CN108958278B - Aerospace vehicle cruise section rapid anti-interference guidance method - Google Patents

Aerospace vehicle cruise section rapid anti-interference guidance method Download PDF

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CN108958278B
CN108958278B CN201810919280.4A CN201810919280A CN108958278B CN 108958278 B CN108958278 B CN 108958278B CN 201810919280 A CN201810919280 A CN 201810919280A CN 108958278 B CN108958278 B CN 108958278B
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乔建忠
韩旭东
郭雷
徐健伟
张丹瑶
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Beihang University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • 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
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models

Abstract

The invention relates to a rapid anti-interference guidance method for an aerospace vehicle cruise section. Aiming at the problem that guidance precision is reduced due to pneumatic parameter uncertainty and gust interference in the cruise segment of the aerospace vehicle, firstly, multi-source interference influence such as the pneumatic parameter uncertainty and the gust interference and transmission mechanism analysis are completed, and an aircraft dynamics model containing equivalent interference is established; secondly, designing a sliding mode disturbance observer according to the dynamic model established in the first step, quickly estimating equivalent disturbance received by the aircraft in a cruise section, and obtaining a disturbance estimated value; thirdly, considering an aircraft dynamics model without interference influence, and designing a proportional guidance control law; and fourthly, designing a composite proportional guidance controller with anti-interference capability by using the interference estimation value obtained in the second step and the proportional guidance control law obtained in the third step, and finishing quick anti-interference guidance of the aerospace vehicle in the cruise section. The invention has the characteristics of high response speed, high guidance precision and strong engineering practicability.

Description

Aerospace vehicle cruise section rapid anti-interference guidance method
Technical Field
The invention relates to the technical field of aerospace vehicle anti-interference, in particular to a rapid anti-interference guidance method for a cruise section of an aerospace vehicle.
Background
Aerospace vehicles are a strategic class of leading edge vehicles with fast reaction maneuverability, such as hypersonic vehicles with flight speeds exceeding mach 5. The strong military application prospect of the method raises the hot tide of researching and developing the related technology in the world.
The strategic significance of aerospace vehicles is high maneuverability, such as hypersonic missiles, which cannot meet the task requirement of rapid attack if they cannot overcome aerodynamic drag to maintain high-speed flight in the cruise section. However, the uncertainty of the pneumatic parameters and the disturbance of gust during the flight of the aircraft during the cruise section seriously affect the high precision requirement of the cruise process. Under the condition of hypersonic speed, the problem of change of the aerodynamic appearance of the aircraft body caused by ablation on the surface of the aircraft shell is inevitable; meanwhile, most aerospace vehicles are made of light materials, aeroelastic vibration is easy to occur due to factors such as disturbance of airflow in the flying process, various complex mechanical processes in the flying process of the aerospace vehicles cannot be completely and finely considered in an aircraft control model for control design, and therefore model error interference with uncertain pneumatic parameters is generated. In addition, in the atmospheric space where the aerospace craft cruises, air convection is strong sometimes, and the flight trajectory and the attitude of the aerospace craft can be directly influenced by gust interference. Due to the characteristics, the design of the high-precision guidance method for the cruise section of the aerospace vehicle is very challenging, and therefore, the design of the cruise guidance method for the aerospace vehicle with the rapid anti-interference capability is particularly important.
At present, scholars at home and abroad also carry out a great deal of research aiming at the problem of guidance of the aerospace vehicle in the cruise section. The Chinese patent application No. 201210258036.0 provides a fine anti-interference tracking controller of a flexible hypersonic aircraft, but the model adopted in the patent is a longitudinal model and is only suitable for the aircraft which is not allowed to generate transverse and lateral motion. The Chinese patent application No. 201510102948.2 provides a longitudinal guidance method for a glide flight segment of a hypersonic aircraft, but various inevitable interferences in the flight process are not considered, and a longitudinal model is used as a research object, so that complex coupling in an actual model is ignored. The article 'hypersonic aircraft cruise section multi-constraint guidance method' takes a three-degree-of-freedom kinetic equation as a model, designs an optimal guidance law which meets various flight process constraints, but does not consider the anti-interference problem under the complex environment. The Chinese patent application No. 201310327296.3 provides a near space vehicle robust control method with input saturation, the method divides system uncertainty and interference into a slow loop subsystem and a fast loop subsystem, adopts an adaptive method to process composite interference in a system for the slow loop system, utilizes a nonlinear interference observer to process the composite interference for the fast loop system, uses a common sliding mode method to design a controller and considers the saturation problem, but even if the nonlinear interference observer can ensure interference observation error convergence through reasonable design, the convergence speed is slow, the observation error has longer time, the deviation of the result and an ideal track is larger, and the requirement of a hypersonic vehicle flying in a complex environment on high accuracy cannot be met. The article near space vehicle robust self-adaptive control based on the trajectory linearization method utilizes the function approximation capability of the single hidden layer neural network and the useful information of the analysis model of the controlled object to construct a single hidden layer neural network interference observer which is used for estimating the uncertainty existing in the system on line, but the interference observer can only estimate the state uncertainty considered in off-line learning and has certain limitation.
In conclusion, the conventional method lacks effective analysis and processing of multi-source interference such as strong uncertainty, gust interference and the like of the aerospace vehicle, cannot ensure fast and high-precision cruise guidance of the aerospace vehicle under a high-demand task, and is urgently needed to design an aerospace vehicle cruise guidance method with fast anti-interference capability.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the defect of weak interference resistance in the prior art, the problem of fast anti-interference high-precision cruise guidance of an aircraft containing uncertainty of pneumatic parameters and interference of gust and the like is solved, and the cruise guidance method combining a sliding mode interference observer and a proportional guidance control law is provided.
The technical scheme adopted by the invention for solving the technical problems is as follows: a quick anti-interference guidance method for an aerospace vehicle cruise section is characterized by establishing a dynamic model containing pneumatic parameter uncertainty and gust equivalent interference, designing a sliding mode disturbance observer to quickly estimate equivalent interference, realizing a vehicle cruise guidance target by utilizing a proportional guidance law, and finally designing a composite cruise section quick anti-interference controller by combining the sliding mode disturbance observer and the proportional guidance law, wherein,
firstly, completing the multi-source interference influence and transmission mechanism analysis of the uncertainty of the pneumatic parameters of the cruise section and the gust interference, wherein the pneumatic parameters comprise a lift coefficient and a resistance coefficient, and establishing an aerospace vehicle dynamic model containing the multi-source interference equivalent interference;
secondly, designing a sliding mode disturbance observer to quickly estimate equivalent disturbance received by the aerospace vehicle cruise section according to the dynamic model in the first step, and obtaining a disturbance estimated value;
thirdly, designing a proportional guidance control law for an aircraft dynamics model with an interference-free hypothesis;
and fourthly, designing a composite proportional guidance controller with anti-interference capability by using the interference estimation value obtained in the second step and the proportional guidance control law obtained in the third step, and finishing the rapid anti-interference guidance of the aerospace vehicle in the cruise section.
The method comprises the following concrete steps:
the method comprises the following steps of firstly, establishing a three-dimensional aircraft dynamics model containing aerodynamic parameter uncertainty and gust interference, wherein starting parameters comprise a lift coefficient and a drag coefficient:
Figure BDA0001763789860000031
wherein V is the speed of the aerospace vehicle relative to the earth,
Figure BDA0001763789860000032
is the first derivative of V, theta is the velocity dip,
Figure BDA0001763789860000033
is the first derivative of theta, sigma is the yaw angle,
Figure BDA0001763789860000034
is the first derivative of sigma, alpha is the attack angle, v is the roll angle, r is the geocentric distance,
Figure BDA0001763789860000035
is the first derivative of r, λ and
Figure BDA0001763789860000036
respectively the longitude and the latitude of the aircraft,
Figure BDA0001763789860000037
and
Figure BDA0001763789860000038
respectively the first derivative of longitude and latitude, m is the mass of the cruise aircraft, S is the effective area of wing, rho is the atmospheric density, mumT, L and D represent thrust, lift and drag, respectively, for the Earth's gravitational constant. d1、d2、d3、d4、d5、d6Representing the equivalent interference of the uncertainty of the aerodynamic parameters and the interference of gusts. The lift and drag expressions are as follows:
Figure BDA0001763789860000039
where ρ is the atmospheric density, S is the reference area of the aircraft, CLAnd CDThe aerodynamic parameter models of the lift coefficient and the resistance coefficient are respectively as follows:
Figure BDA00017637898600000310
wherein M isaMach number, and α is angle of attack; cL1、CL2、CL3、CL4The coefficient is a second-order attack angle coefficient, a first-order attack angle coefficient, a Mach number coefficient and a constant coefficient of the lift coefficient; cD1、CD2、CD3、CD4The coefficient is a second-order attack angle coefficient, a first-order attack angle coefficient, a Mach number coefficient and a constant coefficient of the resistance coefficient; the control quantity is selected as an aircraft roll angle v, an attack angle alpha and a thrust T;
equation (1) is converted to the following state space expression:
Figure BDA00017637898600000311
wherein the content of the first and second substances,
Figure BDA0001763789860000041
x is a variable of the state of the system,
Figure BDA0001763789860000042
is the first derivative of x, f (x) is a non-linear function with respect to the state variable x, u is the system input, and d is the equivalent disturbance.
Secondly, designing a sliding mode disturbance observer aiming at the aerospace vehicle dynamic model in the first step to carry out rapid estimation on the uncertainty of the aerodynamic parameters of the aircraft and the wind gust equivalent disturbance to obtain a disturbance estimation value:
the disturbance observer is designed as follows:
Figure BDA0001763789860000043
wherein z is0In the case of the intermediate variables of the state,
Figure BDA0001763789860000044
is z0First derivative of v0For the intermediate variables of the function, the intermediate variables,
Figure BDA0001763789860000045
is v is0The first derivative of (a) is,
Figure BDA0001763789860000046
for an estimate of the unknown equivalent interference d,
Figure BDA0001763789860000047
is composed of
Figure BDA0001763789860000048
The first derivative of (a) is,
Figure BDA0001763789860000049
for first derivative of unknown equivalent interference
Figure BDA00017637898600000410
Is determined by the estimated value of (c),
Figure BDA00017637898600000411
is composed of
Figure BDA00017637898600000412
First derivative of, λ0、λ1、λ2Is the observer gain and is a positive number. sign (·) denotes the derivation of a sign function.
Thirdly, designing a proportional guidance control law to meet the control task requirement:
the designed proportion guidance law is as follows:
Figure BDA00017637898600000413
wherein the content of the first and second substances,
Figure BDA00017637898600000414
is the projected angular velocity, k, of the aircraft's flight angular velocity in the horizontal planeTFor horizontal guidance factor, λTFor the horizontal line-of-sight angle, λ, of the aircraftTFFor the horizontal line-of-sight angle of the aircraft terminal constraints,
Figure BDA00017637898600000415
in order to achieve a horizontal line-of-sight angular acceleration,
Figure BDA00017637898600000416
where R is the aircraft-to-terminal distance,
Figure BDA00017637898600000417
is the first derivative of R;
from which lateral acceleration can be derived
Figure BDA0001763789860000051
Then overload from side direction
Figure BDA0001763789860000052
ny2The roll angle can be derived from 1
Figure BDA0001763789860000053
After the roll angle is obtained, the attack angle is iteratively solved according to the balance condition, and finally the required thrust is obtained
Figure BDA0001763789860000054
Substituting the calculated roll angle v, attack angle alpha and thrust T control quantity into a state space expression (3) to obtain a proportional guidance equivalent system input ue：
Figure BDA0001763789860000055
Fourthly, designing a composite proportional guidance controller by using the interference estimation value in the second step and the proportional guidance control law in the third step, and completing the rapid anti-interference guidance method in the cruising period of the aerospace vehicle as follows:
designing a composite proportional pilot controller:
Figure BDA0001763789860000056
wherein u iseIn order to scale the equivalent system input,
Figure BDA0001763789860000057
is an interference estimate of the unknown equivalent interference d.
Compared with the prior art, the invention has the advantages that: compared with the prior art, the method fully considers the complex coupling in the practical model and the pneumatic parameter uncertainty and gust interference in the flight process of the cruise section of the aircraft, is suitable for various flight systems and cruise section rapid anti-interference guidance systems of other high-altitude unmanned aircraft, and simultaneously ensures the high precision and rapidity of guidance control.
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FIG. 1 is a design flow chart of a rapid anti-interference guidance method for an aerospace vehicle cruise section.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
As shown in FIG. 1, the invention relates to a rapid anti-interference guidance method for an aerospace vehicle cruise section. Aiming at the problem that the precision is reduced due to the existence of pneumatic parameter uncertainty and gust interference in the conventional cruise guidance method, the method comprises the first step of completing analysis of multi-source interference influence and transmission mechanism such as the pneumatic parameter uncertainty and the gust interference and establishing an aircraft dynamics model containing equivalent interference, wherein the pneumatic parameters comprise a lift coefficient and a drag coefficient; secondly, designing a sliding mode disturbance observer aiming at the aircraft dynamics model established in the first step to quickly estimate the uncertainty of the aerodynamic parameters of the aircraft and the equivalent disturbance of gust disturbance, and obtaining a disturbance estimated value; thirdly, designing a proportional guidance control law for an aircraft dynamics model with an interference-free hypothesis; and fourthly, designing a composite proportional guidance controller with anti-interference capability by using the interference estimation value obtained in the second step and the proportional guidance control law obtained in the third step, and finishing quick anti-interference guidance of the aerospace vehicle in the cruise section. The invention adopts the fast anti-interference guidance method of the cruise section combining the sliding mode interference observer and the proportional guidance, has the characteristics of high precision and strong engineering practicability, and is suitable for the cruise guidance system of a high-altitude flight system and the reentry section of an aircraft.
The specific implementation steps are as follows:
the method comprises the following steps of firstly, establishing an aircraft dynamic model containing aerodynamic parameter uncertainty and gust interference, wherein the aerodynamic parameters comprise a lift coefficient and a drag coefficient:
Figure BDA0001763789860000061
wherein V is the speed of the aerospace vehicle relative to the earth, the initial value is 1806m/s,
Figure BDA0001763789860000062
is the first derivative of V, theta is the velocity dip, the initial value is 0rad,
Figure BDA0001763789860000063
is the first derivative of theta, sigma is the yaw angle, the initial value is 0.3rad,
Figure BDA0001763789860000064
is the first derivative of sigma, alpha is the attack angle, v is the roll angle, r is the geocentric distance, the initial value is 6386km,
Figure BDA0001763789860000065
is the first derivative of r, λ and
Figure BDA0001763789860000066
respectively the longitude and latitude of the aircraft, the initial value is 0 degree,
Figure BDA0001763789860000067
and
Figure BDA0001763789860000068
respectively the first derivative of longitude and latitude, m is the mass of the cruise aircraft, and the value is 35828kg, mumIs the gravitational constant, and takes 398600.4405 multiplied by 109m3/r2T, L and D represent thrust, lift and drag, respectively. d1、d2、d3、d4、d5、d6Representing the equivalent interference of the uncertainty of the aerodynamic parameters and the interference of gusts. The lift and drag expressions are as follows:
Figure BDA0001763789860000071
wherein rho is the atmospheric density and takes the value of 1.225kg/m3S is the effective area of the wing, and the value is 149.4m2，CLAnd CDLift coefficient and drag coefficient, lift coefficient andthe pneumatic parameter model of the drag coefficient is as follows:
Figure BDA0001763789860000072
wherein M isaMach number, initial value 5.3Ma, alpha is attack angle; the control quantity is selected as an aircraft roll angle v, an attack angle alpha and a thrust T;
equation (1) is converted to the following state space expression:
Figure BDA0001763789860000073
wherein the content of the first and second substances,
Figure BDA0001763789860000074
x is a variable of the state of the system,
Figure BDA0001763789860000075
is the first derivative of x, f (x) is a non-linear function with respect to the state variable x, u is the system input, and d is the equivalent disturbance.
Secondly, designing a sliding mode disturbance observer aiming at the aerospace vehicle dynamic model in the first step to carry out rapid estimation on the uncertainty of the aerodynamic parameters of the aircraft and the wind gust equivalent disturbance, and obtaining a disturbance estimation value:
the disturbance observer is designed as follows:
Figure BDA0001763789860000076
wherein z is0In the case of the intermediate variables of the state,
Figure BDA0001763789860000077
is z0First derivative of v0For the intermediate variables of the function, the intermediate variables,
Figure BDA0001763789860000078
is v is0ToThe first derivative of the order of the first,
Figure BDA0001763789860000079
for an estimate of the unknown equivalent interference d,
Figure BDA0001763789860000081
is composed of
Figure BDA0001763789860000082
The first derivative of (a) is,
Figure BDA0001763789860000083
for first derivative of unknown equivalent interference
Figure BDA0001763789860000084
Is determined by the estimated value of (c),
Figure BDA0001763789860000085
is composed of
Figure BDA0001763789860000086
First derivative of, λ0、λ1、λ2For observer gain, 2, 1.5, 1.1 can be taken, respectively. sign (·) denotes the derivation of a sign function.
Thirdly, designing a proportional guidance control law for an aircraft dynamics model with an interference-free hypothesis:
the designed proportion guidance law is as follows:
Figure BDA0001763789860000087
wherein the content of the first and second substances,
Figure BDA0001763789860000088
is the projected angular velocity, k, of the aircraft's flight angular velocity in the horizontal planeTIs a horizontal guidance coefficient with a value of 4, lambdaTFor the horizontal line-of-sight angle, λ, of the aircraftTFFor the horizontal line-of-sight angle of the aircraft terminal constraints,
Figure BDA0001763789860000089
in order to achieve a horizontal line-of-sight angular acceleration,
Figure BDA00017637898600000810
where R is the aircraft-to-terminal distance,
Figure BDA00017637898600000811
is the first derivative of R;
from which lateral acceleration can be derived
Figure BDA00017637898600000812
Then overload from side direction
Figure BDA00017637898600000813
ny2The roll angle can be derived from 1
Figure BDA00017637898600000814
After the roll angle is obtained, the attack angle is iteratively solved according to the balance condition, and finally the required thrust is obtained
Figure BDA00017637898600000815
Substituting the calculated roll angle v, attack angle alpha and thrust T control quantity into a state space expression (3) to obtain a proportional guidance equivalent system input ue：
Figure BDA00017637898600000816
Fourthly, designing a composite proportional guidance controller by using the interference estimation value obtained in the second step and the proportional guidance control law obtained in the third step, and completing the rapid anti-interference guidance method in the cruising segment of the aerospace vehicle as follows:
designing a composite proportional pilot controller:
Figure BDA0001763789860000091
wherein u iseIn order to scale the equivalent system input,
Figure BDA0001763789860000092
is an interference estimate of the unknown equivalent interference d.
The method of the invention is adopted to carry out cruise guidance, high-precision equal-height and constant-speed cruise flight can be realized, after the high-speed cruise flight is kept for 50s, the height error is less than 5 per thousand of the set height, the speed error is less than 1 per thousand of the set speed, and simultaneously, compared with a controller with non-interference estimation and compensation, the interference estimation error can be stable within 1s, so that a compensated system can reach a control target under the control of a proportional guidance law, and the requirements of stability and rapidity are met.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (1)

1. A quick anti-interference guidance method for an aerospace vehicle cruise section is characterized by comprising the following steps:
firstly, completing the multi-source interference influence and transmission mechanism analysis of the uncertainty of the pneumatic parameters of the cruise section and the gust interference, wherein the pneumatic parameters comprise a lift coefficient and a resistance coefficient, and establishing an aerospace vehicle dynamic model containing the multi-source interference equivalent interference;
secondly, designing a sliding mode disturbance observer to quickly estimate equivalent disturbance received by the aerospace vehicle cruise section according to the dynamic model in the first step, and obtaining a disturbance estimated value;
thirdly, designing a proportional guidance control law for an aircraft dynamics model with an interference-free hypothesis;
fourthly, designing a composite proportional guidance controller with anti-interference capability by using the interference estimation value obtained in the second step and the proportional guidance control law in the third step, and completing the rapid anti-interference guidance of the aerospace vehicle in the cruise section;
in the first step, multi-source interference analysis of uncertainty of pneumatic parameters of a cruise section and gust interference is completed, wherein the pneumatic parameters comprise lift coefficients and drag coefficients, and an aerospace vehicle dynamic model containing the multi-source interference equivalent interference is established:
Figure FDA0003011503550000011
wherein V is the speed of the aerospace vehicle relative to the earth,
Figure FDA0003011503550000012
is the first derivative of V, theta is the velocity dip,
Figure FDA0003011503550000013
is the first derivative of theta, sigma is the yaw angle,
Figure FDA0003011503550000014
is the first derivative of sigma, alpha is the attack angle, v is the roll angle, r is the geocentric distance,
Figure FDA0003011503550000015
is the first derivative of r, λ and
Figure FDA0003011503550000016
respectively the longitude and the latitude of the aircraft,
Figure FDA0003011503550000017
and
Figure FDA0003011503550000018
respectively the first derivative of longitude and latitude, m is the mass of the cruise aircraft, S is the effective area of wing, rho is the atmospheric density, mumIs the constant of earth's gravity, T, LAnd D represents thrust, lift and drag, respectively, D1、d2、d3、d4、d5、d6Expressing equivalent interference of uncertainty of aerodynamic parameters and gust interference, and expressing the lift and the resistance as follows:
Figure FDA0003011503550000019
where ρ is the atmospheric density, S is the reference area of the aircraft, CLAnd CDThe aerodynamic parameter models of the lift coefficient and the resistance coefficient are respectively as follows:
Figure FDA0003011503550000021
wherein M isaMach number, and α is angle of attack; cL1、CL2、CL3、CL4The coefficient is a second-order attack angle coefficient, a first-order attack angle coefficient, a Mach number coefficient and a constant coefficient of the lift coefficient; cD1、CD2、CD3、CD4The coefficient is a second-order attack angle coefficient, a first-order attack angle coefficient, a Mach number coefficient and a constant coefficient of the resistance coefficient; the control quantity is selected as an aircraft roll angle v, an attack angle alpha and a thrust T;
equation (1) is converted to the following state space expression:
Figure FDA0003011503550000022
wherein the content of the first and second substances,
Figure FDA0003011503550000023
x is a variable of the state of the system,
Figure FDA0003011503550000024
is the first derivative of x, f (x) is with respect to the state variablex, u is the system input, d is the equivalent interference;
in the second step, according to the dynamic model in the first step, a sliding mode disturbance observer is designed to quickly estimate equivalent disturbance received by the aerospace vehicle cruise section, and a disturbance estimation value is obtained:
Figure FDA0003011503550000025
wherein z is0In the case of the intermediate variables of the state,
Figure FDA0003011503550000026
is z0First derivative of v0For the intermediate variables of the function, the intermediate variables,
Figure FDA0003011503550000027
is v is0The first derivative of (a) is,
Figure FDA0003011503550000028
for an estimate of the unknown equivalent interference d,
Figure FDA0003011503550000029
is composed of
Figure FDA00030115035500000210
The first derivative of (a) is,
Figure FDA00030115035500000211
for first derivative of unknown equivalent interference
Figure FDA00030115035500000212
Is determined by the estimated value of (c),
Figure FDA00030115035500000213
is composed of
Figure FDA00030115035500000214
First derivative of, λ0、λ1、λ2For observer gain and positive number, sign (·) represents solving a sign function;
in the third step, aiming at the aircraft dynamics model without interference hypothesis, a proportion guidance control law is designed as follows:
the designed proportion guidance law is as follows:
Figure FDA0003011503550000031
wherein the content of the first and second substances,
Figure FDA0003011503550000032
is the projected angular velocity, k, of the aircraft's flight angular velocity in the horizontal planeTFor horizontal guidance factor, λTFor the horizontal line-of-sight angle, λ, of the aircraftTFFor the horizontal line-of-sight angle of the aircraft terminal constraints,
Figure FDA0003011503550000033
in order to achieve a horizontal line-of-sight angular acceleration,
Figure FDA0003011503550000034
where R is the aircraft-to-terminal distance,
Figure FDA0003011503550000035
is the first derivative of R;
lateral acceleration can thus be obtained:
Figure FDA0003011503550000036
then overload from side direction
Figure FDA0003011503550000037
ny2The roll angle can be derived as 1:
Figure FDA0003011503550000038
after the roll angle is obtained, the attack angle is solved iteratively according to the balance condition, and finally the required thrust is obtained:
Figure FDA0003011503550000039
Tcosα＝D
substituting the calculated roll angle v, attack angle alpha and thrust T control quantity into a state space expression (3) to obtain a proportional guidance equivalent system input ue：
Figure FDA00030115035500000310
In the fourth step, the composite proportion guidance controller is designed as follows:
Figure FDA00030115035500000311
wherein u iseIn order to scale the equivalent system input,
Figure FDA00030115035500000312
is an interference estimate of the unknown equivalent interference d.
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