CN113885552A - Preset performance control method and system for hypersonic aircraft - Google Patents

Preset performance control method and system for hypersonic aircraft Download PDF

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CN113885552A
CN113885552A CN202111021060.8A CN202111021060A CN113885552A CN 113885552 A CN113885552 A CN 113885552A CN 202111021060 A CN202111021060 A CN 202111021060A CN 113885552 A CN113885552 A CN 113885552A
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CN113885552B (en
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李海燕
韦俊宝
李静
方登建
袁胜智
胡云安
王斌
吴佳栋
高飞
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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
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
    • G05D1/106—Change initiated in response to external conditions, e.g. avoidance of elevated terrain or of no-fly zones

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Abstract

The invention provides a preset performance control method and a preset performance control system for a hypersonic aircraft, wherein the method comprises the following steps: constructing a preset performance function of the hypersonic aircraft based on the tracking error; constructing a speed subsystem controller according to a preset performance function and a saturation function; constructing a height subsystem controller by an inversion control method according to a preset performance function and a limited instruction filter; acquiring an initial state value of the hypersonic aircraft at the current moment, and performing tracking control according to a speed subsystem controller and a height subsystem controller; the saturation function is constructed according to the fuel equivalence ratio and the elevator deflection angle; the limited instruction filter is constructed based on the input saturation problem and according to the ideal control input value of the deflection angle of the elevator. On the basis of improving the steady-state and transient performance of the system, the output tracking error has smaller overshoot; the amplitude and the speed of the system input are ensured to meet the limited requirements, and good tracking performance is provided.

Description

Preset performance control method and system for hypersonic aircraft
Technical Field
The invention relates to the technical field of automatic control, in particular to a preset performance control method and system for a hypersonic aircraft.
Background
The hypersonic aircraft is a novel aircraft flying in a near space at a speed of more than 5 Mach, and has great application potential in both civil and military fields. Currently, research on hypersonic aircraft control techniques has yielded certain results. Considering that the hypersonic flight vehicle has high requirements on the dynamic performance of the control system when flying at high speed. The method for presetting the performance has the unique advantage of simultaneously considering the transient performance and the steady-state performance of the system, and is widely applied to the control research of the hypersonic aircraft.
In practical control systems, the control force provided by the actuator is limited. The problem of output saturation of the actuating mechanism is easily caused due to the high-altitude flight of the aircraft and the influence of the external environment. Once the system is saturated, the ideal control law cannot be effectively executed, which causes a large deviation in instruction tracking and even seriously affects the stability of the system.
Therefore, a preset performance control method and system for hypersonic flight vehicles are needed to solve the above problems.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a preset performance control method and system for a hypersonic aircraft.
The invention provides a preset performance control method for a hypersonic aircraft, which comprises the following steps:
constructing a preset performance function of the hypersonic aircraft based on the tracking error;
constructing a speed subsystem controller according to the preset performance function and the saturation function;
constructing a height subsystem controller by an inversion control method according to the preset performance function and the limited instruction filter;
acquiring an initial state value of the hypersonic aerocraft at the current moment, and performing tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller;
the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
According to the preset performance control method for the hypersonic aircraft, provided by the invention, the construction of the preset performance function of the hypersonic aircraft based on the tracking error comprises the following steps:
the method comprises the following steps of constructing a preset performance function of the hypersonic aircraft by taking the overshoot minimization of the tracking error of the hypersonic aircraft as a target, wherein the preset performance function is as follows:
Figure BDA0003241394980000021
Figure BDA0003241394980000022
p2(t)＜e(t)＜p1(t)；
wherein ,p1(t) and p2(t) represents a preset performance function, e (0) represents a tracking error at an initial time,
Figure BDA0003241394980000023
representing an existing performance function;
Figure BDA0003241394980000024
and mu is a constant number of times,
Figure BDA0003241394980000025
in the case of a steady-state value,
Figure BDA0003241394980000026
and is
Figure BDA0003241394980000027
μ＞0。
According to the preset performance control method for the hypersonic aircraft, provided by the invention, the speed subsystem controller is constructed according to the preset performance function and the saturation function, and the method comprises the following steps:
according to the preset performance function, constructing a speed performance function of the hypersonic aircraft, wherein the speed performance function is as follows:
Figure BDA0003241394980000031
Figure BDA0003241394980000032
υV＝eV-ξV；
eV＝V-Vd；
pV2＜υV＜pV1；
wherein ,pV1(t) and pV2(t) represents a preset performance function, upsilon, constructed for the aircraft velocity, VVIndicating a velocity compensation error, eVIndicating speed tracking error, ξVRepresenting an auxiliary variable to be designed, VdRepresenting a speed command, V representing an aircraft speed; mu.sV、
Figure BDA0003241394980000038
And
Figure BDA0003241394980000039
is a speed performance function parameter; sigmaVIs greater than 0 and is a constant;
and carrying out error transformation on the speed performance function to obtain a speed error transformation function of the hypersonic aircraft, wherein the speed error transformation function is as follows:
Figure BDA0003241394980000033
Figure BDA0003241394980000034
wherein ,εVRepresenting a velocity transformation error;
based on a rigid body model of longitudinal motion of the hypersonic aircraft, a speed subsystem model is obtained as follows:
Figure BDA0003241394980000035
Figure BDA0003241394980000036
Figure BDA0003241394980000037
where Φ represents a fuel equivalence ratio, d1Representing a first disturbance term, a representing an angle of attack, D representing a drag, g representing a gravitational acceleration, gamma representing a track inclination, m representing a mass, T0(α) and TΦ(α) represents a thrust-related aerodynamic parameter;
according to the speed subsystem model, deriving the speed error transformation function, and according to the derived speed error transformation function, constructing a speed subsystem control law:
Figure BDA0003241394980000041
Figure BDA0003241394980000042
Figure BDA0003241394980000043
wherein ,ΦdRepresenting the desired control input value, k, of the fuel equivalence ratioV and λVIs a positive parameter of the number of the bits,
Figure BDA0003241394980000044
the first derivative of the velocity command is represented,
Figure BDA0003241394980000045
representing the first derivative, k, of an existing performance function parameterVξThe parameters of the auxiliary system are represented,
Figure BDA0003241394980000046
an estimate representing a first interference term;
and constructing a speed subsystem controller according to the speed subsystem control law on the basis of a fuel equivalence ratio saturation function:
Figure BDA0003241394980000047
the fuel equivalence ratio saturation function is as follows:
Figure BDA0003241394980000048
wherein the constant phimax and ΦminRespectively the upper and lower limits of the fuel equivalence ratio phi amplitude.
According to the preset performance control method for the hypersonic aircraft provided by the invention, before the fuel equivalence ratio-based saturation function and the speed subsystem control law are constructed, the method further comprises the following steps:
according to the ideal control input value of the fuel equivalence ratio and the actual input value of the fuel equivalence ratio, a first auxiliary system is constructed for ensuring stable tracking when the fuel equivalence ratio is saturated, and the first auxiliary system comprises:
Figure BDA0003241394980000051
where Φ represents a fuel equivalence ratio actual input value.
According to the preset performance control method for the hypersonic aircraft provided by the invention, the height subsystem controller is constructed through an inversion control method according to the preset performance function and the limited instruction filter, and the method comprises the following steps:
according to the preset performance function, constructing an altitude performance function of the hypersonic aircraft, wherein the altitude performance function is as follows:
Figure BDA0003241394980000052
Figure BDA0003241394980000053
eh＝h-hd；
ph2＜eh＜ph1；
wherein ,ph1(t) and ph2(t) represents a preset performance function constructed for the aircraft altitude h, ehIndicating the altitude error, h the aircraft altitude, hdIndicating a height instruction, μh、
Figure BDA0003241394980000054
And
Figure BDA0003241394980000055
is a height performance function parameter; sigmahIs greater than 0 and is a constant;
and carrying out error transformation on the altitude performance function to obtain an altitude error transformation function of the hypersonic aircraft, wherein the altitude error transformation function is as follows:
Figure BDA0003241394980000056
Figure BDA0003241394980000057
wherein ,εhRepresenting a height transformation error;
based on a hypersonic aircraft longitudinal motion rigid body model, the obtained altitude subsystem model is as follows:
Figure BDA0003241394980000061
Figure BDA0003241394980000062
where V represents aircraft speed, γ represents track inclination, θ represents pitch angle, q represents pitch angle speed, d represents aircraft speed, and2representing a second interference term, d3Representing a third interference term, δeIndicating elevator yaw angle, L0 and LαRepresenting lift-related aerodynamic parameters, g representing gravitational acceleration, M representing mass, MT、M0(α) and
Figure BDA0003241394980000067
a parameter of interest representing the pitching moment, IyyRepresenting the moment of inertia;
constructing a first virtual control law gamma based on the altitude commanddAccording to said first virtual control law γdDefining track inclination error as eγ＝γ-γdAnd according to the height subsystem model, calculating the derivation of the track inclination error to obtain the derived track inclination error:
Figure BDA0003241394980000063
constructing a second virtual control law based on the track inclination error, and constructing the track inclination control law according to the second virtual control law and the derived track inclination error:
Figure BDA0003241394980000064
wherein ,kγIf the inclination angle is more than 0, the relevant parameters of the track inclination angle are obtained;
Figure BDA0003241394980000065
is d2Estimated value of eγRepresenting track inclination error, thetadIs the second virtual control law, χγ2Representing the first derivative
Figure BDA0003241394980000066
An estimated value of (d);
according to the second virtual control law thetadDefining the pitch angle error as eθ＝θ-θdAnd according to the height subsystem model, deriving the pitch angle error to obtain the derived pitch angle error:
Figure BDA0003241394980000071
constructing a third virtual control law based on the pitch angle error and the track inclination angle error, and constructing a pitch angle control law according to the third virtual control law and the derived pitch angle error:
Figure BDA0003241394980000072
wherein ,kθIf the pitch angle is more than 0, the pitch angle is a related design parameter; xiqIs an auxiliary variable to be designed; x is the number ofθ2For the second virtual control law derivative
Figure BDA0003241394980000073
An estimated value of (d);
defining a pitch rate error as eq＝q-qdThe pitch angle compensation error is upsilonq＝eq-ξqAnd according to the height subsystem model, carrying out derivation on the pitch angle compensation error to obtain a derived pitch angle compensation error:
Figure BDA0003241394980000074
wherein ,qdA pitch angle speed command;
based on an elevator deflection angle saturation function, constructing a limited instruction filter according to an ideal elevator deflection angle control input value, and obtaining an actual elevator deflection angle input value:
Figure BDA0003241394980000075
the elevator deflection angle saturation function is as follows:
Figure BDA0003241394980000081
Figure BDA0003241394980000082
wherein ,τδ and ωδBeing a positive parameter, δedFor ideal control input value of elevator deflection angle, constant deltamax and δminRespectively the rudder deflection angle deltaeUpper and lower limits of amplitude;
Figure BDA0003241394980000085
is the derivative of the elevator yaw angle;
Figure BDA0003241394980000086
constant psimax and ψminRespectively the rudder deflection angle deltaeUpper and lower limits of rate;
according to the ideal control input value of the elevator deflection angle and the actual input value of the elevator deflection angle, a second auxiliary system for counteracting the influence of input saturation is constructed:
Figure BDA0003241394980000083
and constructing an elevator deflection angle control law:
Figure BDA0003241394980000084
wherein ,kqIf the pitch angle is more than 0, the pitch angle is a related design parameter of the pitch angle speed;
Figure BDA0003241394980000087
is the third interference term d3Estimated value of χq2As derivatives of a third virtual control law
Figure BDA0003241394980000088
Estimated value of kqξ1 and kqξ2Auxiliary system parameters;
constructing a pitch angle speed compensation error control law according to the second auxiliary system, the elevator yaw angle control law and the derived pitch angle compensation error:
Figure BDA0003241394980000089
and constructing a height subsystem controller according to the track inclination angle control law, the pitch angle control law and the pitch angle speed compensation error control law.
According to the preset performance control method for the hypersonic aircraft provided by the invention, before the initial state value of the hypersonic aircraft at the current moment is obtained and the hypersonic aircraft is subjected to tracking control according to the speed subsystem controller and the altitude subsystem controller, the method further comprises the following steps:
based on the interference existing in the operation of the hypersonic aircraft, a second-order linear extended state observer is constructed and used for observing and compensating the interference, and the formula of the second-order linear extended state observer is as follows:
Figure BDA0003241394980000091
Figure BDA0003241394980000092
Figure BDA0003241394980000093
wherein ,
Figure BDA0003241394980000094
is an estimate of the speed V of the aircraft,
Figure BDA0003241394980000095
as an estimate of the track inclination y,
Figure BDA0003241394980000096
is an estimated value of pitch angle velocity q;
Figure BDA0003241394980000097
as interference term di(ii) an observed value of (i ═ 1,2, 3); lV1,lV2,lγ1,lγ2,lq1,lq2Are all positive parameters, ω0Representing the bandwidth of the observer, parameter ai3! I! (3-i)! (i ═ 1, 2); phi represents fuel equivalence ratio, theta represents pitch angle, q represents pitch angle speed, gamma represents track inclination angle, deltaeIndicating the elevator yaw angle.
The invention also provides a preset performance control system for a hypersonic aircraft, comprising:
the performance function building module is used for building a preset performance function of the hypersonic aircraft based on the tracking error;
the speed subsystem controller construction module is used for constructing a speed subsystem controller according to the preset performance function and the saturation function;
the height subsystem controller building module is used for building a height subsystem controller through an inversion control method according to the preset performance function and the limited instruction filter;
the preset performance control module is used for acquiring the initial state value of the hypersonic aerocraft at the current moment and carrying out tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller;
the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and operable on the processor, wherein the processor, when executing the program, implements the steps of any of the above-described preset performance control methods for hypersonic aircraft.
The invention also provides a non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, carries out the steps of the method for preset performance control of a hypersonic aircraft as described in any one of the above.
The invention also provides a computer program product comprising a computer program which, when executed by a processor, carries out the steps of the method for preset performance control of a hypersonic aircraft as described in any one of the above.
According to the preset performance control method and system for the hypersonic aircraft, provided by the invention, the output tracking error has smaller overshoot on the basis of improving the steady-state and transient performances of the hypersonic aircraft system by designing a new preset performance function; meanwhile, the amplitude and the speed of system input are ensured to meet the limited requirements by constructing a limited instruction filter, so that good tracking performance can be provided on the basis of solving the problem that the amplitude and the speed of the system input are limited.
Drawings
In order to more clearly illustrate the technical solutions of the present invention or the prior art, the drawings needed for the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a preset performance control method for a hypersonic aircraft according to the invention;
FIG. 2 is a diagram illustrating an inequality constraint curve of the prior art default performance provided by the present invention;
FIG. 3 is a diagram illustrating an inequality constraint curve of a predetermined performance function according to the present invention;
FIG. 4 is a schematic diagram comparing velocity and tracking error curves provided by the present invention;
FIG. 5 is a schematic diagram illustrating a comparison of height and tracking error curves provided by the present invention;
FIG. 6 is a schematic diagram comparing state variable curves of the system provided by the present invention;
FIG. 7 is a schematic diagram comparing the tracking error curves of the system state variables provided by the present invention;
FIG. 8 is a comparative schematic of a fuel equivalent ratio curve provided by the present invention;
FIG. 9 is a comparative schematic of an elevator deflection angle curve provided by the present invention;
FIG. 10 is a comparative schematic of an elevator yaw rate curve provided by the present invention;
FIG. 11 is a comparative schematic of auxiliary variable curves provided by the present invention;
FIG. 12 is a schematic comparison of LESO observation curves provided by the present invention;
FIG. 13 is a schematic structural diagram of a default performance control system for a hypersonic aircraft according to the present invention;
fig. 14 is a schematic structural diagram of an electronic device provided in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention decomposes the preset performance control of the hypersonic aircraft into a speed subsystem and a height subsystem through a longitudinal motion rigid body model of the hypersonic aircraft, thereby realizing the preset performance control of the hypersonic aircraft according to the two subsystems, wherein the longitudinal motion rigid body model of the hypersonic aircraft comprises the following components:
Figure BDA0003241394980000121
Figure BDA0003241394980000122
Figure BDA0003241394980000123
Figure BDA0003241394980000124
Figure BDA0003241394980000125
the speed V of the aircraft, the altitude h of the aircraft, the track inclination angle gamma, the pitch angle theta and the pitch angle speed q are rigid state variables; alpha is an attack angle and alpha is theta-gamma; m is mass, g is acceleration of gravity, IyyIs the moment of inertia; t, D, L, M thrust, drag, lift, and pitching moment, respectively, the corresponding equations can be described as:
Figure BDA0003241394980000126
wherein Q is 0.5 rho V2Aircraft dynamic pressure, rho is air density; s is the aircraft reference area, phi is the fuel equivalence ratio, deltaeIs the elevator deflection angle;
Figure BDA0003241394980000127
and
Figure BDA0003241394980000128
is a related aerodynamic parameter of resistance, L0 and LαRelated aerodynamic parameters, T, for liftΦ(α) and T0(α) is a related aerodynamic parameter of thrust; mT，M0(α) and
Figure BDA0003241394980000134
is a relevant parameter of the pitching moment.
In the rigid body model of longitudinal motion of the hypersonic aircraft, the numerical value of the Tsin α term in the formula 3 is assumed to be far smaller than the value of the lift force L, so that the term can be ignored, and the invention takes the term as assumption 1.
Further, the output of the system model is the speed V and the altitude h of the aircraft; control inputs are fuel equivalence ratio phi and elevator yawAngle deltae. Combining formulas 1 to 5 of a rigid body model of longitudinal motion of the hypersonic aircraft and assuming 1 to know that the change of the speed V of the aircraft is mainly controlled by the fuel equivalence ratio phi; elevator declination angle deltaeThe change of the pitch angle speed q is directly controlled, so that the change of the pitch angle theta and the track inclination angle gamma is controlled, and the change of the height h of the aircraft is mainly influenced by the deflection angle delta of the elevatoreAnd (4) controlling. In order to facilitate control law design, the method can be decomposed into a speed subsystem model and a height subsystem model based on formulas 1 to 5 of a rigid body model of longitudinal motion of the hypersonic aircraft:
Figure BDA0003241394980000131
Figure BDA0003241394980000132
Figure BDA0003241394980000133
wherein ,di(i ═ 1,2,3) is an interference term, including external interference and parameter perturbation, and for the interference term, the present invention defines that assume 2: interference term di(i ═ 1,2,3) is continuous and bounded in the first derivative.
Further, in order to avoid the thermal resistance phenomenon of the hypersonic aircraft in actual flight, the fuel equivalence ratio phi value needs to be in a certain range, so that the scramjet engine always keeps a reasonable working state, otherwise, the engine stops working. In addition, since the actual physical mechanism has a deflection limit, the elevator deflection angle δeThe output is also limited. Therefore, the present invention is based on the fuel equivalence ratio Φ and the elevator yaw angle δeIn the limited case, constructing a corresponding saturation function can be described as:
Figure BDA0003241394980000141
Figure BDA0003241394980000142
Figure BDA0003241394980000143
wherein ,ΦdFor ideal control of input value, delta, for fuel equivalence ratioedFor ideal control of input value of elevator deflection angle, constant phimax and ΦminRespectively an upper limit and a lower limit of the fuel equivalence ratio phi amplitude (namely the actual input value of the fuel equivalence ratio phi), and a constant deltamax and δminRespectively the rudder deflection angle deltaeAmplitude (i.e. elevator yaw angle delta)eActual input values) upper and lower limits;
Figure BDA0003241394980000144
is the derivative of the elevator yaw angle;
Figure BDA0003241394980000145
constant psimax and ψminRespectively the rudder deflection angle deltaeUpper and lower limits of rate.
Fig. 1 is a schematic flow chart of a preset performance control method for a hypersonic aircraft according to the present invention, and as shown in fig. 1, the present invention provides a preset performance control method for a hypersonic aircraft, which is characterized by comprising:
and 101, constructing a preset performance function of the hypersonic aircraft based on the tracking error.
The constraint of the existing performance function can ensure that the tracking error has a smaller steady-state value, has a certain effect on improving the transient performance of the error, and still has the problem that the overshoot of the tracking error is overlarge. Based on the defects of the existing preset performance method, the invention constructs a new preset performance function by taking the overshoot minimization of the tracking error as a target, and can make the overshoot of the tracking error smaller and improve the dynamic performance of the tracking error of the system on the basis of considering the transient and steady-state performance of the system.
Specifically, in the existing default performance control method, the tracking error is limited to a preset convergence region, so that the system meets the default transient and steady-state performance requirements. The existing constraint inequality of the preset performance on the error is as follows:
Figure BDA0003241394980000151
wherein, sigma is a constant, and sigma is more than 0 and less than or equal to 1;
Figure BDA0003241394980000158
for the existing performance function, the expression is:
Figure BDA0003241394980000152
wherein ,
Figure BDA0003241394980000153
μ and
Figure BDA0003241394980000154
are all constant, and
Figure BDA0003241394980000159
μ＞0，
Figure BDA00032413949800001510
in the case of a steady-state value,
Figure BDA00032413949800001511
as can be seen from the above existing formulas for performance functions, the performance function has the property of being continuously bounded, monotonically decreasing.
Fig. 2 is a schematic diagram of an inequality constraint curve of the existing preset performance provided by the present invention, which can be referred to as fig. 2, and although the constraint of the existing performance function can ensure a steady-state value with a small tracking error and has a certain effect on improving the transient performance of the error, the problem that the overshoot of the tracking error is too large still may occur. Therefore, the existing performance presetting method has certain defects for improving the transient performance of the tracking error. Based on the above problem, the present invention designs a new performance function, and specifically, the step 101 includes:
the method comprises the following steps of constructing a preset performance function of the hypersonic aircraft by taking the overshoot minimization of the tracking error of the hypersonic aircraft as a target, wherein the preset performance function is as follows:
Figure BDA0003241394980000155
Figure BDA0003241394980000156
it is clear that,
Figure BDA0003241394980000157
further, the inequality constraints are set as:
p2(t)＜e(t)＜p1(t); formula (15)
wherein ,p1(t) and p2(t) represents a preset performance function, e (0) represents a tracking error at an initial time,
Figure BDA0003241394980000164
representing an existing performance function;
Figure BDA0003241394980000165
and mu is a constant number of times,
Figure BDA0003241394980000166
in the case of a steady-state value,
Figure BDA0003241394980000167
and is
Figure BDA0003241394980000168
μ＞0。
FIG. 3 is a schematic diagram of an inequality constraint curve of a predetermined performance function according to the present invention, as shown in FIG. 3, taking e (0) > 0 as an example, by designing parameters such that p is2(0) If greater than 0, the maximum deviation of the tracking error is less than
Figure BDA0003241394980000169
Error steady state value at
Figure BDA00032413949800001610
Within the range. Therefore, compared with the existing performance function, the preset performance function provided by the invention can improve the error tracking precision and ensure that the error has smaller overshoot. When the initial error is zero, the inequality (15) is still true, that is, when e (0) is 0, the inequality is true
Figure BDA00032413949800001611
The inequality (15) is changed into
Figure BDA00032413949800001612
Because the controller is difficult to design by directly utilizing inequality (15), the invention converts inequality constraint into equality constraint, and carries out error conversion to obtain:
Figure BDA0003241394980000161
Figure BDA0003241394980000162
based on the above formula, the invention sets theorem 1: if ε (t) is bounded, then the inequality (15) holds, i.e., the system tracking error is not only bounded but also limited to a preset range.
Further, the theorem 1 proves that:
equation (17) can be transformed into:
Figure BDA0003241394980000163
further, in the present invention,
Figure BDA0003241394980000171
since ε (t) is bounded, then
Figure BDA0003241394980000172
Combining equation (16) and equation (19), one can obtain:
Figure BDA0003241394980000173
thus, p2(t)＜e(t)＜p1(t)。
And 102, constructing a speed subsystem controller according to the preset performance function and the saturation function.
In the present invention, the control targets are: under the condition that the input of a hypersonic aircraft control system is limited, the output of the system can stably track a command signal, and the amplitude and the speed of an actuating mechanism meet the limitation requirements; and when the system is saturated, the tracking error output by the system reaches the preset requirements on transient and steady-state performance. The step 102 specifically includes:
according to the preset performance function, constructing a speed performance function of the hypersonic aircraft, wherein the speed performance function is as follows:
Figure BDA0003241394980000174
Figure BDA0003241394980000175
eV＝V-Vd(ii) a Formula (23)
υV＝eV-ξV(ii) a Formula (24)
pV2＜υV＜pV1(ii) a Equation (25)
wherein ,pV1(t) and pV2(t) represents a preset performance function, upsilon, constructed for the aircraft velocity, VVIndicating a velocity compensation error, eVIndicating speed tracking error, ξVRepresenting an auxiliary variable to be designed, VdRepresenting a speed command, V representing an aircraft speed; mu.sV、
Figure BDA0003241394980000186
And
Figure BDA0003241394980000187
is a speed performance function parameter; sigmaVIs constant if > 0. In the invention, the tracking error of the aircraft speed, namely the formula (23), is defined through the formula (7), and then the compensation error is defined, namely the formula (24). Compensating for error v for velocityVThe constraint inequality (i.e., equation 25) is established.
And carrying out error transformation on the speed performance function to obtain a speed error transformation function of the hypersonic aircraft, wherein the speed error transformation function is as follows:
Figure BDA0003241394980000181
Figure BDA0003241394980000182
wherein ,εVRepresenting a velocity transformation error;
based on a rigid body model of longitudinal motion of the hypersonic aircraft, a speed subsystem model is obtained as follows:
Figure BDA0003241394980000183
Figure BDA0003241394980000184
Figure BDA0003241394980000185
wherein, f isV and gVAs a substitute symbol, the two formulas are convenient to quote; phi denotes the fuel equivalence ratio, d1Representing a first disturbance term, a representing an angle of attack, D representing a drag, g representing a gravitational acceleration, gamma representing a track inclination, m representing a mass, T0(α) and TΦ(α) represents a thrust-related aerodynamic parameter;
deriving the velocity error transformation function according to the velocity subsystem model, specifically, deriving equation (26) in combination with equation (7), to obtain:
Figure BDA0003241394980000188
and according to the derived speed error transformation function, constructing a speed subsystem control law:
Figure BDA0003241394980000191
Figure BDA0003241394980000192
Figure BDA0003241394980000193
wherein ,ΦdRepresenting the desired control input value, k, of the fuel equivalence ratioV and λVIs a positive parameter of the number of the bits,
Figure BDA0003241394980000196
a first derivative representing a speed command; likewise, v will beV and rVAs a substitute symbol, the two formulas are convenient to quote;
Figure BDA0003241394980000197
representing the first derivative, k, of an existing performance function parameterVξThe parameters of the auxiliary system are represented,
Figure BDA0003241394980000198
an estimate representing a first interference term;
introducing a formula (9) in the saturation function for constraining the ideal control input phi in view of the input saturation problem based on the fuel equivalence ratio saturation functiondAnd obtain the actual input:
Φ＝HΦ(Φd) (ii) a Formula (29)
And according to the speed subsystem control law, constructing a speed subsystem controller, namely substituting a formula (28) and a formula (29) into a formula (27) to obtain:
Figure BDA0003241394980000194
the fuel equivalence ratio saturation function is as follows:
Figure BDA0003241394980000195
wherein the constant phimax and ΦminRespectively the upper and lower limits of the fuel equivalence ratio phi amplitude.
On the basis of the above embodiment, before the building the speed subsystem controller according to the speed subsystem control law based on the fuel equivalence ratio saturation function, the method further includes:
according to the ideal control input value of the fuel equivalence ratio and the actual input value of the fuel equivalence ratio, a first auxiliary system is constructed for ensuring stable tracking when the fuel equivalence ratio is saturated, and the first auxiliary system comprises:
Figure BDA0003241394980000201
where Φ represents a fuel equivalence ratio actual input value. By designing the first auxiliary system, the stable tracking of the system is ensured when the fuel equivalence ratio phi is saturated.
And 103, constructing a height subsystem controller by an inversion control method according to the preset performance function and the limited instruction filter. Step 103 specifically comprises:
according to the preset performance function, constructing an altitude performance function of the hypersonic aircraft, wherein the altitude performance function is as follows:
Figure BDA0003241394980000202
Figure BDA0003241394980000203
eh＝h-hd；
ph2＜eh＜ph1(ii) a Formula (33)
wherein ,ph1(t) and ph2(t) represents a preset performance function constructed for the aircraft altitude h, ehIndicating the altitude error, h the aircraft altitude, hdIndicating a height instruction, μh、
Figure BDA0003241394980000206
And
Figure BDA0003241394980000207
is a height performance function parameter; sigmahIs greater than 0 and is a constant;
and carrying out error transformation on the altitude performance function to obtain an altitude error transformation function of the hypersonic aircraft, wherein the altitude error transformation function is as follows:
Figure BDA0003241394980000204
Figure BDA0003241394980000205
wherein ,εhIndicating the height transformation error.
Based on a hypersonic aircraft longitudinal motion rigid body model, the obtained altitude subsystem model is as follows:
Figure BDA0003241394980000211
Figure BDA0003241394980000212
wherein V represents aircraft speed and gamma represents track inclination; for ease of reference, fγ、gγ、fq and gqAs a substitute symbol for several of the above formulas; theta denotes pitch angle, q denotes pitch angle velocity, d2Representing a second interference term, d3Representing a third interference term, δeIndicating elevator yaw angle, L0 and LαRepresenting lift-related aerodynamic parameters, g representing gravitational acceleration, M representing mass, MT、M0(α) and
Figure BDA0003241394980000216
a parameter of interest representing the pitching moment, IyyRepresenting the moment of inertia;
constructing a first virtual control law gamma based on the altitude commandd. In the invention, the height instruction h is realized in order to ensure that the aircraft height h isdThe following virtual control laws are designed for the fast tracking, namely the first virtual control law:
Figure BDA0003241394980000213
Figure BDA0003241394980000214
Figure BDA0003241394980000215
wherein ,kh> 0, is a parameter. It should be noted that, in the present invention, when the track inclination γ is implemented to γdWhile tracking, the conversion error epsilonh(t) satisfies
Figure BDA0003241394980000224
I.e. epsilonh(t) bounded. Thus, from the above theorem 1, when γ → γdHeight tracking error ehAnd the preset transient and steady-state performance requirements are met.
Further, a height subsystem control law is designed through an inversion control method.
According to the first virtual control law gammadDefining track inclination error as eγ＝γ-γdAnd according to the height subsystem model, namely combining with a formula (8), calculating the derivative of the track inclination error to obtain the derivative track inclination error:
Figure BDA0003241394980000221
in the conventional instruction filter, the following may be specifically mentioned:
Figure BDA0003241394980000222
wherein ,xdIs the filter input; output chi1,χ2Are respectively xdAnd xdFirst derivative of
Figure BDA0003241394980000225
An estimated value of (d); τ, ω are filter parameters, and τ ∈ (0, 1)]，ω＞0，
Figure BDA0003241394980000226
Figure BDA0003241394980000227
The present invention therefore defines a hypothesis 3: existence of unknown constant eta1＞0,η2> 0, such that | χ1-xd|≤η1，
Figure BDA0003241394980000228
In the present invention, the virtual command γ can be estimated using a command filter considering that the virtual command is hard to be derived in the inversion controller designdAnd derivatives thereof
Figure BDA0003241394980000229
Figure BDA0003241394980000223
wherein ,τγ,ωγAre all positive parameters.
Then, constructing a second virtual control law based on the track inclination error:
Figure BDA0003241394980000231
wherein ,kγThe parameter is more than 0, and the content is more than 0,
Figure BDA0003241394980000233
is d2And (6) estimating the value.
And substituting a formula (39) into a formula (36) according to the second virtual control law and the derived track inclination error to construct a track inclination control law:
Figure BDA0003241394980000234
wherein ,kγIf the inclination angle is more than 0, the relevant parameters of the track inclination angle are obtained;
Figure BDA0003241394980000235
is d2Estimated value of eγRepresenting track inclination error, thetadIs the second virtual control law, χγ2Representing the first derivative
Figure BDA0003241394980000236
An estimated value of (d);
according to the second virtual control law thetadDefining the pitch angle error as eθ＝θ-θdAnd according to the height subsystem model, namely formula (8), the pitch angle error is derived to obtain the derived pitch angle error:
Figure BDA0003241394980000237
constructing a third virtual control law based on the pitch angle error and the track inclination angle error, which specifically comprises the following steps:
qd＝-kθeθ+gγeγ-ξq+χθ2(ii) a Formula (42)
wherein ,k θ0 is a design parameter, xiqIs an auxiliary variable to be designed; chi shapeθ2Is a second
Derivative of the virtual control law
Figure BDA0003241394980000238
The estimated value of (c) can be obtained by instructing the filter to:
Figure BDA0003241394980000232
wherein ,τθ,ωθAre all positive parameters.
And substituting a formula (42) into a formula (41) according to the third virtual control law and the derived pitch angle error to construct a pitch angle control law:
Figure BDA0003241394980000244
wherein ,kθIf the pitch angle is more than 0, the pitch angle is a related design parameter; xiqIs an auxiliary variable to be designed; chi shapeθ2For the second virtual control law derivative
Figure BDA0003241394980000245
An estimated value of (d);
further, a pitch angle rate error is defined as eq＝q-qdThe pitch angle compensation error is upsilonq＝eq-ξqAnd according to the height subsystem model, namely combining a formula (8), calculating the derivative of the pitch angle compensation error to obtain the calculated pitch angle compensation error:
Figure BDA0003241394980000246
wherein ,qdA pitch angle speed command;
and constructing a limited instruction filter according to the ideal control input value of the deflection angle of the elevator based on the saturation function of the deflection angle of the elevator, and obtaining the actual input value of the deflection angle of the elevator. In the present invention, the constrained command filter is constructed to constrain the desired control input δ in view of the input saturation problemedAnd obtain the actual input:
Figure BDA0003241394980000241
the elevator deflection angle saturation function is as follows:
Figure BDA0003241394980000242
Figure BDA0003241394980000243
wherein ,τδ and ωδBeing a positive parameter, δedFor ideal control input value of elevator deflection angle, constant deltamax and δminRespectively the rudder deflection angle deltaeUpper and lower limits of amplitude;
Figure BDA0003241394980000254
is the derivative of the elevator yaw angle;
Figure BDA0003241394980000255
constant psimax and ψminRespectively the rudder deflection angle deltaeUpper and lower limits of rate. It should be noted that, by constructing the limited command filter, the ideal control law δ of the elevator drift angle is input into the limited command filteredAnd the output is the actual control law delta of the deflection angle of the elevatoreThe function of the filter is to make the actual control law deltaeSatisfying the limited requirements of amplitude and rate.
In order to counteract the influence caused by input saturation, the invention constructs a second auxiliary system for counteracting the influence of input saturation according to the ideal control input value of the elevator deflection angle and the actual input value of the elevator deflection angle:
Figure BDA0003241394980000251
and constructing an elevator deflection angle control law:
Figure BDA0003241394980000252
wherein ,kqIf the pitch angle is more than 0, the pitch angle is a related design parameter of the pitch angle speed;
Figure BDA0003241394980000256
is the third interference term d3Estimated value of χq2As derivatives of a third virtual control law
Figure BDA0003241394980000257
Estimated value of kqξ1 and kqξ2As an auxiliary system parameter. In the present invention, χq2This can be obtained by the following instruction filter:
Figure BDA0003241394980000253
wherein ,τq,ωqAre all positive parameters.
And (3) substituting a formula (47) and a formula (48) into a formula (45) according to the second auxiliary system, the elevator yaw angle control law and the derived pitch angle compensation error to construct a pitch angle speed compensation error control law:
Figure BDA0003241394980000261
and finally, constructing a height subsystem controller according to the track inclination angle control law, the pitch angle control law and the pitch angle speed compensation error control law. Therefore, the altitude subsystem controller is constructed to perform tracking control on the aircraft.
104, acquiring an initial state value of the hypersonic aircraft at the current moment, and performing tracking control on the hypersonic aircraft according to the speed subsystem controller and the altitude subsystem controller;
and the saturation function is constructed according to the fuel equivalence ratio and the elevator deflection angle.
In the present invention, theorem 2 is set: for formulas (1) to (5) of rigid body models of longitudinal motion of hypersonic flight vehicles, by adopting formulas (29) and (46) and constraint system input, the method can be used for solving the problem that the rigid body models of longitudinal motion of hypersonic flight vehicles are not stable in the prior artEnsuring the fuel equivalence ratio phi and the elevator deflection angle deltaeAlways satisfies the limited condition, i.e. phi epsilon [ phi ]min,Φmax]，δe∈[δmin,δmax]，
Figure BDA0003241394980000264
Further, the proof theorem 2 is performed by the following steps: because phi is HΦ(Φd)，δe＝Hδ(χδ1) According to the saturation function HΦ(·) and HδDefining to obtain phi epsilonmin,Φmax]，δe∈[δmin,δmax]。
For the limited instruction filter constructed by the invention, namely the formula (46), the formula
Figure BDA0003241394980000262
Transforming to obtain:
Figure BDA0003241394980000263
wherein ,cδ＝2τδωδ. Due to saturation function
Figure BDA0003241394980000265
Then it is further obtained according to equation (51):
Figure BDA0003241394980000266
multiplying the above inequalities, i.e., equation (52), by exp (c) at the same timeδt), obtaining:
cδψminexp(cδt)≤(χδ2exp(cδt))′≤cδψmaxexp(cδt); formula (53)
Further, integrating the above inequality (53) yields:
Figure BDA0003241394980000271
according to the actual situation, the deflection angle delta of the elevatoreUpper and lower limits psi of output ratemin＜0,ψmaxIs greater than 0. Taking an initial value χδ2(0) When 0, equation (54) can be simplified to:
ψmin≤χδ2≤ψmax(ii) a Formula (55)
When xδ1∈(δmin,δmax) When is then deltae＝Hδ(χδ1)＝χδ1It is obvious that
Figure BDA0003241394980000274
When in use
Figure BDA0003241394980000275
δe(t)＝δminOr deltae(t)＝δmaxThen, then
Figure BDA0003241394980000276
In view of the above, it can be seen that,
Figure BDA0003241394980000277
it should be noted that, in the prior art, for the problem of limiting the control input amplitude and rate, the limited instruction filter is constructed as follows:
Figure BDA0003241394980000272
if the function H is as shown in equation (56)ψ(. cndot.) reaches a saturation value, at which point equation (56) becomes:
Figure BDA0003241394980000273
wherein the constant psim＝ψminOr psim＝ψmax. Obviously, the formula (57) cannot guarantee the output δeSatisfies the limited condition. Therefore, the limited instruction filter constructed in the prior art cannot guarantee that effective constraint on control input can be realized.
Further, the present invention sets theorem 3: for formulas 1 to 5 of rigid body models of longitudinal motion of hypersonic aircrafts, based on the assumptions 1 to 3, a formula (28) corresponding to a speed subsystem control law and a formula (48) corresponding to an elevator deflection angle control law are adopted, all errors in a closed loop system are finally bounded consistently, and after system input is out of saturation, speed and altitude tracking errors can be guaranteed to be limited within a preset range, so that the preset transient and steady-state performance requirements are met. Theorem 3 is demonstrated by the following steps: constructing a Lyapunov function for the whole closed-loop system:
Figure BDA0003241394980000281
the derivation of equation (58) in conjunction with equation (30), equation (39), equation (44), and equation (50) yields:
Figure BDA0003241394980000282
wherein ,
Figure BDA0003241394980000285
and
Figure BDA0003241394980000286
are all instruction filter errors;
Figure BDA0003241394980000287
all are errors observed by a linear extended state observer (LESO for short). Aiming at the disturbance existing in the speed subsystem and the height subsystem, the invention respectively designs a second-order LESO (Leso) for the disturbance d1,d2,d3Observing and compensating, specifically:
based on the interference existing in the operation of the hypersonic aircraft, a second-order linear extended state observer is constructed and used for observing and compensating the interference, and the formula of the second-order linear extended state observer is as follows:
Figure BDA0003241394980000283
Figure BDA0003241394980000284
Figure BDA0003241394980000291
wherein ,
Figure BDA0003241394980000292
is an estimate of the speed V of the aircraft,
Figure BDA0003241394980000293
as an estimate of the track inclination y,
Figure BDA0003241394980000294
is an estimated value of pitch angle velocity q;
Figure BDA0003241394980000295
as interference term di(ii) an observed value of (i ═ 1,2, 3); lV1,lV2,lγ1,lγ2,lq1,lq2All are positive parameters, the invention adopts a bandwidth configuration method to ensure that the parameters meet the requirement of lV1,lV2]＝[ωV0a1,ωV0a2]，[lγ1,lγ2]＝[ωγ0a1,ωγ0a2]，[lq1,lq2]＝[ωq0a1,ωq0a2]；ω0Representing the bandwidth of the observer, parameter ai＝3！/i！·(3-i)！(i＝1,2)；fV、gV、fγ、gγ、fq and gqAs an alternative notation, the specific formula may refer to the above embodiments; phi represents fuel equivalence ratio, theta represents pitch angle, q represents pitch angle speed, gamma represents track inclination angle, deltaeIndicating the elevator yaw angle. For the demonstration of the convergence of the LESO, the following assumption 4 is made: error in LESO Observation
Figure BDA0003241394980000296
Is bounded and there are unknown constants
Figure BDA0003241394980000297
So that
Figure BDA0003241394980000298
Further, according to the above assumption 3, there is an unknown constant Ni(i ═ 1,2,3) > 0, such that | η |, isγ|≤N1，|ηθ|≤N2，|ηq|≤N3(ii) a From assumption 4 above, there are unknown constants
Figure BDA0003241394980000299
So that
Figure BDA00032413949800002910
Note that in equation (59):
Figure BDA0003241394980000301
in conjunction with equation (63), equation (59) can be reduced to:
Figure BDA0003241394980000302
let Λ ═ epsilonV,eγ,eθ,υq]T，
Figure BDA0003241394980000304
From the previous analysis, there is a constant NW> 0, such that
Figure BDA0003241394980000305
Thus, equation (64) can further yield:
Figure BDA0003241394980000303
then when
Figure BDA0003241394980000306
Equation (65) then has:
Figure BDA0003241394980000307
thus, W can be said to be bounded, and ε can be obtained by the definition of WV,eγ,eθ,υqIs bounded. In the invention, when the track inclination angle gamma is realized to gammadWhile tracking, the conversion error epsilonh(t) satisfies
Figure BDA0003241394980000308
I.e. epsilonh(t) bounded. Thus, from the above theorem 1, when γ → γdHeight tracking error ehAnd the preset transient and steady-state performance requirements are met. By eγBounded available epsilonh∈l∞. According to the above theorem 1, the formula is defined by ∈V,εhHas a boundary and can obtain upsilonV,ehBounded and meets preset transient and steady state performance requirements.
When the system input is out of saturation, the first auxiliary system, equation (31), now becomes
Figure BDA0003241394980000312
Then the auxiliary variable xiV→ 0, i.e. vV→eVFurther obtain an error eVAnd the preset transient and steady-state performance requirements are met.
For the second auxiliary system, equation (47) construction, the Lyapunov function is constructed
Figure BDA0003241394980000313
And deriving to obtain:
Figure BDA0003241394980000311
when the system input is out of saturation, deltaed∈[δmin,δmax]At this time
Figure BDA0003241394980000314
δe＝Hδ(χδ1) Therefore, in the formula (67), there is (δ)e-δed)∈l∞. When the auxiliary variable | ξq|≥|(δe-δed)/kqξ2When | it is clear that the formula (67) can be simplified to
Figure BDA0003241394980000315
Hence xiqIs bounded, thereby obtaining eqIs bounded.
According to the preset performance control method for the hypersonic aircraft, provided by the invention, the output tracking error has smaller overshoot on the basis of improving the steady-state and transient performances of the hypersonic aircraft system by designing a new preset performance function; meanwhile, the amplitude and the speed of system input are ensured to meet the limited requirements by constructing a limited instruction filter, so that good tracking performance can be provided on the basis of solving the problem that the amplitude and the speed of the system input are limited.
In an embodiment, the effectiveness of the control scheme provided by the invention is verified, and MATLAB simulation is performed by using the speed subsystem controller and the altitude subsystem controller constructed in the above embodiments by taking rigid body model formulas (1) to (5) of longitudinal motion of the hypersonic aircraft as objects. The aircraft model-related parameters may be selected based on existing parameters.
Specifically, the controller parameters: k is a radical ofV＝0.1，λV＝0.01，kh＝0.1，kγ＝0.8，kθ＝2，k q2; presetting performance parameters: mu.sV＝0.2，μh＝0.15，
Figure BDA0003241394980000323
σV＝0.6，σh0.5; auxiliary system parameters: k is a radical ofVξ＝0.8，kqξ1＝10，kqξ20.02; instruction filter parameters: tau isγ＝τθ＝τq＝0.8，τq＝0.5，ωγ＝ωθ＝10，ωq＝25，ω δ90; the LESO parameters are: bandwidth omegaV0＝ωγ0＝ωq0(ii) 5; the system output and state initial values are set as: v0＝7702ft/s，h0＝85000ft，γ0＝0rad，θ0＝0.0264rad，q 00 rad/s; disturbance d1,d2,d3The external interference is set to be sin (0.2t), 0.0002sin (0.2t) and 0.1sin (0.2t) respectively; consider a system parameter perturbation of + 20%.
The control input constraints are set to phi e [0.05,1.5 respectively]，δe∈[-30°,30°]，
Figure BDA0003241394980000324
Setting speed and height step commands respectively as
Figure BDA0003241394980000325
And respectively generates signal instructions V through the following filtersd,hd：
Figure BDA0003241394980000321
Figure BDA0003241394980000322
In order to verify the superiority of the control scheme (denoted as control scheme a) proposed by the present invention, a comparative simulation was performed on an adaptive anti-saturation control scheme (denoted as control scheme B) in the prior art. To reflect comparative "fairness," the control gain parameter values for control scheme B are the same as control scheme a, and the LESO observations with the same parameters are taken and the system disturbances are compensated.
Fig. 4 is a schematic diagram comparing speed curves and tracking error curves provided by the present invention, fig. 5 is a schematic diagram comparing height curves and tracking error curves provided by the present invention, fig. 6 is a schematic diagram comparing system state variable curves provided by the present invention, fig. 7 is a schematic diagram comparing system state variable tracking error curves provided by the present invention, fig. 8 is a schematic diagram comparing fuel equivalent ratio curves provided by the present invention, fig. 9 is a schematic diagram comparing elevator deflection angle curves provided by the present invention, fig. 10 is a schematic diagram comparing elevator deflection angle rate curves provided by the present invention, fig. 11 is a schematic diagram comparing auxiliary variable curves provided by the present invention, fig. 12 is a schematic diagram comparing LESO observation curves provided by the present invention, and simulation results can be referred to fig. 4 to fig. 12. Obviously, both of the above control schemes enable the system to achieve stable tracking of instructions (as shown in fig. 4 to 7). However, referring to fig. 4 and 5, the speed error and height error curves of the control scheme a are always within the preset range, and the error convergence rate is better than that of the control scheme B, which indicates that the transient performance of the control system under the control scheme a is better. Referring to fig. 8 to 10, the control input curves of the control scheme a and the control scheme B satisfy the amplitude constraint condition, but for the speed limit requirement of the elevator rudder deflection angle, only the control scheme a can satisfy the requirement, which means that the limited instruction filter constructed by the control scheme a can effectively limit the amplitude and the speed of the control input, and ensure that the actual output of the actuator satisfies the limit condition.
Further, as shown in fig. 11, when the control input is saturated, the auxiliary variable quickly responds to compensate the tracking error, and the stability of the system is ensured; when the system comes out of saturation, the auxiliary variable quickly converges to zero. Referring to fig. 12, LESO can realize fast and effective observation of system disturbance, which indicates that the system has a certain anti-interference capability. In summary, by comparison, the control scheme provided by the invention can enable the system to have good transient and steady-state performance while solving the problem of limited control input amplitude and rate.
The invention provides a preset performance control scheme based on a limited instruction filter, aiming at the problem of the tracking performance of a hypersonic aircraft considering the limitation of input amplitude and speed. In order to improve the transient and steady-state performance of the system, a preset performance inversion controller is designed, and a new performance function is designed, so that the overshoot of a tracking error is smaller; secondly, introducing an instruction filter to process the problem that derivation is difficult to solve in the design of an inversion controller, constructing a limited instruction filter to restrict a system control law aiming at the problem of limited input, ensuring that control input meets the limitation requirements of amplitude and speed, and carrying out corresponding theoretical proof; in addition, the uncertainty of system parameters and external interference are considered, and a linear extended state observer is adopted for observation and compensation. And based on the Lyapunov stabilization theory, the method proves that all tracking errors of the system are finally consistent and bounded. Finally, the effectiveness of the method is verified through simulation.
Fig. 13 is a schematic structural diagram of a preset performance control system for a hypersonic aircraft according to the present invention, and as shown in fig. 13, the present invention provides a preset performance control system for a hypersonic aircraft, which includes a performance function building module 1301, a speed subsystem controller building module 1302, an altitude subsystem controller building module 1303, and a preset performance control module 1304, where the performance function building module 1301 is configured to build a preset performance function of the hypersonic aircraft based on a tracking error; the speed subsystem controller building module 1302 is configured to build a speed subsystem controller according to the preset performance function and the saturation function; the height subsystem controller building module 1303 is used for building a height subsystem controller according to the preset performance function and the limited instruction filter by an inversion control method; the preset performance control module 1304 is used for acquiring an initial state value of the hypersonic aerocraft at the current moment, and performing tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller; the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
According to the preset performance control system for the hypersonic aircraft, provided by the invention, the output tracking error has smaller overshoot on the basis of improving the steady-state and transient performances of the hypersonic aircraft system by designing a new preset performance function; meanwhile, the amplitude and the speed of system input are ensured to meet the limited requirements by constructing a limited instruction filter, so that good tracking performance can be provided on the basis of solving the problem that the amplitude and the speed of the system input are limited.
The system provided by the embodiment of the present invention is used for executing the above method embodiments, and for details of the process and the details, reference is made to the above embodiments, which are not described herein again.
Fig. 14 is a schematic structural diagram of an electronic device provided in the present invention, and as shown in fig. 14, the electronic device may include: a processor (processor)1401, a communication interface (communication interface)1402, a memory (memory)1403, and a communication bus 1404, wherein the processor 1401, the communication interface 1402, and the memory 1403 are communicated with each other via the communication bus 1404. The processor 1401 may invoke logic instructions in the memory 1403 to perform a preset performance control method for a hypersonic aircraft, the method comprising: constructing a preset performance function of the hypersonic aircraft based on the tracking error; constructing a speed subsystem controller according to the preset performance function and the saturation function; constructing a height subsystem controller by an inversion control method according to the preset performance function and the limited instruction filter; acquiring an initial state value of the hypersonic aerocraft at the current moment, and performing tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller; the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
In addition, the logic instructions in the memory 1403 can be implemented in the form of software functional units and stored in a computer readable storage medium when the software functional units are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
In another aspect, the present invention also provides a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the preset performance control method for a hypersonic aircraft provided by the above methods, the method comprising: constructing a preset performance function of the hypersonic aircraft based on the tracking error; constructing a speed subsystem controller according to the preset performance function and the saturation function; constructing a height subsystem controller by an inversion control method according to the preset performance function and the limited instruction filter; acquiring an initial state value of the hypersonic aerocraft at the current moment, and performing tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller; the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
In yet another aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored, the computer program being implemented by a processor to execute the preset performance control method for a hypersonic flight vehicle provided in the above embodiments, the method comprising: constructing a preset performance function of the hypersonic aircraft based on the tracking error; constructing a speed subsystem controller according to the preset performance function and the saturation function; constructing a height subsystem controller by an inversion control method according to the preset performance function and the limited instruction filter; acquiring an initial state value of the hypersonic aerocraft at the current moment, and performing tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller; the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
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 (10)

1. A preset performance control method for a hypersonic aircraft, comprising:
constructing a preset performance function of the hypersonic aircraft based on the tracking error;
constructing a speed subsystem controller according to the preset performance function and the saturation function;
constructing a height subsystem controller by an inversion control method according to the preset performance function and the limited instruction filter;
acquiring an initial state value of the hypersonic aerocraft at the current moment, and performing tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller;
the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
2. The preset performance control method for the hypersonic aircraft according to claim 1, characterized in that the constructing the preset performance function of the hypersonic aircraft based on the tracking error comprises:
the method comprises the following steps of constructing a preset performance function of the hypersonic aircraft by taking the overshoot minimization of the tracking error of the hypersonic aircraft as a target, wherein the preset performance function is as follows:
Figure FDA0003241394970000011
Figure FDA0003241394970000012
p2(t)＜e(t)＜p1(t)；
wherein ,p1(t) and p2(t) represents a preset performance function, e (0) represents a tracking error at an initial time,
Figure FDA0003241394970000013
representing an existing performance function;
Figure FDA0003241394970000014
and mu is a constant number of times,
Figure FDA0003241394970000015
in the case of a steady-state value,
Figure FDA0003241394970000021
and is
Figure FDA0003241394970000022
μ＞0。
3. The method of claim 2, wherein the constructing a velocity subsystem controller from the preset performance function and the saturation function comprises:
according to the preset performance function, constructing a speed performance function of the hypersonic aircraft, wherein the speed performance function is as follows:
Figure FDA0003241394970000023
Figure FDA0003241394970000024
υV＝eV-ξV；
eV＝V-Vd；
pV2＜υV＜pV1；
wherein ,pV1(t) and pV2(t) represents a preset performance function, upsilon, constructed for the aircraft velocity, VVIndicating a velocity compensation error, eVIndicating speed tracking error, ξVRepresenting an auxiliary variable to be designed, VdRepresenting a speed command, V representing an aircraft speed; mu.sV、
Figure FDA0003241394970000025
And
Figure FDA0003241394970000026
is a speed performance function parameter; sigmaVIs greater than 0 and is a constant;
and carrying out error transformation on the speed performance function to obtain a speed error transformation function of the hypersonic aircraft, wherein the speed error transformation function is as follows:
Figure FDA0003241394970000027
Figure FDA0003241394970000028
wherein ,εVRepresenting a velocity transformation error;
based on a rigid body model of longitudinal motion of the hypersonic aircraft, a speed subsystem model is obtained as follows:
Figure FDA0003241394970000031
Figure FDA0003241394970000032
Figure FDA0003241394970000033
where Φ represents a fuel equivalence ratio, d1Representing a first disturbance term, a representing an angle of attack, D representing a drag, g representing a gravitational acceleration, gamma representing a track inclination, m representing a mass, T0(α) and TΦ(α) represents a thrust-related aerodynamic parameter;
according to the speed subsystem model, deriving the speed error transformation function, and according to the derived speed error transformation function, constructing a speed subsystem control law:
Figure FDA0003241394970000034
Figure FDA0003241394970000035
Figure FDA0003241394970000036
wherein ,ΦdRepresenting the desired control input value, k, of the fuel equivalence ratioV and λVIs a positive parameter of the number of the bits,
Figure FDA0003241394970000037
the first derivative of the velocity command is represented,
Figure FDA0003241394970000038
representing the first derivative, k, of an existing performance function parameterVξThe parameters of the auxiliary system are represented,
Figure FDA0003241394970000039
an estimate representing a first interference term;
and constructing a speed subsystem controller according to the speed subsystem control law on the basis of a fuel equivalence ratio saturation function:
Figure FDA00032413949700000310
the fuel equivalence ratio saturation function is as follows:
Figure FDA00032413949700000311
wherein the constant phimax and ΦminRespectively the upper and lower limits of the fuel equivalence ratio phi amplitude.
4. The preset performance control method for hypersonic aircraft according to claim 3, wherein before said fuel equivalence ratio-based saturation function building a speed subsystem controller according to said speed subsystem control law, the method further comprises:
according to the ideal control input value of the fuel equivalence ratio and the actual input value of the fuel equivalence ratio, a first auxiliary system is constructed for ensuring stable tracking when the fuel equivalence ratio is saturated, and the first auxiliary system comprises:
Figure FDA0003241394970000041
where Φ represents a fuel equivalence ratio actual input value.
5. The method of claim 2, wherein the constructing the altitude subsystem controller by an inversion control method according to the predetermined performance function and the limited instruction filter comprises:
according to the preset performance function, constructing an altitude performance function of the hypersonic aircraft, wherein the altitude performance function is as follows:
Figure FDA0003241394970000042
Figure FDA0003241394970000043
eh＝h-hd；
ph2＜eh＜ph1；
wherein ,ph1(t) and ph2(t) represents a preset performance function constructed for the aircraft altitude h, ehIndicating the altitude error, h the aircraft altitude, hdIndicating a height instruction, μh、
Figure FDA0003241394970000044
And
Figure FDA0003241394970000045
is a height performance function parameter; sigmahIs greater than 0 and is a constant;
and carrying out error transformation on the altitude performance function to obtain an altitude error transformation function of the hypersonic aircraft, wherein the altitude error transformation function is as follows:
Figure FDA0003241394970000046
Figure FDA0003241394970000051
wherein ,εhRepresenting a height transformation error;
based on a hypersonic aircraft longitudinal motion rigid body model, the obtained altitude subsystem model is as follows:
Figure FDA0003241394970000052
Figure FDA0003241394970000053
where V represents aircraft speed, γ represents track inclination, θ represents pitch angle, q represents pitch angle speed, d represents aircraft speed, and2representing a second interference term, d3Representing a third interference term, δeIndicating elevator yaw angle, L0 and LαRepresenting lift-related aerodynamic parameters, g representing gravitational acceleration, M representing mass, MT、M0(α) and
Figure FDA0003241394970000054
a parameter of interest representing the pitching moment, IyyRepresenting the moment of inertia;
constructing a first virtual control law gamma based on the altitude commanddAccording to said first virtual control law γdDefining track inclination error as eγ＝γ-γdAnd according to the height subsystem model, calculating the derivation of the track inclination error to obtain the derived track inclination error:
Figure FDA0003241394970000055
constructing a second virtual control law based on the track inclination error, and constructing the track inclination control law according to the second virtual control law and the derived track inclination error:
Figure FDA0003241394970000056
wherein ,kγIf the inclination angle is more than 0, the relevant parameters of the track inclination angle are obtained;
Figure FDA0003241394970000061
is d2Estimated value of eγRepresenting track inclination error, thetadIs the second virtual control law, χγ2Representing the first derivative
Figure FDA0003241394970000062
An estimated value of (d);
according to the second virtual control law thetadDefining the pitch angle error as eθ＝θ-θdAnd according to the height subsystem model, deriving the pitch angle error to obtain the derived pitch angle error:
Figure FDA0003241394970000063
constructing a third virtual control law based on the pitch angle error and the track inclination angle error, and constructing a pitch angle control law according to the third virtual control law and the derived pitch angle error:
Figure FDA0003241394970000064
wherein ,kθIf the pitch angle is more than 0, the pitch angle is a related design parameter; xiqIs an auxiliary variable to be designed; chi shapeθ2For the second virtual control law derivative
Figure FDA0003241394970000065
An estimated value of (d);
defining a pitch rate error as eq＝q-qdCompensation error of pitch angle is vq＝eq-ξqAnd according to the height subsystem model, carrying out derivation on the pitch angle compensation error to obtain a derived pitch angle compensation error:
Figure FDA0003241394970000066
wherein ,qdA pitch angle speed command;
based on an elevator deflection angle saturation function, constructing a limited instruction filter according to an ideal elevator deflection angle control input value, and obtaining an actual elevator deflection angle input value:
Figure FDA0003241394970000071
the elevator deflection angle saturation function is as follows:
Figure FDA0003241394970000072
Figure FDA0003241394970000073
wherein ,τδ and ωδBeing a positive parameter, δedFor ideal control input value of elevator deflection angle, constant deltamax and δminRespectively the rudder deflection angle deltaeUpper and lower limits of amplitude;
Figure FDA0003241394970000074
is the derivative of the elevator yaw angle;
Figure FDA0003241394970000075
constant psimax and ψminRespectively the rudder deflection angle deltaeUpper and lower limits of rate;
according to the ideal control input value of the elevator deflection angle and the actual input value of the elevator deflection angle, a second auxiliary system for counteracting the influence of input saturation is constructed:
Figure FDA0003241394970000076
and constructing an elevator deflection angle control law:
Figure FDA0003241394970000077
wherein ,kqIf the pitch angle is more than 0, the pitch angle is a related design parameter of the pitch angle speed;
Figure FDA0003241394970000078
is the third interference term d3Estimated value of χq2As derivatives of a third virtual control law
Figure FDA0003241394970000079
Estimated value of kqξ1 and kqξ2Auxiliary system parameters;
constructing a pitch angle speed compensation error control law according to the second auxiliary system, the elevator yaw angle control law and the derived pitch angle compensation error:
Figure FDA0003241394970000081
and constructing a height subsystem controller according to the track inclination angle control law, the pitch angle control law and the pitch angle speed compensation error control law.
6. The preset performance control method for the hypersonic flight vehicle according to claim 1, wherein before the obtaining of the initial value of the state of the hypersonic flight vehicle at the current moment and the tracking control of the hypersonic flight vehicle according to the speed subsystem controller and the altitude subsystem controller, the method further comprises:
based on the interference existing in the operation of the hypersonic aircraft, a second-order linear extended state observer is constructed and used for observing and compensating the interference, and the formula of the second-order linear extended state observer is as follows:
Figure FDA0003241394970000082
Figure FDA0003241394970000083
Figure FDA0003241394970000084
wherein ,
Figure FDA0003241394970000085
is an estimate of the speed V of the aircraft,
Figure FDA0003241394970000086
as an estimate of the track inclination y,
Figure FDA0003241394970000087
is an estimated value of pitch angle velocity q;
Figure FDA0003241394970000088
as interference term di(ii) an observed value of (i ═ 1,2, 3); lV1,lV2,lγ1,lγ2,lq1,lq2Are all positive parameters, ω0Representing the bandwidth of the observer, parameter ai3! I! (3-i)! (i ═ 1, 2); phi represents fuel equivalence ratio, theta represents pitch angle, q represents pitch angle speed, and gamma represents navigationTrack inclination angle, deltaeIndicating the elevator yaw angle.
7. A preset performance control system for a hypersonic aircraft, comprising:
the performance function building module is used for building a preset performance function of the hypersonic aircraft based on the tracking error;
the speed subsystem controller construction module is used for constructing a speed subsystem controller according to the preset performance function and the saturation function;
the height subsystem controller building module is used for building a height subsystem controller through an inversion control method according to the preset performance function and the limited instruction filter;
the preset performance control module is used for acquiring the initial state value of the hypersonic aerocraft at the current moment and carrying out tracking control on the hypersonic aerocraft according to the speed subsystem controller and the altitude subsystem controller;
the saturation function is constructed according to a fuel equivalence ratio and an elevator deflection angle; the limited instruction filter is constructed and obtained based on an input saturation problem and according to an ideal control input value of an elevator deflection angle.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements the steps of the preset performance control method for hypersonic aircraft according to any of claims 1 to 6.
9. A non-transitory computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the preset performance control method for hypersonic aircraft according to any one of claims 1 to 6.
10. A computer program product comprising a computer program, characterized in that the computer program, when being executed by a processor, carries out the steps of the preset performance control method for hypersonic aircraft according to any one of claims 1 to 6.
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