002500490580000013
wherein z is a state variable, A (t) is a state equation, B (t) is an input matrix, u is a control input, and t is time;
Figure FDA0002500490580000021
the method for calculating the frequency domain performance robustness of the standard model comprises the following steps:
calculating the PD spectrum of the standard model under the condition of uncertain parameters and the perturbation condition of the line PD characteristic vector through a scalar polynomial differential algorithm;
according to the perturbation conditions of the PD spectrum and the line PD feature vectors, in combination with the time domain response of the standard model, analyzing the norm of the perturbation range of the time domain performance parameter vector of the standard model, and calculating the frequency domain performance robustness of the standard model;
wherein, the method for analyzing the performance limit of the standard model comprises the following steps: calculating the relation between the time domain performance index and the PD characteristic structure, and analyzing the constraint mechanism of the unstable zero dynamics on the time domain performance index of the system: and when a single unstable zero z and a single unstable pole p existing in the system are given, the limits of system overshoot and undershoot are respectively as follows:
Figure FDA0002500490580000022
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