Aircraft sensor measurement error transfer algorithm based on linearization

Abstract

The invention belongs to the field of flight control, and particularly relates to an aircraft sensor measurement error transfer algorithm based on linearization, which comprises the following steps: introducing a sensor measurement error, and calculating a Jacobian matrix coefficient; selecting the state error amount of the aircraft according to the error transfer equation; and adopting a polynomial fitting method to derive discrete data in the fitted error transfer matrix # imgabs0 # to obtain corresponding partial derivatives, and substituting the partial derivatives into an error transfer equation to obtain the influence of the measurement error on other flight states. A longitudinal dynamic model and a kinematic model in the landing process of an aircraft are researched, the transmission process of the measurement error of the sensor is analyzed by adopting a linearization method, and finally a transmission model of the measurement error of the airborne sensor in the landing process of the aircraft is established. The model can provide theoretical support and index requirements for optimizing the measurement performance of various sensors of an aircraft and optimizing the performance of a flight control system, so that the landing precision of the aircraft is improved.

Description

Technical Field

[0001] The present application belongs to the field of flight control, and in particular relates to an aircraft sensor measurement error propagation algorithm based on linearization. Background Art

[0002] Controlling an aircraft's safe landing has always been a challenging problem in the aerospace field. When studying an aircraft's flight control system, it's necessary to consider the errors inherent in the aircraft's onboard sensors' measurements of flight status, such as airspeed, altitude, angle of attack, pitch rate, and pitch angle. Currently, many studies related to flight control have analyzed the statistical characteristics of the errors in sensor-measured flight status variables and designed various filtering algorithms to reduce these errors. However, no research has examined the impact of these errors on the aircraft during landing. Without a clear understanding of how these errors are transferred within the aircraft's mathematical model during landing, it's impossible to quantify their impact on the aircraft's flight status. This makes it impossible to provide theoretical support and indicators for optimizing the measurement performance of the aircraft's various sensors and flight control systems, ultimately impacting the aircraft's landing accuracy.

[0003] Therefore, how to ensure the landing accuracy of the aircraft is a problem that needs to be solved. Summary of the Invention

[0004] The purpose of this application is to provide an aircraft sensor measurement error propagation algorithm based on linearization to solve the problem in the prior art that it is impossible to determine the impact of the error amount of sensor measurement of flight status on the aircraft and thus affect landing accuracy.

[0005] The technical solution of this application is: a linearization-based aircraft sensor measurement error propagation algorithm, comprising: Based on the aircraft's landing index requirements, including the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, and pitch angle, a nominal motion model of the aircraft's ideal landing process is established. The nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitching moment coefficient of the aircraft in the nominal state are calculated using the nominal motion model. Obtain the aircraft's mass, gravitational acceleration, pitch rate, and altitude in the aircraft's trajectory coordinate system, analyze the aircraft's motion trajectory, and establish a nonlinear model of the aircraft's landing. Sensor measurement errors are introduced, and the nonlinear model of aircraft landing is linearized using a first-order Taylor expansion. The Jacobian matrix coefficients are calculated and substituted into the nominal motion model to obtain the error transfer equation. The aircraft's state error is selected based on the error transfer equation, and based on the state error, the error transfer equation is converted into an error transfer matrix. The error transfer matrix is fitted using the polynomial fitting method. The discrete data in the equation are differentiated to obtain the corresponding partial derivatives of the discrete data, which are then substituted into the error transfer equation to obtain the impact of the measurement error on other flight states.

[0006] Preferably, the thrust of the aircraft , lift ,resistance , pitching moment The expression is: ; ; ; ; in Indicates the throttle size. represents the air density, Indicates airspeed, represents the wing reference area, represents the mean aerodynamic chord length; represents the thrust coefficient; 、 represent the lift coefficient and drag coefficient respectively; represents the tilting moment coefficient.

[0007] Preferably, within the nominal motion model, the engine thrust, lift, drag and pitching moment are decomposed in the aircraft's flight path system, and the pitching moment is made zero to solve the nominal flight state of the aircraft landing, thereby obtaining the nominal engine thrust, nominal lift coefficient, nominal drag coefficient and nominal pitching moment coefficient.

[0008] Preferably, the nonlinear model of the aircraft landing is: ; ; ; ; ; ; in 、 、 and Represent the mass, gravitational acceleration, pitch rate and altitude of the aircraft respectively, is the moment of inertia in the y direction, For time, is the angle of attack, is the pitch angle, is the trajectory inclination angle.

[0009] Preferably, the sensor measurement error is: , where is the flight state error, To control the amount; For time; After linearization of the first-order Taylor expansion, we get: Where, is the flight state error deviation, is the control quantity deviation, is the nominal value of the flight state error, is the nominal value of the control quantity; Then the error and transfer equations are obtained as follows: ; ; ; ; ; ; Where, 、 、 、 、 、 、 、 、 Respectively represent the differences in the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, pitch angle, and altitude; 、 、 、 They respectively represent the nominal state values corresponding to the aircraft's airspeed, thrust, angle of attack, and track inclination angle.

[0010] Preferably, the method for obtaining the state error is: In the absence of airflow disturbances and without considering the input of throttle, control surfaces, etc., the error expression for obtaining the longitudinal force and longitudinal moment of the aircraft is: ; ; ; ; Where, , , , , , , , , , , , are the partial derivatives of the parameters corresponding to each subscript, Indicates the height difference, express The first derivative of express The first derivative of ; Substituting the error expressions of the aircraft longitudinal force and longitudinal moment into the error transfer equation, the state error is obtained as follows: ; ; ; ; ; ; Express the state error in vector form: ; The error transfer equation is converted into the expression of the error transfer matrix A, which is: .

[0011] The linearization-based aircraft sensor measurement error propagation algorithm of this application studies the longitudinal dynamic model and kinematic model of the aircraft landing process, uses a linearization method to analyze the propagation process of the sensor measurement error, and finally establishes a propagation model of the onboard sensor measurement error during aircraft landing. This model can provide theoretical support and index requirements for optimizing the measurement performance of various aircraft sensors and optimizing the performance of the flight control system, thereby improving the landing accuracy of the aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the technical solutions provided by this application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of this application.

[0013] Figure 1 This is a schematic diagram of the overall process of this application; Figure 2 Schematic diagram of the aircraft landing process for this application; Figure 3 Plot of fitted curves for discrete aerodynamic data for this application. DETAILED DESCRIPTION

[0014] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0015] A linearization-based aircraft sensor measurement error propagation algorithm, such as Figure 1 , including the following steps: Step S100, according to the landing index requirements of the aircraft, including the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle and pitch angle, such as Figure 2 , in the figure 、 、 、 、 、 、 、 where represents the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, and pitch angle, respectively. A nominal motion model for the aircraft's ideal landing process is established. The nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitching moment coefficient are calculated from this nominal motion model when the aircraft is in its nominal state.

[0016] Preferably, the thrust of the aircraft , lift ,resistance , pitching moment The expression is: ; ; ; ;

[0017] in Indicates the throttle size. represents the air density, Indicates airspeed, represents the wing reference area, represents the mean aerodynamic chord length. represents the thrust coefficient, which is a function of airspeed and flight altitude; 、 They represent the lift coefficient and the drag coefficient respectively, both of which are functions of angle of attack, airspeed, and flight altitude; It represents the pitch moment coefficient and is a function of angle of attack, airspeed, pitch rate, angle of attack rate and flight altitude.

[0018] Under nominal conditions, the aircraft needs to maintain constant attitude, angle of attack, airspeed, and track inclination angle during landing. The nominal angle of attack, pitch angle, airspeed, and track inclination angle are usually set as follows: 、 、 、 .

[0019] Preferably, within the nominal motion model, the engine thrust, lift, drag and pitching moment are decomposed in the aircraft's flight path system, and the pitching moment is made zero to solve the nominal flight state of the aircraft landing, thereby obtaining the nominal engine thrust, nominal lift coefficient, nominal drag coefficient and nominal pitching moment coefficient.

[0020] The corresponding state parameters are shown in Table 1: Table 1: Aircraft landing nominal state parameters

[0021] Step S200: Establish a nonlinear model of the aircraft landing process: The mass, gravitational acceleration, pitch rate, and altitude of the aircraft are obtained in the aircraft's track coordinate system. The aircraft's motion trajectory is analyzed and a nonlinear model of the aircraft's landing is established. The nonlinear model of the aircraft's landing is shown below: ; ; ; ; ; ; in 、 、 and Represent the mass, gravitational acceleration, pitch rate and altitude of the aircraft respectively, is the moment of inertia in the y direction, For time, is the angle of attack, is the pitch angle, is the trajectory inclination angle.

[0022] Step S300: Obtain the error propagation equation of the aircraft state based on the linearization method: Sensor measurement errors are introduced, and a first-order Taylor expansion is performed on the nonlinear model of aircraft landing to linearize it. The Jacobian matrix coefficients are calculated and substituted into the nominal motion model to obtain the error propagation equation. The aircraft's state error is selected based on the error propagation equation, and based on the state error, the error propagation equation is converted into an error propagation matrix.

[0023] Preferably, the sensor measurement error is: , where is the flight state error, For control quantities, such as rudder deviation and throttle command; For time; After linearization of the first-order Taylor expansion, we get: Where, is the flight state error deviation, is the control quantity deviation, is the nominal value of the flight state error, is the nominal value of the control quantity; Then the error and transfer equations are obtained as follows: ; ; ; ; ; ; Where, 、 、 、 、 、 、 、 、 Respectively represent the differences in the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, pitch angle, and altitude; 、 、 、 They respectively represent the nominal state values corresponding to the aircraft's airspeed, thrust, angle of attack, and track inclination angle.

[0024] Preferably, the method for obtaining the state error is: In the absence of airflow disturbances and without considering the input of throttle, control surfaces, etc., the error expression for obtaining the longitudinal force and longitudinal moment of the aircraft is: ; ; ; ; Where, , , , , , , , , , , , are the partial derivatives of the parameters corresponding to each subscript, Indicates the height difference, express The first derivative of express The first derivative of .

[0025] Substituting the error expressions of the aircraft longitudinal force and longitudinal moment into the error transfer equation, the state error is obtained as follows: ; ; ; ; ; ; Express the state error in vector form: ; The error transfer equation is converted into the expression of the error transfer matrix A, which is: .

[0026] Step S400, calculate the parameters of the error transfer matrix: The error transfer matrix is fitted using the polynomial fitting method. The discrete data in the equation are differentiated to obtain the corresponding partial derivatives of the discrete data, and then substituted into the error transfer equation to obtain the impact of the measurement error on other flight states.

[0027] In the error transfer matrix The most complex parameters are the partial derivatives of various aerodynamic forces and aerodynamic moments with respect to different aircraft state quantities. Continuous data refers to data with a refresh rate higher than 10Hz. Data with a refresh rate lower than 10Hz is discrete data and requires fitting. Since aerodynamic data is generally discrete, it is necessary to fit the discrete points before calculating the derivatives. Specifically, the partial derivative of the lift coefficient with respect to the angle of attack is solved using a polynomial fitting method:

[0028]

[0029] in It represents the lift coefficient of the fuselage and wings as a whole, represents the lift coefficient of the horizontal tail, represents the lift coefficient of the canard, is a fixed parameter.

[0030] The partial derivative of lift with respect to angle of attack is:

[0031] Lift coefficient For example, the lift coefficient The relationship with the angle of attack is shown in Table 2: Table 2: Lift coefficients for different angles of attack value

[0032] Then perform a third-order polynomial fitting on the discrete data to obtain a third-order polynomial function. The result is as follows: Figure 3 As shown, the obtained third-order polynomial function is:

[0033] In the aircraft's nominal landing state , .

[0034] According to the same method, other partial derivatives can be obtained to obtain the error transfer matrix The parameters are as follows: ; Finally, the transmission model of the sensor's measurement error is obtained.

[0035] In summary, this application studies the longitudinal dynamic model and kinematic model of the aircraft landing process, uses a linearization method to analyze the transmission process of sensor measurement errors, and finally establishes a transmission model of airborne sensor measurement errors during aircraft landing. This model can provide theoretical support and index requirements for optimizing the measurement performance of various aircraft sensors and optimizing the performance of the flight control system, thereby improving the landing accuracy of the aircraft.

[0036] Finally, it should be noted that the drawings of the embodiments disclosed in the present invention only involve structures related to the embodiments disclosed in the present invention. Other structures can refer to common designs. In the absence of conflicts, the same embodiment and different embodiments of the present invention can be combined with each other. Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A linearization-based aircraft sensor measurement error propagation algorithm, characterized in that: include: Based on the aircraft's landing index requirements, including the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, and pitch angle, a nominal motion model of the aircraft's ideal landing process is established. The nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitching moment coefficient of the aircraft in the nominal state are calculated using the nominal motion model. Obtain the aircraft's mass, gravitational acceleration, pitch rate, and altitude in the aircraft's trajectory coordinate system, analyze the aircraft's motion trajectory, and establish a nonlinear model of the aircraft's landing. Sensor measurement errors are introduced, and the nonlinear model of aircraft landing is linearized using a first-order Taylor expansion. The Jacobian matrix coefficients are calculated and substituted into the nominal motion model to obtain the error transfer equation. Selecting the state error of the aircraft according to the error transfer equation, and converting the error transfer equation into an error transfer matrix based on the state error; The error transfer matrix is fitted using the polynomial fitting method. The discrete data in the equation are differentiated to obtain the corresponding partial derivatives of the discrete data, which are then substituted into the error transfer equation to obtain the impact of the measurement error on other flight states.

2. The linearization-based aircraft sensor measurement error propagation algorithm according to claim 1, characterized in that: The thrust of the aircraft , lift ,resistance , pitching moment The expression is: ； ； ； ； in Indicates the throttle size. represents the air density, Indicates airspeed, represents the wing reference area, represents the mean aerodynamic chord length; represents the thrust coefficient; 、 represent the lift coefficient and drag coefficient respectively; represents the tilting moment coefficient.

3. The linearization-based aircraft sensor measurement error propagation algorithm according to claim 2, characterized in that: In the nominal motion model, the engine thrust, lift, drag, and pitching moment are decomposed in the aircraft's flight path system, and the pitching moment is set to zero to solve the nominal flight state of the aircraft landing, thereby obtaining the nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitching moment coefficient.

4. The linearization-based aircraft sensor measurement error propagation algorithm according to claim 2, wherein: The nonlinear model of the aircraft landing is: ； ； ； ； ； ； in 、 、 and Represent the mass, gravitational acceleration, pitch rate and altitude of the aircraft respectively, is the moment of inertia in the y direction, For time, is the angle of attack, is the pitch angle, is the trajectory inclination angle.

5. The linearization-based aircraft sensor measurement error propagation algorithm according to claim 4, wherein: The sensor measurement error is: , where is the flight state error, To control the amount; For time; After linearization of the first-order Taylor expansion, we get: Where, is the flight state error deviation, is the control quantity deviation, is the nominal value of the flight state error, is the nominal value of the control quantity; Then the error and transfer equations are obtained as follows: ； ； ； ； ； ； Where, 、 、 、 、 、 、 、 、 Respectively represent the differences in the aircraft's airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, pitch angle, and altitude; 、 、 、 They respectively represent the nominal state values corresponding to the aircraft's airspeed, thrust, angle of attack, and track inclination angle.

6. The linearization-based aircraft sensor measurement error propagation algorithm according to claim 5, characterized in that: The method for obtaining the state error is: In the absence of airflow disturbances and without considering the input of throttle, control surfaces, etc., the error expression for obtaining the longitudinal force and longitudinal moment of the aircraft is: ； ； ； ； Where, , , , , , , , , , , , are the partial derivatives of the parameters corresponding to each subscript, Indicates the height difference, express The first derivative of express The first derivative of ; Substituting the error expressions of the aircraft longitudinal force and longitudinal moment into the error transfer equation, the state error is obtained as follows: ； ； ； ； ； ； Express the state error in vector form: ； The error transfer equation is converted into the expression of the error transfer matrix A, which is: 。

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