CN113900448B - Aircraft prediction correction composite guidance method based on sliding mode interference observer - Google Patents
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Abstract
The invention relates to an aircraft prediction correction composite guidance method based on a sliding mode interference observer, which comprises the following steps of: firstly, establishing a three-degree-of-freedom nonlinear model of the hypersonic aircraft containing multi-source interference according to nonlinear kinematics and dynamics characteristics of the hypersonic aircraft, and representing the multi-source interference; secondly, designing a sliding mode interference observer to carry out quick on-line estimation on lumped interference; thirdly, respectively designing a longitudinal guidance law and a lateral guidance law according to the flight state and control input of the aircraft at the current moment, and converting the heat flux density, overload and dynamic pressure constraint into a roll angle amplitude constraint by using a quasi-balanced gliding condition and an interference estimated value so as to ensure that the process constraint is met; and fourthly, designing a composite guidance law according to the interference estimated value and the output value of the prediction correction guidance, and finally completing the design of the guidance method. The invention has strong anti-interference capability and high guidance precision, and is suitable for various hypersonic aircrafts with unpowered reentry.
Description
Technical Field
The invention relates to the field of hypersonic aircraft guidance, in particular to an aircraft prediction correction composite guidance method based on a sliding mode interference observer.
Background
Hypersonic aircraft are aircraft with a flight speed higher than Mach 5, and the flight height of hypersonic aircraft is between that of a common aircraft and that of an orbital aircraft (20-100 km). The aircraft has the advantages of high speed, long range, high maneuverability and the like, and has important application prospects in the fields of military use, civil use and the like. Due to the complexity of the aircraft itself and the flight environment, guidance and control of hypersonic aircraft face many challenges, mainly in terms of strong nonlinearity, fast time-variation, strong coupling and uncertainty. The hypersonic aircraft has huge flight span, and the aerodynamic characteristics of high and low altitudes are greatly different, so that the dynamic characteristics and model parameters of the aircraft are finally caused to have strong uncertainty. Furthermore, the flight test data and the ground test data make it difficult to describe hypersonic aerodynamics and dynamics precisely. The above complex aircraft dynamics cannot be taken into account exactly in the model, resulting in modeling errors for hypersonic aircraft.
Aiming at the problems of reentry guidance of hypersonic aircrafts and the like, the current common methods comprise nominal track guidance, prediction correction guidance and the like.
The standard track guidance is to store a standard reentry track in an airborne computer in advance, generate an error signal according to an actual flight track and the standard track, and adjust the gesture of the aircraft through a gesture control system so as to realize accurate tracking of the standard track. However, in the actual reentry process of the hypersonic aircraft, the actual flight trajectory deviates from the nominal trajectory due to the influence of various factors such as initial condition errors, atmospheric environment changes, aerodynamic coefficient changes and the like.
The prediction correction guidance is to predict the drop point of the reentry terminal according to the current flight state and the virtual control signal, and compare the predicted reentry terminal with the theoretical terminal drop point to generate an error signal so as to correct the guidance instruction on line to realize accurate control of the drop point. The prediction correction guidance is insensitive to initial conditions, the flight track can be corrected on line, and the development prospect is wider.
At present, research on prediction correction guidance of a reentry aircraft is mainly focused on two aspects of numerical prediction correction guidance and analytic prediction correction guidance, and a literature 'short range reentry analytic prediction correction guidance method' aims at the problem of reentry guidance of a lunar exploration spacecraft, a predicted range analytic form is obtained through a pre-designed glide segment track, and then a residual range and a correction roll angle instruction are calculated. However, the method only considers the nominal situation, but does not consider the influence of multi-source interference on the system, and has poor guidance precision and robustness. The literature reentry prediction correction guidance with terminal height constraint aims at the problem of terminal height constraint, a roll angle section is designed in a segmented mode, and the requirement of quasi-equilibrium gliding conditions is met by introducing the change rate of height error as negative feedback. The document hypersonic speed aircraft reentry prediction correction fault-tolerant guidance based on deep learning aims at the fault-tolerant guidance problem under the aircraft fault condition, and the fault information is utilized to train the deep neural network offline to replace an integral link in the traditional prediction correction guidance so as to reduce the calculated amount and improve the system instantaneity. The patent number CN202010347697.5 proposes a predictive correction robust guidance method for re-entry sections of a reusable carrier, and can realize accurate guidance under the conditions of parameter uncertainty and multiple constraints. The patent number CN201911187178.0 proposes a reusable carrier full-stage reentry return guidance method, aiming at external disturbance and uncertainty factors, the whole reentry process is divided into a plurality of flight stages, different flight stages adopt different guidance schemes, and finally full-stage guidance is realized. An improved prediction guidance method for RLV reentry heat flow rate tracking is proposed in the patent number CN201911124407.4, and is aimed at process constraint and geographic constraint, a heat flow rate tracking compensation term is introduced in the longitudinal guidance law design to correct the tilting angle amplitude, and the geographic constraint is processed by utilizing transverse guidance logic designed by an improved artificial potential field method in the transverse guidance law, so that the drop point precision is ensured. The five methods only use prediction correction guidance to inhibit the uncertainty of a model, do not consider interference characteristics, lack active anti-interference capability and have larger conservation.
The problems of hypersonic aircraft reentry guidance and the like which are caused by nonlinear dynamics, atmospheric density uncertainty, pneumatic parameter uncertainty, sensor noise and other factors at the same time are still a problem to be solved at present. In addition, the process constraints of heat flux density, overload, dynamic pressure and the like are also important research contents of guidance problems. The problems of mixing and influencing of various interferences, simultaneous satisfaction of a plurality of constraints and the like all bring about serious challenges to the design of the guidance system. Therefore, the multi-source interference characteristic needs to be fully considered, and the advantages of the sliding mode interference observer and the prediction correction guidance are combined, so that the real-time estimation and compensation of the uncertainty of the atmospheric density and the uncertainty of the aerodynamic parameters are realized, and the guidance precision and the robustness of the hypersonic aircraft are improved.
Disclosure of Invention
The invention solves the technical problems that: aiming at the problem of reentry section guidance of an unpowered hypersonic aircraft with uncertainty of atmospheric density and uncertainty of aerodynamic parameters, the defect of the prior art is overcome, and the composite guidance method for prediction correction of the aircraft based on the sliding mode interference observer is provided, so that the rapid estimation and compensation of complex interference are realized, a set of guidance strategy is adopted to generate guidance instructions, process constraint conditions such as heat flux density, overload and dynamic pressure are guaranteed to be met, and the accuracy, autonomy and anti-interference capability of the hypersonic aircraft guidance process are improved.
The technical scheme of the invention is as follows: the invention provides an aircraft prediction correction composite guidance method based on a sliding mode interference observer, which establishes an aircraft three-degree-of-freedom model containing atmospheric density uncertainty and aerodynamic parameter uncertainty, designs the sliding mode interference observer and a prediction correction guidance strategy on the basis, combines the advantages of the sliding mode interference observer and the prediction correction guidance strategy to design a composite guidance law, and completes the precise guidance of the reentry section of a hypersonic aircraft, and the method comprises the following specific implementation steps:
Firstly, establishing a three-degree-of-freedom nonlinear model of the hypersonic aircraft containing multi-source interference according to nonlinear kinematics and dynamics characteristics of the hypersonic aircraft, and characterizing the uncertainty of the atmospheric density and the uncertainty of aerodynamic parameters, wherein the specific form is as follows:
(1) Based on the aircraft kinematics and dynamics model, the related state variables of the centroid motion are expressed in the form of a differential equation set:
Wherein R is the dimensionless earth center distance, the dimensionless parameter is the earth radius R e, θ is the longitude, phi is the latitude, V is the dimensionless speed, and the dimensionless parameter is G 0 is the earth surface gravity acceleration, gamma is the track dip angle, ψ is the track offset angle, sigma is the roll angle, τ is the dimensionless time, and the dimensionless parameters areOmega is the rotation angular velocity of the dimensionless earth, and dimensionless parameters areF represents lumped interference caused by the uncertainty of the atmospheric density and the uncertainty of the lift coefficient, L, D is lift acceleration and drag acceleration respectively, and the expression is as follows:
L＝0.5ρ′V2ReSC′L/m
D＝0.5ρ′V2ReSC′D/m
Wherein ρ ' is the atmospheric density, C ' L is the lift coefficient, C ' D is the drag coefficient, S is the wing reference area, and m is the aircraft mass;
(2) Introducing an atmospheric density uncertainty and a pneumatic parameter uncertainty on the basis of a nominal atmosphere and a pneumatic model;
Consider the following atmospheric density uncertainty and aerodynamic parameter uncertainty:
ρ′＝(1+Δρ)ρ
C′L＝(1+ΔCL)CL
C′D＝(1+ΔCD)CD
Where ρ is the nominal atmospheric density, C L is the nominal lift coefficient, C D is the nominal drag coefficient, Δρ is the atmospheric density uncertainty, ΔC L is the lift coefficient uncertainty, ΔC D is the drag coefficient uncertainty.
Secondly, aiming at track dip angle channel interference, designing a sliding mode interference observer to rapidly estimate the lumped interference of the uncertainty of the air density and the uncertainty of the aerodynamic parameters of the aircraft, and obtaining an estimated value of the lumped interference:
Neglecting the earth rotation effect, the track dip dynamic equation can be simplified as:
Assuming that the first derivative of the disturbance f present in the track dip channel is bounded, denoted G, then the following is satisfied
The following sliding mode interference observer is designed as follows:
Wherein z 1 and z 2 are sliding mode disturbance observer state variables, the first derivatives of which are respectively AndC 1 and c 2 are the gains of the sliding mode disturbance observer, and c 1 > 0 and c 2 > 1, g is the upper bound of the first derivative of the disturbance f,Sign (·) represents a signed function for the estimate of the interference f.
Thirdly, designing a longitudinal guidance law and a lateral guidance law by utilizing the flight state at the current moment and a virtual control instruction, and converting the heat flow density, overload and dynamic pressure constraint into a roll angle amplitude constraint by utilizing a quasi-balanced gliding condition and an interference estimated value to ensure that the process constraint is satisfied:
(1) The longitudinal guidance adopts a prediction correction guidance method to determine the tilting angle amplitude;
the longitudinal guidance law is designed as follows:
Wherein, sigma 0 adopts Newton method to solve, and the specific contents are as follows:
wherein, Representing the step length, k representing the current iteration number;
The solving end condition of Newton method is as follows:
wherein epsilon > 0 is a calculation tolerance;
(2) The lateral guidance adopts a guidance method based on a track deflection angle error corridor to determine a tilting angle symbol;
The track offset angle error Δψ is defined as:
Δψ＝ψ-Φ
wherein, phi is the track deflection angle, phi is the azimuth angle of the sight from the current position to the target position, and the calculation mode is as follows:
Φ＝sin(θ-θ0)/(cos(ψ0)tan(ψ)-cos(θ-θ0)sin(θ0))
Wherein θ 0 is the initial longitude, ψ 0 is the initial track offset;
a track deflection angle error corridor taking a to-be-flown range s as an independent variable is defined, and the specific contents are as follows:
Cd＝-Cu
wherein, C u is the upper boundary of the corridor, C d is the lower boundary of the corridor, the unit is radian, s is the range to be flown, and the unit is radian;
in order to ensure the accuracy of lateral guidance, when the track deflection angle error exceeds the error corridor boundary value, the roll angle symbol is turned once, namely:
Σ5:sign(σ)＝-sign(Δψ)
(3) Converting the heat flux density, overload and dynamic pressure constraint into a roll angle amplitude constraint by using a quasi-equilibrium gliding condition and an interference estimated value;
the reentry process should meet the process constraints such as heat flux density, overload and dynamic pressure constraints, and the specific forms are as follows:
wherein, a、Respectively representing the heat flux density, overload and dynamic pressure,amax、Respectively representing maximum allowable heat flux density, maximum allowable overload and maximum allowable dynamic pressure, and k Q represents heat flux density coefficient;
In combination with the atmospheric density model, the above process constraints are further translated into a height-velocity corridor, specifically as follows:
wherein, H is the height in meters and g (-) represents the inverse function of the atmospheric density;
In the reentry process, the track dip angle is small and changes slowly, which is approximately considered Meanwhile, the estimated errors of the earth rotation and sliding mode interference observer are ignored, the dynamic equation of the track dip angle channel is simplified, and the quasi-equilibrium gliding condition is obtained, which is specifically as follows:
according to the actual situation, a smaller lower boundary constraint value sigma E of the roll angle is given, and a quasi-equilibrium glide constraint is obtained:
Wherein, sigma E > 0 is a given constant value, which represents the lower boundary constraint value of the roll angle;
According to the quasi-equilibrium glide condition Σ 7, the constraint of the altitude-speed corridor Σ 6 is converted into the constraint of the roll angle magnitude, specifically as follows:
wherein, Respectively representing maximum amplitude values of tilting angles corresponding to the heat flux density, the dynamic pressure and the overload constraint;
Taking out Available roll angle constraint
Σ8:σE≤|σ|≤|σ|max
Wherein min { · } represents the minimum;
Meanwhile, the reentry process meets the following terminal constraint conditions:
Wherein R f、Vf respectively represents the ground center distance and the speed of the terminal, Respectively representing the expected ground center distance and the expected ground center speed;
The roll angle command is obtained according to formulas Σ 4、Σ5 and Σ 8:
And step four, designing a composite guidance law, and combining the guidance law in the step three to finish the aircraft prediction correction composite guidance method based on the sliding mode interference observer:
The following compound guidance laws are designed:
u0＝cos(σb)
Wherein sigma b is the output of predictive correction guidance, u 0 is a virtual control signal, u is a composite control signal, Is an estimate of interference f.
Compared with the prior art, the invention has the advantages that: the invention relates to an aircraft prediction correction composite guidance method based on a sliding mode interference observer, which aims at the defect of insufficient guidance precision of the existing method under the condition of containing atmospheric density uncertainty and aerodynamic parameter uncertainty, designs a lumped disturbance formed by complex interference by the sliding mode interference observer to estimate and compensate, realizes the aircraft guidance law design with strong robustness, and ensures the guidance precision under multi-source interference; moreover, the heat flux density, overload and dynamic pressure constraint are converted into roll angle amplitude constraint by using quasi-equilibrium gliding conditions and interference estimated values, so that the reentry section of the hypersonic aircraft can meet the process constraint of heat flux density, overload and dynamic pressure under the condition of multi-source interference, and the speed and height errors can be controlled within a smaller range.
Drawings
FIG. 1 is a flow chart of a design of a composite guidance method for aircraft prediction correction based on a sliding mode disturbance observer.
FIG. 2 is a block diagram of a lane boundary for a composite guidance method for aircraft predictive correction based on a sliding mode disturbance observer.
FIG. 3 is a control block diagram of an aircraft predictive correction compound guidance method based on a sliding mode interference observer.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
As shown in FIG. 1, the invention relates to an aircraft prediction correction compound guidance method based on a sliding mode interference observer. Firstly, establishing a three-degree-of-freedom nonlinear model containing multi-source interference according to nonlinear kinematics and dynamics characteristics of a hypersonic aircraft, and representing the multi-source interference; secondly, designing a sliding mode interference observer to estimate lumped interference consisting of the uncertainty of the atmospheric density and the uncertainty of the aerodynamic parameters on the basis of the three-degree-of-freedom nonlinear model and the interference characterization of the aircraft; thirdly, respectively designing a longitudinal guidance law and a lateral guidance law according to the flight state and virtual control input of the aircraft at the current moment, and converting the heat flux density, overload and dynamic pressure constraint into a roll angle amplitude constraint by using a quasi-balanced gliding condition and an interference estimated value to ensure that the process constraint is met; and fourthly, designing a composite guidance law according to the interference estimation value and the output value of the prediction correction guidance, and finally completing the design of the aircraft prediction correction composite guidance method based on the sliding mode interference observer. The method for forecasting, correcting and compounding guidance of the aircraft with strong robustness can realize precise guidance of the reentry section under the condition of multi-source interference, meets the process constraints of heat flux density, overload, dynamic pressure and the like, simultaneously controls the terminal speed and the height error within a smaller range, has the characteristics of high precision and strong robustness, and is suitable for various hypersonic aircraft guidance systems without power reentry.
The specific implementation steps are as follows:
Firstly, establishing a three-degree-of-freedom nonlinear model of the hypersonic aircraft, which contains uncertainty of atmospheric density and uncertainty of aerodynamic parameters, according to nonlinear kinematics and dynamics characteristics of the hypersonic aircraft, and characterizing multi-source interference in a specific form;
(1) Based on the aircraft kinematics and dynamics model, the related state variables of the centroid motion are expressed in the form of a differential equation set:
wherein R e = 6378135m is the earth radius, g 0＝9.81m/s2 is the earth surface gravity acceleration, R is the dimensionless earth center distance, the initial value is 1.012543, θ is longitude, the initial value is 10 °, Φ is latitude, the initial value is-20 °, V is the dimensionless speed, the initial value is 0.859815, γ is the track dip angle, the initial value is-1 °, ψ is the track offset angle, and the initial value is 45 °;
L, D are lift acceleration and drag acceleration respectively, and the expression is as follows:
L＝0.5ρ′V2ReSC′L/m
D=0.5ρ 'V 2ReSC′D/m where ρ' is the atmospheric density, C 'L is the lift coefficient, C' D is the drag coefficient, S is the wing reference area, and m is the aircraft mass;
(2) Introducing an atmospheric density uncertainty and a pneumatic parameter uncertainty on the basis of a nominal atmosphere and a pneumatic model;
Consider the following atmospheric density uncertainty and aerodynamic parameter uncertainty:
ρ′＝(1+Δρ)ρ
C′L＝(1+ΔCL)CL
C′D＝(1+ΔCD)CD
Wherein ρ is the nominal atmospheric density, C L is the nominal lift coefficient, C D is the nominal drag coefficient, Δρ is the atmospheric density uncertainty, the value is 0.1, ΔC L is the lift coefficient uncertainty, the value is-0.3, ΔC D is the drag coefficient uncertainty, the value is 0.3;
the nominal atmospheric density model is as follows:
ρ＝ρ0eβh
wherein ρ 0 =1.225,
Secondly, on the basis of modeling and interference characterization, a sliding mode interference observer is designed to estimate lumped interference consisting of the uncertainty of the atmospheric density and the uncertainty of the aerodynamic parameters, and the sliding mode interference observer is designed as follows:
Wherein z 1 and z 2 are sliding mode disturbance observer state variables, the first derivatives of which are respectively AndC 1 and c 2 are gains of the sliding mode interference observer, take on values c 1 =200 and c 2 =15, g is the upper bound of the first derivative of the interference f, take on a value of 10,Is an estimate of interference f.
Thirdly, designing and designing a longitudinal guidance law and a lateral guidance law by utilizing the flight state at the current moment and a virtual control instruction:
(1) The longitudinal guidance adopts a prediction correction guidance method to determine the tilting angle amplitude;
the longitudinal guidance law is designed as follows:
wherein, R 0 is the initial center distance of the current guidance period, the value is 1.012543, V 0 is the initial speed, and the value is 0.859815; R f is the expected ground center distance of the terminal, the value is 1.003136, V f is the expected speed of the terminal, the value is 0.151732, sigma f is a constant value, the expected tilting angle of the terminal is indicated, and the value is 30 degrees;
sigma 0 is solved by Newton method, and the specific contents are as follows:
wherein lambda k represents the step length, takes a value of 0.5, The value of the terminal is 0.003126 for the desired terminal to fly;
The solving end condition of Newton method is as follows:
wherein epsilon > 0 is the calculation allowable error and the value is 10 -10.
(2) The lateral guidance adopts a guidance method based on a track deflection angle error corridor to determine a tilting angle symbol;
The track offset angle error Δψ is defined as:
Δψ＝ψ-Φ
wherein, phi is the track deflection angle, phi is the azimuth angle of the sight from the current position to the target position, and the calculation mode is as follows:
Φ＝sin(θ-θ0)/(cos(ψ0)tan(ψ)-cos(θ-θ0)sin(θ0))
Wherein, θ 0 is the initial longitude, the value is 10 DEG, ψ 0 is the initial track deflection angle, the value is-20 DEG;
As shown in fig. 2, a track deflection angle error corridor with the flight path s to be flown as an independent variable is defined as follows:
Cd＝-Cu
wherein, C u is the upper boundary of the corridor, C d is the lower boundary of the corridor, the unit is radian, s is the range to be flown, and the unit is radian;
in order to ensure the accuracy of lateral guidance, when the track deflection angle error exceeds the error corridor boundary value, the roll angle symbol is turned once, namely:
Σ5:sign(σ)＝-sign(Δψ)
(3) Converting the heat flux density, overload and dynamic pressure constraint into a roll angle amplitude constraint by using a quasi-equilibrium gliding condition and an interference estimated value;
the reentry process should meet the process constraints such as heat flux density, overload and dynamic pressure constraints, and the specific forms are as follows:
wherein, a、Respectively representing the heat flux density, overload and dynamic pressure,amax、Respectively representing the maximum allowable heat flux density, the maximum allowable overload and the maximum allowable dynamic pressure, wherein the values are respectively 1.5 multiplied by 10 6W/m2, 2.5 and 2 multiplied by 10 5Pa,kQ＝1.794141×108, and the heat flux density coefficients are respectively represented;
In combination with the atmospheric density model, the above process constraints are further translated into a height-velocity corridor, specifically as follows:
wherein, H is the height in meters;
In the reentry process, the track dip angle is small and changes slowly, which is approximately considered Meanwhile, the estimated errors of the earth rotation and sliding mode interference observer are ignored, the dynamic equation of the track dip angle channel is simplified, and the quasi-equilibrium gliding condition is obtained, which is specifically as follows:
according to the actual situation, a smaller lower boundary constraint value sigma E of the roll angle is given, and a quasi-equilibrium glide constraint is obtained:
wherein, sigma E represents a lower boundary constraint value of the roll angle, and the value is 1.0472;
According to the quasi-equilibrium glide condition Σ 7, the constraint of the altitude-speed corridor Σ 6 is converted into the constraint of the roll angle magnitude, specifically as follows:
wherein, Respectively representing maximum amplitude values of tilting angles corresponding to the heat flux density, the dynamic pressure and the overload constraint;
Taking out Available roll angle constraint
Σ8:σE≤|σ|≤|σ|max
Wherein min { · } represents the minimum;
Meanwhile, the reentry process meets the following terminal constraint conditions:
wherein, The expected distance and speed are respectively represented, and the values are 1.003136 and 0.151732 respectively.
The roll angle command is obtained according to formulas Σ 4、Σ5 and Σ 8:
And step four, designing a composite guidance law, and combining the guidance law in the step three to finish the aircraft prediction correction composite guidance method based on the sliding mode interference observer:
as shown in fig. 3, the following compound guidance laws are designed:
u0＝cos(σb)
Wherein sigma b is the output of predictive correction guidance, u 0 is a virtual control signal, u is a composite control signal, Is an estimate of interference f.
The hypersonic aircraft reentry guidance is carried out by adopting the method provided by the invention, a set of anti-interference prediction correction guidance method can be used in the reentry section, and the process constraint condition can be better met. Meanwhile, compared with guidance without interference estimation and compensation, the guidance precision can bear larger uncertainty of atmospheric density and uncertainty of aerodynamic parameters, and the requirements of high precision and strong robustness are met.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art.
Claims (3)
1. The aircraft prediction correction composite guidance method based on the sliding mode interference observer is characterized by comprising the following steps of:
Firstly, establishing a three-degree-of-freedom nonlinear model of the hypersonic aircraft containing multi-source interference according to nonlinear kinematics and dynamics characteristics of the hypersonic aircraft, and representing the multi-source interference;
Secondly, on the basis of the three-degree-of-freedom nonlinear model of the aircraft and the multi-source interference characterization, designing a sliding mode interference observer to perform on-line estimation on lumped interference, wherein the lumped interference comprises atmospheric density uncertainty and pneumatic parameter uncertainty;
Thirdly, respectively designing a longitudinal guidance law and a lateral guidance law according to the flight state and control input of the aircraft at the current moment, determining a roll angle amplitude by adopting a prediction correction guidance method by longitudinal guidance, determining a roll angle symbol by adopting a guidance method based on a track deflection angle error corridor by lateral guidance, and converting heat flow density, overload and dynamic pressure constraint into a roll angle amplitude constraint by utilizing a quasi-balanced glide condition and an interference estimated value to ensure that process constraint is met;
Designing a composite guidance law according to the interference estimation value and the output value of the prediction correction guidance, and finally completing the prediction correction composite guidance of the aircraft based on the sliding mode interference observer;
in the second step, on the basis of the three-degree-of-freedom nonlinear model and interference characterization of the aircraft, a sliding mode interference observer is designed to estimate lumped interference:
Neglecting the earth rotation effect, the track dip dynamic equation can be simplified as:
assuming that the first derivative of the disturbance f present in the track pitch channel is bounded, denoted as G, i.e
The following sliding mode interference observer is designed as follows:
Wherein z 1 and z 2 are sliding mode disturbance observer state variables, the first derivatives of which are respectively AndC 1 and c 2 are the gains of the sliding mode disturbance observer, and c 1 > 0 and c 2 > 1, g is the upper bound of the first derivative of the disturbance f,Sign (·) represents a sign function for the estimated value of the interference f;
in the third step, a longitudinal guidance law and a lateral guidance law are designed, and the heat flux density, overload and dynamic pressure constraint are converted into a roll angle amplitude constraint by using a quasi-balanced gliding condition and an interference estimated value, so that the process constraint is ensured to be satisfied, and the method specifically comprises the following steps:
(1) The longitudinal guidance adopts a prediction correction guidance method to determine the tilting angle amplitude, and is concretely as follows;
Defining the range s to be flown as the large arc between the current position of the aircraft and the target position, wherein the unit is radian, and when the deviation between the track deflection angle and the line-of-sight azimuth angle from the current position to the target position is ignored, the differential equation of the range s to be flown is simplified to be
Considering that the aircraft reentry process end time τ f is difficult to determine, while the reentry process is more concerned with the energy dissipation regime, the class energy variable e is introduced as defined below:
Wherein e represents a negative value of mechanical energy per unit mass, Represents the potential energy of unit mass, the zero potential energy point of which is located at infinity,A negative value representing kinetic energy per unit mass;
The three degree of freedom equation Σ 1 and the differential equation Σ 2 are expressed as differential equations with respect to the argument e as follows:
wherein y= [ R, θ, φ, γ, ψ, s ] T;
According to the flight state y and the virtual control input sigma at the current moment, integrating a differential equation sigma 3 to obtain a terminal to-be-flown range s f, and correcting the roll angle amplitude by adopting a linear model sigma 4 to obtain a corrected roll angle amplitude |sigma (e) |, wherein the specific form is as follows:
wherein, R 0 is the initial center distance, V 0 is the initial speed; For the terminal energy, R f is the desired terminal ground center distance, V f is the desired terminal speed, σ f is a constant value, representing the desired terminal roll angle, σ 0 is the roll angle variable to be solved;
in equation Σ 4, once the variable σ 0 is determined, the roll angle magnitude |σ (e) | is then determined; considering that the aircraft re-entry procedure should be when the terminal constraints are met:
wherein, The terminal is expected to wait for the flight distance;
The above terminal constraints are converted into the following zero point solving problem:
Further translating into a h (σ 0) minimum solution problem:
wherein h (σ 0) is a nonlinear function;
The following solution σ 0 was performed using newton's method:
wherein, Representing the step length, k representing the current iteration number;
The solving end condition of Newton method is as follows:
wherein epsilon > 0 is a calculation tolerance;
(2) The lateral guidance adopts a guidance method based on a track deflection angle error corridor to determine a roll angle symbol, and the method specifically comprises the following steps:
The track offset angle error Δψ is defined as:
Δψ＝ψ-Φ
wherein, phi is the track deflection angle, phi is the azimuth angle of the sight from the current position to the target position, and the calculation mode is as follows:
Φ＝sin(θ-θ0)/(cos(ψ0)tan(ψ)-cos(θ-θ0)sin(θ0))
Wherein θ 0 is the initial longitude, ψ 0 is the initial track offset;
a track deflection angle error corridor taking a to-be-flown range s as an independent variable is defined, and the specific contents are as follows:
Cd＝-Cu
wherein, C u is the upper boundary of the corridor, C d is the lower boundary of the corridor, the unit is radian, s is the range to be flown, and the unit is radian;
in order to ensure the accuracy of lateral guidance, when the track deflection angle error exceeds the error corridor boundary value, the roll angle symbol is turned once, namely:
Σ5:sign(σ)＝-sign(Δψ)
(3) Converting the heat flux density, overload and dynamic pressure constraint into a roll angle amplitude constraint by using a quasi-equilibrium gliding condition and an interference estimated value;
The reentry process should meet the heat flux density, overload and dynamic pressure constraint process constraints in the following specific form:
wherein, a、Respectively representing the heat flux density, overload and dynamic pressure,amax、Respectively representing maximum allowable heat flux density, maximum allowable overload and maximum allowable dynamic pressure, and k Q represents heat flux density coefficient;
In combination with the atmospheric density model, the above process constraints are further translated into a height-velocity corridor, specifically as follows:
wherein, H is the height in meters and g (-) represents the inverse function of the atmospheric density;
In the reentry process, the track dip angle is small and changes slowly, which is approximately considered Meanwhile, the estimated errors of the earth rotation and sliding mode interference observer are ignored, the dynamic equation of the track dip angle channel is simplified, and the quasi-equilibrium gliding condition is obtained, which is specifically as follows:
according to the actual situation, a smaller lower boundary constraint value sigma E of the roll angle is given, and a quasi-equilibrium glide constraint is obtained:
Wherein, sigma E > 0 is a given constant value, which represents the lower boundary constraint value of the roll angle;
According to the quasi-equilibrium glide condition Σ 7, the constraint of the altitude-speed corridor Σ 6 is converted into the constraint of the roll angle magnitude, specifically as follows:
wherein, Respectively representing maximum amplitude values of tilting angles corresponding to the heat flux density, the dynamic pressure and the overload constraint;
Taking out Available roll angle constraint
Σ8:σE≤|σ|≤|σ|max
Wherein min { · } represents the minimum;
Meanwhile, the reentry process meets the following terminal constraint conditions:
Wherein R f、Vf respectively represents the ground center distance and the speed of the terminal, Respectively representing the expected ground center distance and the expected ground center speed;
The roll angle command is obtained according to formulas Σ 4、Σ5 and Σ 8:
2. the composite guidance method for prediction correction of an aircraft based on a sliding mode interference observer according to claim 1, wherein: in the first step, an aircraft three-degree-of-freedom nonlinear model containing multi-source interference is established, wherein the multi-source interference comprises atmospheric density uncertainty and pneumatic parameter uncertainty, and the method comprises the following specific steps of:
(1) Based on the aircraft kinematics and dynamics model, the related state variables of the centroid motion are expressed in the form of a differential equation set:
Wherein R is the dimensionless earth center distance, the dimensionless parameter is the earth radius R e, θ is the longitude, phi is the latitude, V is the dimensionless speed, and the dimensionless parameter is G 0 is the earth surface gravity acceleration, gamma is the track dip angle, ψ is the track offset angle, sigma is the roll angle, τ is the dimensionless time, and the dimensionless parameters areOmega is the rotation angular velocity of the dimensionless earth, and dimensionless parameters areF represents equivalent interference caused by the uncertainty of the atmospheric density and the uncertainty of the lift coefficient, L, D is lift acceleration and drag acceleration respectively, and the expression is as follows:
L＝0.5ρ′V2ReSC′L/m
D＝0.5ρ′V2ReSC′D/m
Wherein ρ ' is the atmospheric density, C ' L is the lift coefficient, C ' D is the drag coefficient, S is the wing reference area, and m is the aircraft mass;
(2) Introducing an atmospheric density uncertainty and a pneumatic parameter uncertainty on the basis of a nominal atmosphere and a pneumatic model;
Consider the following atmospheric density uncertainty and aerodynamic parameter uncertainty:
ρ′＝(1+Δρ)ρ
C′L＝(1+ΔCL)CL
C′D＝(1+ΔCD)CD
Where ρ is the nominal atmospheric density, C L is the nominal lift coefficient, C D is the nominal drag coefficient, Δρ is the atmospheric density uncertainty, ΔC L is the lift coefficient uncertainty, ΔC D is the drag coefficient uncertainty.
3. The composite guidance method for prediction correction of an aircraft based on a sliding mode interference observer according to claim 1, wherein: the fourth step, designing a composite guidance law according to the interference estimation value and the output value of the prediction correction guidance, and finishing the aircraft prediction correction composite guidance based on the sliding mode interference observer:
The following compound guidance laws are designed:
u0＝cos(σb)
Wherein sigma b is the output of predictive correction guidance, u 0 is a virtual control signal, u is a composite control signal, Is an estimate of interference f.
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