CN111596686B - Method for controlling preset performance of longitudinal system of hypersonic aircraft - Google Patents

Method for controlling preset performance of longitudinal system of hypersonic aircraft Download PDF

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CN111596686B
CN111596686B CN202010404397.6A CN202010404397A CN111596686B CN 111596686 B CN111596686 B CN 111596686B CN 202010404397 A CN202010404397 A CN 202010404397A CN 111596686 B CN111596686 B CN 111596686B
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flying
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alpha
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CN111596686A (en
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李海燕
李静
韦俊宝
周源
方登建
董海迪
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Naval University of Engineering PLA
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The embodiment of the invention provides a preset performance control method for a longitudinal system of a hypersonic aircraft, which comprises the following steps: an error function of the flying speed V and an error function of the flying height h of the aircraft are respectively constructed, and corresponding transformedError function S of the flight speed1And the error function S of the flying height2(ii) a Designing a controllable portion alpha of the higher derivative of the flying speed V of an aircraftvAnd a controllable fraction alpha of the higher derivative of the flying height hhSo that S1And S2Is bounded; according to alphavAnd alphahAnd under the condition that the control direction of the aircraft is unknown, the control quantity of the aircraft is obtained, and the aircraft is controlled. The control method and the control device can realize the preset performance control of the longitudinal system of the hypersonic aircraft under the condition that the control direction is unknown.

Description

Method for controlling preset performance of longitudinal system of hypersonic aircraft
Technical Field
The invention belongs to the technical field of control, and particularly relates to a preset performance control method for a longitudinal system of a hypersonic aircraft.
Background
For aircraft systems with unknown control directions, there are two main methods for achieving control.
The first method is the Nussbaum gain method, which is applied to various different forms of systems, such as adaptive systems, strict feedback nonlinear systems, etc.; the second method is to directly estimate the unknown parameters of the direction, but the method is very limited and needs to be established under strict assumption conditions.
Disclosure of Invention
In order to overcome the existing problems or at least partially solve the problems, an embodiment of the present invention provides a method for controlling preset performance of a longitudinal system of a hypersonic aircraft, where the method specifically includes:
an error function of the flying speed V and an error function of the flying height h of the aircraft are respectively constructed, and an error function S of the flying speed after transformation is constructed1And the error function S of the flying height2；
Design ofControllable component alpha of the higher derivative of the flying speed V of an aircraftvAnd a controllable fraction alpha of the higher derivative of the flying height hhSo that S1And S2Is bounded;
controllable fraction alpha of the higher derivative according to the flying speed VvAnd a controllable fraction alpha of the higher derivative of the flying height hhUnder the condition that the control direction of the aircraft is unknown, the control quantity of the aircraft is obtained;
and controlling the aircraft based on the control quantity.
Preferably, in the method, the error function of the flying speed V and the error function of the flying height h of the aircraft are constructed separately, and the error function S of the transformed flying speed is constructed1And the error function S of the flying height2The method specifically comprises the following steps:
calculating the higher derivative of the flying speed V of the aircraft, and extracting the controllable part alpha in the higher derivativevAccording to the controllable part alphavConstructing an error function e of the flying speed V of an aircraftv＝V-VdWhere V is the actual flying speed of the aircraft, VdIs the desired value of the flying speed;
according to error function evConstructing slip-form surfaces s of a airspeed subsystemvAccording to the slip form surface svConstructing an error transformation function e of the flight speed V1And the transformed error function S1；
Calculating the high-order derivative of the flying height h of the aircraft, and extracting the controllable part alpha in the high-order derivativehAccording to the controllable part alphahConstructing an error function e of the altitude h of an aircrafth＝h-hdWhere h is the actual flight altitude of the aircraft, hdA desired value for the flight altitude;
according to error function ehSlip form surface s for constructing flying height subsystemhAccording to the slip form surface shConstructing an error transformation function e of the flying height h2And the transformed error function S2。
Preferably, in the method, the flight of said aircraftControllable fraction alpha of the higher derivative of the velocity VvExpressed as:
αv＝b11βc+b12δe；
wherein, betacFor inputting a command signal for the fuel equivalence ratio beta, deltaeIs the elevator deflection angle;
calculating evThird derivative of (d):
Figure BDA0002490732220000021
wherein f isvIs a calculable value;
determining the sliding mode surface of the flight speed subsystem of the aircraft as follows:
Figure BDA0002490732220000022
wherein λ isvIs a constant;
constructing an error transformation function e of the flight speed V1Comprises the following steps:
e1＝sv+ksv∫svdt；
wherein k isIvIs a constant greater than 0, ksvIs a constant greater than 0, and kIvAnd ksvAre all design parameters;
defining an error transformation function as
Figure BDA00024907322200000310
Wherein the content of the first and second substances,
Figure BDA0002490732220000039
for a predetermined performance function, phi is a smooth, strongly increasing and reversible function, e1And S1The derivative of (c) is:
Figure BDA0002490732220000031
Figure BDA0002490732220000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002490732220000033
wherein the content of the first and second substances,
Figure BDA0002490732220000034
Figure BDA0002490732220000035
where ρ is the air density, V is the flight speed, S is the wing area, and ω isnIs the natural oscillation frequency, m is the aircraft mass, alpha is the angle of attack,
Figure BDA0002490732220000036
for the mean aerodynamic chord length of the wing, IyyIs moment of inertia, T is thrust, and D is resistance;
ce＝0.0292
Figure BDA0002490732220000037
preferably, in the method, the controllable part α of the higher derivative of the height of flight h of the aircraft is a variablehExpressed as:
αh＝b21βc+b22δe；
wherein, betacFor inputting a command signal for the fuel equivalence ratio beta, deltaeIs the elevator deflection angle;
calculating ehFourth derivative of (d):
Figure BDA0002490732220000038
wherein f ishIs a calculable value;
determining the sliding mode surface of the flying height subsystem of the aircraft as follows:
Figure BDA0002490732220000041
wherein λ ishIs a constant;
constructing an error transformation function e of the flight speed h2Comprises the following steps:
e2＝sh+ksh∫shdt；
wherein k isIhIs a constant greater than 0, kshIs a constant greater than 0, and kIhAnd kshAre all design parameters;
defining an error transformation function as
Figure BDA00024907322200000410
Wherein the content of the first and second substances,
Figure BDA00024907322200000411
for a predetermined performance function, phi is a smooth, strongly increasing and reversible function, e2And S2Is a derivative of
Figure BDA0002490732220000042
Figure BDA0002490732220000043
In the formula (I), the compound is shown in the specification,
Figure BDA0002490732220000044
wherein the content of the first and second substances,
Figure BDA0002490732220000045
Figure BDA0002490732220000046
where ρ is the air density, V is the flight velocity, S is the wing area, ω isnIs the natural oscillation frequency, m is the aircraft mass, alpha is the angle of attack, gamma is the ballistic inclination,
Figure BDA0002490732220000047
for the mean aerodynamic chord length of the wing, IyyIs rotational inertia, T is thrust, L is lift, and D is resistance;
ce＝0.0292
Figure BDA0002490732220000048
preferably, in the method, the controllable portion α of the higher derivative of the flying speed V of the design aircraft isvSo that S1The bounding includes:
design of
Figure BDA0002490732220000049
In the formula, k1＞0，ksv> 0 is a design parameter that is,
Figure BDA0002490732220000051
defining the Lyapunov function:
Figure BDA0002490732220000052
then there are:
Figure BDA0002490732220000053
general formula
Figure BDA0002490732220000054
Substitution intoThe above formula can be obtained:
Figure BDA0002490732220000055
determination of S1Is bounded.
Preferably, in the method, the controllable part α of the higher derivative of the flying height h of the design aircraft is a variablehSo that S2The bounding includes:
design of
Figure BDA0002490732220000056
In the formula, k2＞0，ksh> 0 is a design parameter that is,
Figure BDA0002490732220000057
selecting a Lyapunov function as
Figure BDA0002490732220000058
Then there are:
Figure BDA0002490732220000059
will be a formula
Figure BDA00024907322200000510
Substituting the above formula can obtain:
Figure BDA00024907322200000511
determination of S1And S2Is bounded.
Preferably, in the method, said controllable portion α of the higher derivative according to the flight speed V isvAnd control of the higher derivative of the flight height hPart alphahIn the case where the control direction of the aircraft is unknown, the determining the control quantity of the aircraft includes:
at b11、b12、b21And b22When the sign is unknown, let the control quantity u be [ beta ]c,δe]U is calculated using the following formula:
u＝N(ζn)ηn；
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002490732220000061
ηn＝[αv αh]T，N(ζn) Is a function of the Nussbaum,
Figure BDA0002490732220000062
rn11and rn22Is a constant to be given.
The embodiment of the invention provides a preset performance control method for a longitudinal system of a hypersonic aircraft, which is implemented by constructing an error function S of a flight speed1And the error function S of the flying height2Determining the energy of S1And S2Controllable fraction alpha of the higher derivative of the bounded flight speedvAnd a controllable fraction alpha of the higher derivative of the flight heighthBased on the determination of alphavAnd alphahAnd finally, controlling the aircraft according to the control quantity, realizing preset performance tracking under the condition that the control direction is unknown, and further keeping the aircraft in a stable state in the flight process.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief description will be given below of the drawings required for the embodiments or the technical solutions in the prior art, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a schematic overall flow chart of a preset performance control method for a longitudinal system of a hypersonic aircraft according to an embodiment of the present invention;
FIG. 2 is a graph illustrating an angle of attack tracking simulation provided by an embodiment of the present invention;
FIG. 3 is a graph of a simulation of height error provided by an embodiment of the present invention;
FIG. 4 is a graph illustrating a simulation of a flight speed error function according to an embodiment of the present invention;
FIG. 5 shows δ according to an embodiment of the present inventioneThe simulation curve graph of (2);
FIG. 6 is a graph of input fuel equivalence ratio β provided by 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 inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
Fig. 1 is a schematic overall flow chart of a method for controlling a preset performance of a longitudinal system of a hypersonic aircraft according to an embodiment of the present invention, and referring to fig. 1, the method for controlling the preset performance of the longitudinal system of the hypersonic aircraft according to the embodiment of the present invention includes:
step 110, respectively constructing an error function of the flying speed V and an error function of the flying height h of the aircraft, and constructing an error function S of the flying speed after transformation1And the error function S of the flying height2；
Step 120, designing a controllable component alpha of the higher derivative of the flying speed V of the aircraftvAnd a controllable fraction alpha of the higher derivative of the flying height hhSo that S1And S2Is bounded;
step 130, depending on the controllable fraction α of the higher derivative of the flying speed VvAnd a controllable part of the higher derivative of the flying height hαhUnder the condition that the control direction of the aircraft is unknown, the control quantity of the aircraft is obtained;
and 140, controlling the aircraft based on the control quantity.
It can be understood that an error function of the flight speed V of the aircraft is calculated according to a dynamic model description equation of a longitudinal system of the hypersonic aircraft and according to the actual flight speed and the expected flight speed of the aircraft in the dynamic model description equation; and calculating an error function of the flying height h of the aircraft according to the actual flying height and the expected flying height of the aircraft.
Constructing an error function S of the flying speed after transformation according to the error function of the flying speed V and the error function of the flying height h of the aircraft1And the error function S of the flying height2。
Respectively calculating the high-order derivative of the flying speed V and the high-order derivative of the flying height h of the hypersonic speed aircraft according to a dynamic model description equation of a longitudinal system of the hypersonic speed aircraft, and designing the controllable parts of the high-order derivatives of the flying speed V and the flying height h to ensure that an error function S of the flying speed after transformation1And the error function S of the flying height2Are bounded.
And according to the designed controllable part of the high-order derivative of the flying speed V and the high-order derivative of the flying height h, under the condition that the control direction of the aircraft is unknown, the control quantity of the aircraft is obtained, and the aircraft is controlled according to the control quantity.
By adopting the control design of the controllable part of the high-order derivative of the flying speed V and the high-order derivative of the flying height h provided by the embodiment of the invention, the preset performance tracking can be realized under the condition that the control direction of the aircraft is unknown, and the aircraft can be kept in a stable state in the flying process.
As an alternative embodiment, an error function of the flying speed V and an error function of the flying height h of the aircraft are constructed separately, and an error function S of the transformed flying speed is constructed1And the error function S of the flying height2The method comprises the following steps:
calculating the higher derivative of the flying speed V of the aircraft, and extracting the controllable part alpha in the higher derivativevAccording to the controllable part alphavConstructing an error function e of the flying speed V of an aircraftv＝V-VdWhere V is the actual flying speed of the aircraft, VdIs the desired value of the flying speed;
according to error function evConstructing slip-form surfaces s of a airspeed subsystemvAccording to the slip form surface svConstructing an error transformation function e of the flight speed V1And the transformed error function S1；
Calculating the high-order derivative of the flying height h of the aircraft, and extracting the controllable part alpha in the high-order derivativehAccording to the controllable part alphahConstructing an error function e of the altitude h of an aircrafth＝h-hdWhere h is the actual flight altitude of the aircraft, hdA desired value for the flight altitude;
according to error function ehSlip form surface s for constructing flying height subsystemhAccording to the slip form surface shConstructing an error transformation function e of the flying height h2And the transformed error function S2。
It will be appreciated that the higher order derivatives of the aircraft's flight speed V and the higher order derivatives of the altitude h are calculated from the hypersonic aircraft longitudinal system dynamics model description equations. For example, the dynamics model of the longitudinal system of the air-breathing hypersonic aircraft can be described by the following equation:
Figure BDA0002490732220000091
Figure BDA0002490732220000092
Figure BDA0002490732220000093
Figure BDA0002490732220000094
Figure BDA0002490732220000095
wherein V is the flying speed of the aircraft, T is the thrust, alpha is the angle of attack, D is the drag, M is the aircraft mass, mu is the gravity constant, gamma is the ballistic inclination, L is the lift, h is the flying height, q is the pitch angular velocity, M is the aircraft massyyFor pitching moment, IyyIs the moment of inertia. Lift L, drag D, thrust T and pitching moment MyyThe method comprises the following steps:
Figure BDA0002490732220000096
Figure BDA0002490732220000097
Figure BDA0002490732220000098
Figure BDA0002490732220000099
r＝h+RE(ii) a (formula 10)
In formulas 6-10, ρ is the air density, S is the wing area, CLIs the coefficient of lift, CDIs a coefficient of resistance, CTIn order to be the thrust coefficient,
Figure BDA00024907322200000910
for the mean aerodynamic chord length of the wing, REIs the radius of the earth, deltaeIs the elevator yaw angle and is the input to the system.
The correlation coefficients in equations 6-10 are as follows:
CL0.6203 α; (formula 11)
CD＝0.6450α2+0.0043378 α + 0.003772; (formula 12)
Figure BDA0002490732220000101
CM(α)＝-0.035α2+0.036617α+5.3261×10-6(ii) a (formula 14)
Figure BDA0002490732220000102
CM(δe)＝ce(δe- α); (formula 16)
ce0.0292. (formula 17)
The engine dynamics equation can be described by:
Figure BDA0002490732220000103
in the formulas 11-18, β is the input fuel equivalence ratio and is the input amount of the system,
Figure BDA00024907322200001011
as damping coefficient, ωnIs the natural oscillation frequency, betacA command signal of β.
The above equation is a description equation of a dynamics model of a longitudinal system of the air-breathing hypersonic aircraft, and two assumptions are made in the longitudinal system of the aircraft:
assume that 1: neglecting elevator yaw angle δ in lift LeThe effect thereon;
assume 2: the change of the flying speed V of the hypersonic aircraft is slow, and the hypersonic aircraft belongs to slow variables compared with the incidence angle alpha and the pitch angle speed q.
According to the dynamic model description equation of the longitudinal system of the aircraft, solving the various derivatives of the flying speed V and the flying height h of the aircraft to obtain:
Figure BDA0002490732220000104
Figure BDA0002490732220000105
Figure BDA0002490732220000106
Figure BDA0002490732220000107
Figure BDA0002490732220000108
Figure BDA0002490732220000109
Figure BDA00024907322200001010
Figure BDA0002490732220000111
Figure BDA0002490732220000112
in the formulae 19 to 27, xT＝[Vγαβh]，f1、f2Are respectively concise expressions of right polynomials with equal signs of formula 1 and formula 2,
Figure BDA0002490732220000113
Figure BDA0002490732220000114
wherein, ω is1，Ω2，π1And pi2Given below:
Figure BDA0002490732220000115
Figure BDA0002490732220000116
Ω2＝[ω21 ω22 ω23 ω24 ω25]. (equation 30)
In the formula 30, the first step is,
Figure BDA0002490732220000121
Figure BDA0002490732220000122
Figure BDA0002490732220000123
Figure BDA0002490732220000124
Figure BDA0002490732220000131
Π2＝[π21 π22 π23 π24 π25]. (equation 36)
In the formula 36, the process is as follows,
Figure BDA0002490732220000132
Figure BDA0002490732220000133
Figure BDA0002490732220000141
Figure BDA0002490732220000142
Figure BDA0002490732220000143
as an alternative example, the second derivatives of α and β are included in the above equations 19 to 24, and can be decomposed into terms with and without control, specifically expressed as:
Figure BDA0002490732220000144
Figure BDA0002490732220000145
in the formula (I), the compound is shown in the specification,
Figure BDA0002490732220000146
Figure BDA0002490732220000147
order to
Figure BDA0002490732220000151
Then
Figure BDA0002490732220000152
And h(4)Can be expressed as:
Figure BDA0002490732220000153
h(4)＝fh+b21βc+b22δe(ii) a (formula 47)
In the formula (I), the compound is shown in the specification,
Figure BDA0002490732220000154
Figure BDA0002490732220000155
Figure BDA0002490732220000156
Figure BDA0002490732220000157
Figure BDA0002490732220000158
Figure BDA0002490732220000159
Figure BDA00024907322200001510
Figure BDA00024907322200001511
Figure BDA00024907322200001512
introduction 1: consider a second order differentiator:
Figure BDA00024907322200001513
wherein f (t) is an input signal, z1Is the first differential of f (t), if a suitable parameter λ is selected0And λ1Then equation 58 holds for a finite time and dynamic system equation 57 stabilizes for a finite time.
Figure BDA0002490732220000161
As an alternative embodiment, the uncontrollable part and the controllable part are included in the formula 46, wherein the controllable part α of the higher derivative of the flying speed V of the aircraft is the controllable partvExpressed as:
αv＝b11βc+b12δe(ii) a (formula 59)
Wherein, betacAnd deltaeIs a control quantity.
According to ev＝V-VdI.e. the error function between the actual flying speed and the desired speed of the aircraft, e is calculatedvThird derivative of (d):
Figure BDA0002490732220000162
the sliding mode surface of the flight speed subsystem of the aircraft is as follows:
Figure BDA0002490732220000163
further constructing an error transformation function e according to the sliding mode surface of the flight speed subsystem1Comprises the following steps:
e1＝sv+ksv∫svdt; (formula 62)
Defining an error transformation function as
Figure BDA0002490732220000169
，e1And S1The derivative of (c) is:
Figure BDA0002490732220000164
Figure BDA0002490732220000165
in the formula (I), the compound is shown in the specification,
Figure BDA0002490732220000166
as an alternative embodiment, the controllable fraction α of the higher derivative of the flying speed V of the aircraft is designedvSo that S1The bounding includes:
design of
Figure BDA0002490732220000167
In the formula, k1＞0，ksvThe value > 0 is a design parameter,
Figure BDA0002490732220000168
defining the Lyapunov function:
Figure BDA0002490732220000171
then there are:
Figure BDA0002490732220000172
substituting equation 65 into equation 68 yields:
Figure BDA0002490732220000173
as an alternative embodiment, likewise, equation 47 also includes an uncontrollable part and a controllable part, where the controllable part α of the higher derivative of the altitude h of the aircraft is a controllable parthExpressed as:
αh＝b21βc+b22δe(ii) a (formula 70)
According to eh＝h-hdI.e. the error function between the actual and the desired flying height of the aircraft, e is calculatedhFourth derivative of (d):
Figure BDA0002490732220000174
the slip form surface of the flight height subsystem of the aircraft is:
Figure BDA0002490732220000175
error transformation function e of flight speed h2Comprises the following steps:
e2＝sh+ksh∫shdt; (equation 73)
Defining an error transformation function as
Figure BDA0002490732220000176
e2And S2Is a derivative of
Figure BDA0002490732220000177
Figure BDA0002490732220000178
In the formula (I), the compound is shown in the specification,
Figure BDA0002490732220000179
as an alternative embodiment, the controllable part α of the higher derivative of the flying height h of the aircraft is designedhSo that it is bounded including:
design of
Figure BDA0002490732220000181
In the formula, k2＞0，ksh> 0 is a design parameter that is,
Figure BDA0002490732220000182
selecting a Lyapunov function as
Figure BDA0002490732220000183
Then there are:
Figure BDA0002490732220000184
substituting equation 76 into equation 79 above yields:
Figure BDA0002490732220000185
from the above equations 69 and 80, S1、S2Are bounded.
The preset performance and the error transformation function of the aircraft longitudinal system are described below:
assuming e as tracking error, preset performance
Figure BDA0002490732220000186
Is a positive decreasing function, and satisfies for all t ≧ 0:
Figure BDA0002490732220000187
wherein, the sigma is more than 0 and less than or equal to 1,
Figure BDA0002490732220000188
is the maximum allowable value of the steady-state error.
The constraints of equation 81 are converted to an unconstrained form by an error transformation function:
Figure BDA0002490732220000189
wherein S is the transformed error function, phi (S) is a smooth, severely increased and reversible function, and satisfies the following properties:
Figure BDA00024907322200001810
Figure BDA00024907322200001811
from equation 84, if S is bounded, then equation 83 holds. In addition, by
Figure BDA0002490732220000191
And equation 82, when e (0) > 0,
Figure BDA0002490732220000192
when e (0) < 0
Figure BDA0002490732220000193
Equation 81 holds. Therefore, as long as S ∈ L∞We can achieve the preset performance.
Theorem 2 holds for any constant η > 0 and variable p ∈ R
Figure BDA0002490732220000194
Lesion 3, define set
Figure BDA0002490732220000195
Then to any
Figure BDA0002490732220000198
The following inequality holds
[1-2tanh2(S/ε)]Is less than 0. (equation 86)
As can be seen from the above, S1、S2Are all bounded, then e1、e2The preset performance tracking is realized, namely the actual flying speed of the designed aircraft meets the expected flying speed, and the actual flying height of the aircraft meets the expected flying height.
As an alternative embodiment, the controllable fraction α of the higher derivative according to the flight speed VvAnd a controllable fraction alpha of the higher derivative of the flying height hhIn a case where the control direction of the aircraft is unknown, the determining the control quantity of the aircraft includes:
at b11、b12、b21And b22When the sign is unknown, let the control quantity u be [ beta ]c,δe]U is calculated using the following formula:
u＝N(ζn)ηn(ii) a (formula 87)
Wherein the content of the first and second substances,
Figure BDA0002490732220000196
ηn＝[αv αh]T，N(ζn) Is a function of the Nussbaum,
Figure BDA0002490732220000197
rn11and rn22Is a constant to be given.
For the systems (represented by equations 46 and 47, in the presence of control direction unknowns, if the control law is chosen according to equations 65, 76 and 87, then all signals of the aircraft longitudinal system are bounded and achieve the preset tracking performance.
The method for controlling the preset performance of the longitudinal system of the hypersonic aircraft provided by the embodiment of the invention is subjected to simulation verification as follows:
in order to verify the effectiveness of the preset performance control method, aiming at a longitudinal dynamics model system (represented by formula 46 and formula 47) of an air-breathing hypersonic aircraft, the embodiment of the invention provides a process for simulating an inner ring control system of the hypersonic aircraft, wherein the control target is to enable the aircraft to track a given attack angle instruction, and the tracking control has preset performance.
The initial conditions for the simulation were set as follows: 2900 for V, 3.5 for α (0), 0.6 for q, and αdThe relevant parameters of the preset performance controller are designed as follows: k is a radical of1＝0.01，ksv＝10.9，k2＝0.001，ksh＝86.5，kIv＝0.001，kIh＝0.01，
Figure BDA0002490732220000201
Figure BDA0002490732220000202
rn11＝0.0005，rn22＝0.0005。
Fig. 2 is a simulation curve of angle of attack tracking in a simulation result provided by an embodiment of the present invention, fig. 3 is a simulation curve of altitude error in a simulation result provided by an embodiment of the present invention, fig. 4 is a simulation curve of a flight speed error function in a simulation result provided by an embodiment of the present invention, and fig. 5 is a simulation curve of δ in a simulation result provided by an embodiment of the present inventioneFig. 6 is a graph of input fuel equivalence ratio β in the simulation results provided by the embodiment of the present invention. Thus, the simulation results are shown in FIGS. 2-6, where FIG. 2 depicts the angle of attack α tracking the desired signal αdWherein the dashed line is the desired signal alphadThe solid line is the actual angle of attack α, FIG. 2The dotted line in (B) is coincident with the solid line and is visually a solid line; FIG. 3 depicts height h tracking desired height hdAnd corresponding predetermined performance curve, wherein the solid line tracks the expected height h for the height hdError curve e ofhThe dotted line is the desired height hd(ii) a FIG. 4 depicts velocity V tracking desired velocity VdAnd a corresponding predetermined performance curve, wherein the solid line tracks the desired velocity v for the velocity vdError curve e ofvThe dotted line is the desired velocity vd(ii) a FIG. 5 depicts the rudder deflection angle δeFig. 6 depicts the input fuel equivalence ratio beta curve, from which it can be seen that the angle of attack tracks well the desired angle of attack signal, the velocity tracks well the desired velocity signal, and ehAnd evThe preset performance is realized, and the effectiveness of the designed controller is verified. In addition, as can be seen from fig. 2 to 6, the designed controller well solves the design problem under the condition of position control direction, the performance of the system is not influenced, and tracking is still well realized.
The method for controlling the preset performance of the longitudinal system of the hypersonic aircraft provided by the embodiment of the invention is researched aiming at the inversion preset performance control method of the nonlinear system under the condition that the control direction is unknown, the control of the hypersonic aircraft is designed by combining a Nussbaum gain technology and a preset performance inversion control technology, the non-matching uncertainty existing in the longitudinal system of the hypersonic aircraft is processed by the inversion control technology, and the problem that the control direction is unknown is processed by using the Nussbaum gain method. Then, the design of the system controller is completed by applying the Lyapunov stability theory, the preset performance control technology and the robust technology. Finally, the method is applied to the design of a longitudinal control system of the supersonic aircraft, the inversion design concept of the preset performance of the double integral sliding mode is further provided, and the stability of the designed longitudinal system of the aircraft is ensured.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (5)

1. A preset performance control method for a longitudinal system of a hypersonic aircraft is characterized by comprising the following steps:
an error function of the flying speed V and an error function of the flying height h of the aircraft are respectively constructed, and an error function S of the flying speed after transformation is constructed1And the error function S of the flying height2；
Designing a controllable component alpha of the higher derivative of the flying speed V of an aircraftvAnd a controllable fraction alpha of the higher derivative of the flying height hhSo that S1And S2Is bounded;
controllable fraction alpha of the higher derivative according to the flying speed VvAnd a controllable part alpha of the higher derivative of the flying height hhUnder the condition that the control direction of the aircraft is unknown, the control quantity of the aircraft is obtained;
controlling the aircraft based on the control quantity;
respectively constructing an error function of the flying speed V and an error function of the flying height h of the aircraft, and constructing an error function S of the flying speed after transformation1And the error function S of the flying height2The method comprises the following steps:
calculating the higher derivative of the flying speed V of the aircraft, and extracting the controllable part alpha in the higher derivativevAccording to the controllable part alphavConstructing an error function e of the flying speed V of an aircraftv＝V-VdWhere V is the actual flying speed of the aircraft, VdIs the desired value of the flying speed;
according to error function evConstructing slip-form surfaces s of a airspeed subsystemvAccording to the slip form surface svConstructing an error transformation function e of the flight speed V1And the transformed error function S1；
Calculating the high-order derivative of the flying height h of the aircraft, and extracting the controllable part alpha in the high-order derivativehAccording to the controllable part alphahConstructing an error function e of the altitude h of an aircrafth＝h-hdWhere h is the actual flight altitude of the aircraft, hdA desired value for the flight altitude;
according to error function ehSlip form surface s for constructing flying height subsystemhAccording to the slip form surface shConstructing an error transformation function e of the flying height h2And the transformed error function S2；
Controllable portion alpha of the higher derivative of the flying speed V of the aircraftvExpressed as:
αv＝b11βc+b12δe；
wherein beta iscFor inputting a command signal for the fuel equivalence ratio beta, deltaeIs the elevator deflection angle;
calculating evThird derivative of (d):
Figure FDA0003582606920000011
wherein f isvIs a calculable value;
determining the sliding mode surface of the flight speed subsystem of the aircraft as follows:
Figure FDA0003582606920000021
wherein λ isvIs a constant;
constructing an error transformation function e of the flying speed V1Comprises the following steps:
Figure FDA0003582606920000022
wherein k isIvIs a constant greater than 0, ksvIs a constant greater than 0, and kIvAnd ksvAre all design parameters;
defining an error transformation function as
Figure FDA0003582606920000023
Wherein the content of the first and second substances,
Figure FDA0003582606920000024
for a predetermined performance function, phi is a smooth, strongly increasing and reversible function, e1And S1The derivative of (c) is:
Figure FDA0003582606920000025
Figure FDA0003582606920000026
in the formula (I), the compound is shown in the specification,
Figure FDA0003582606920000027
wherein the content of the first and second substances,
Figure FDA0003582606920000028
Figure FDA0003582606920000029
where ρ is the air density, V is the flight velocity, S is the wing area, ω isnIs the natural oscillation frequency, m is the aircraft mass, alpha is the angle of attack,
Figure FDA00035826069200000212
for the mean aerodynamic chord length of the wing, IyyIs moment of inertia, T is thrust, and D is resistance；
ce＝0.0292
Figure FDA00035826069200000210
2. Control method according to claim 1, characterized in that the controllable fraction α of the higher derivative of the flying height h of the aircraft is ahExpressed as:
αh＝b21βc+b22δe；
wherein beta iscFor inputting a command signal for the fuel equivalence ratio beta, deltaeIs the elevator declination;
calculating ehFourth derivative of (d):
Figure FDA00035826069200000211
wherein f ishIs a calculable value;
determining a sliding mode surface of a flying height subsystem of the aircraft as follows:
Figure FDA0003582606920000031
wherein λ ishIs a constant;
constructing an error transformation function e of the flight speed h2Comprises the following steps:
e2＝sh+ksh∫shdt；
wherein k isIhIs a constant greater than 0, kshIs a constant greater than 0, and kIhAnd kshAre all design parameters;
defining an error transformation function as
Figure FDA0003582606920000032
Wherein，
Figure FDA0003582606920000033
For a predetermined performance function, phi is a smooth, strongly increasing and reversible function, e2And S2Is a derivative of
Figure FDA0003582606920000034
Figure FDA0003582606920000035
In the formula (I), the compound is shown in the specification,
Figure FDA0003582606920000036
wherein the content of the first and second substances,
Figure FDA0003582606920000037
Figure FDA0003582606920000038
where ρ is the air density, V is the flight velocity, S is the wing area, ω isnIs the natural oscillation frequency, m is the aircraft mass, alpha is the angle of attack, gamma is the ballistic inclination,
Figure FDA0003582606920000039
for the mean aerodynamic chord length of the wing, IyyIs rotational inertia, T is thrust, L is lift, and D is resistance;
ce＝0.0292
Figure FDA00035826069200000310
3. root of herbaceous plantControl method according to claim 1, characterized in that the controllable part α of the higher derivative of the flying speed V of the design aircraft is avSo that S1The method comprises the following steps:
design of
Figure FDA00035826069200000311
In the formula, k1＞0，ksv> 0 is a design parameter that is,
Figure FDA00035826069200000312
defining the Lyapunov function:
Figure FDA00035826069200000313
then there are:
Figure FDA0003582606920000041
general formula
Figure FDA0003582606920000042
Substitution into the above formula yields:
Figure FDA0003582606920000043
determination of S1Is bounded.
4. A control method according to claim 3, characterized in that the controllable fraction α of the higher derivative of the flying height h of the design aircraft is ahSo that S2The bounding includes:
design of
Figure FDA0003582606920000044
In the formula, k2＞0，kshThe value > 0 is a design parameter,
Figure FDA0003582606920000045
selecting a Lyapunov function as
Figure FDA0003582606920000046
Then there are:
Figure FDA0003582606920000047
will be a formula
Figure FDA0003582606920000048
Substituting the above formula can obtain:
Figure FDA0003582606920000049
determination of S1And S2Is bounded.
5. Control method according to claim 3 or 4, characterized in that the controllable fraction a of the higher derivative according to the flying speed V isvAnd a controllable fraction alpha of the higher derivative of the flying height hhIn the case where the control direction of the aircraft is unknown, the determining the control quantity of the aircraft includes:
at b11、b12、b21And b22When the sign is unknown, let the control quantity u be [ beta ]c,δe]U is calculated using the following formula:
u＝N(ζn)ηn；
wherein the content of the first and second substances,
Figure FDA00035826069200000410
ηn＝[αv αh]T，N(ζn) Is a function of the number of Nussbaum,
Figure FDA00035826069200000411
Figure FDA00035826069200000412
rn11and rn22Is a constant to be given.
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