Aircraft system state estimation method based on adaptive interval observer

Abstract

The invention belongs to the technical field of aircraft detection and maintenance, and particularly relates to an aircraft system state estimation method based on a self-adaptive interval observer. The method comprises the following steps: step 1, establishing a discrete linear system model according to characteristics of an aircraft longitudinal motion system; step 2, performing dimensionality reduction on the discrete linear system model by adopting nonsingular transformation; 3, introducing an adaptive law, and designing an adaptive interval observer to realize state upper and lower bound estimation; and 4, based on a robust stability theory, designing linear short matrix inequality conditions, solving specific observation parameters, and ensuring the stability and robustness of the observer. Aiming at the problem that the existing state estimation method based on the interval observer is large in conservative property, the adaptive law is designed to replace the disturbance upper and lower bounds, and the accuracy of state estimation is improved.

Description

Technical Field

[0001] The present application belongs to the technical field of aircraft detection and maintenance, and in particular to an aircraft system state estimation method based on an adaptive interval observer. Background Art

[0002] The integrated flight control system is developing towards electrification and intelligence. As the complexity of flight missions gradually increases, the requirements for the real-time, reliability and stability of the aircraft integrated system are becoming higher and higher. However, due to the complex and harsh flight environment and the large number of unknown factors in the flight process, it is easy to cause failures in the aircraft system and affect its safe operation. Therefore, it is urgent to carry out research to improve the accuracy of aircraft system state estimation to ensure the safe operation of the aircraft. The rise of interval observer theory provides a new idea for state estimation. The so-called interval observer refers to a range or interval of state changes given by constructing upper and lower bound observers when there are uncertain factors in the system. The method is simple and intuitive.

[0003] The state estimation method based on interval observer in the prior art detects system faults by judging whether the residual signal crosses zero. Currently, there are few studies on reducing the conservatism of interval estimation of interval observers. Most of them use the upper and lower bounds of disturbances to design interval observers, which often leads to a larger interval range. The accuracy of state estimation still has room for improvement.

[0004] Therefore, it is desired to have a technical solution to overcome or at least alleviate at least one of the above-mentioned defects of the prior art. Summary of the invention

[0005] The purpose of the present application is to provide an aircraft system state estimation method based on an adaptive interval observer to solve at least one problem existing in the prior art.

[0006] The technical solution of this application is:

[0007] A method for estimating an aircraft system state based on an adaptive interval observer, comprising:

[0008] Step 1: Establish a discrete linear system model based on the characteristics of the aircraft longitudinal motion system;

[0009] Step 2: Using non-singular transformation to reduce the dimension of the discrete linear system model;

[0010] Step 3: Introduce the adaptive law and design an adaptive interval observer to realize the estimation of the upper and lower bounds of the state;

[0011] Step 4: Based on the robust stability theory, linear matrix inequality conditions are designed to solve specific observation parameters to ensure the stability and robustness of the adaptive interval observer.

[0012] In at least one embodiment of the present application, in step 1, a discrete linear system model is established according to the longitudinal motion system characteristics of the aircraft, including:

[0013] The discrete linear system model is:

[0014] x(k+1)=Ax(k)+Bu(k)+Fd(k)

[0015] y(k)=Cx(k)+v(k)

[0016] Among them, x(k) is the state variable, u(k) is the control input, y(k) is the measurable output of the system, A, B, C, and F are known constant matrices of appropriate dimensions, and the columns of matrices B and F are full rank, and the rows of matrix C are full rank. d(k) and v(k) represent disturbance and noise, respectively.

[0017] In at least one embodiment of the present application, in step 2, the discrete linear system model is reduced in dimension using a non-singular transformation, including:

[0018] Using three non-singular transformations The discretized linear model is transformed into a state:

[0019]

[0020] in, is a non-singular matrix such that There exists an orthogonal matrix Make

[0021] Make For Schur stability,

[0022] In at least one embodiment of the present application, in step 3, an adaptive law is introduced and an adaptive interval observer is designed to realize the estimation of the upper and lower bounds of the state, including:

[0023] make We can get:

[0024]

[0025] in, According to the Sylvester equation, we can solve Stable and non-negative;

[0026] According to the above formula, we can get The upper and lower bounds of :

[0027]

[0028] Design the adaptive interval observer as:

[0029]

[0030] in, and y(k) are the upper and lower bounds of the state estimate, and A y are the interval observer parameters to be designed, and t (k) is the adaptive law.

[0031] In at least one embodiment of the present application, the adaptive law and t (k) is:

[0032]

[0033] in,

[0034]

[0035] Among them, sgn is the sign function, σ i ,δ i is the design parameter that affects the interval width, λ i is the rate of change.

[0036] In at least one embodiment of the present application, in step 4, based on the robust stability theory, a linear matrix inequality condition is designed to solve specific observation parameters to ensure the stability and robustness of the adaptive interval observer, including:

[0037] Construct an optimization problem with linear matrix inequality constraints:

[0038] If there is a matrix:

[0039]

[0040] This solves the following problems:

[0041] minγs.t.

[0042]

[0043] Then the interval observer parameters to be determined are:

[0044]

[0045] in,

[0046]

[0047]

[0048] e=-(1-α)P 31 ,

[0049] f=-(1-α)P 32 ,

[0050] g=-(1-α)P 42 ,

[0051]

[0052] Among them, P means that the matrix is ​​positive definite, and the matrix is a symmetric matrix and Indicates that the matrix is ​​negatively definite, and the symbol ≥0 means that every element is greater than or equal to 0; V 11 、V 22 is a diagonal positive matrix, ∏ n2 =V 22g a gh ,g,h=1,2,…,n;V 11g Represents the matrix V 11 The gth element on the diagonal, V 22g Represents the matrix V 22 The gth element on the diagonal; and a gh The matrices to be determined are With A y The elements are in g rows and h columns, γ and μ are scalars greater than 0, 0<α<1, and T is a diagonal positive matrix.

[0053] The invention has at least the following beneficial technical effects:

[0054] The aircraft system state estimation method based on adaptive interval observer in this application first constructs a discrete linear model of the aircraft longitudinal motion system, then designs an adaptive interval observer, and uses linear matrix inequality technology to optimize and improve the robustness of state estimation. Compared with traditional methods, this method effectively improves the accuracy of the observer's estimation of the system state. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of an aircraft system state estimation method based on an adaptive interval observer according to an embodiment of the present application. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical scheme and advantages of the implementation of this application clearer, the technical scheme in the embodiment of this application will be described in more detail below in conjunction with the drawings in the embodiment of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of this application, not all of them. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain this application, and should not be construed as limitations on this application. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The embodiments of this application are described in detail below in conjunction with the drawings.

[0057] In the description of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the scope of protection of the present application.

[0058] The following is combined with Figure 1 This application is described in further detail.

[0059] The present application provides an aircraft system state estimation method based on an adaptive interval observer, comprising the following steps:

[0060] Step 1: Establish a discrete linear system model based on the characteristics of the aircraft longitudinal motion system;

[0061] Step 2: Use non-singular transformation to reduce the dimension of discrete linear system model;

[0062] Step 3: Introduce the adaptive law and design an adaptive interval observer to realize the estimation of the upper and lower bounds of the state;

[0063] Step 4: Based on the robust stability theory, design linear matrix inequality conditions and solve specific observation parameters to ensure the stability and robustness of the adaptive interval observer.

[0064] The aircraft system state estimation method based on the adaptive interval observer of the present application, first, in step 1, a discrete linear system model is established as:

[0065]

[0066] Where x(k)∈R n is the state quantity, u(k)∈R mis the control input, y(k)∈R p is the measurable output of the system, A, B, C, and F are known constant matrices of appropriate dimensions, and the columns of matrices B and F are full rank, the rows of matrix C are full rank, and d(k) and v(k)∈L2[0,∞) represent disturbance and noise, respectively.

[0067] In step 2, non-singular transformation is used to reduce the dimension of the discrete linear system model, including:

[0068] Using three non-singular transformations The discretized linear model is transformed into a state:

[0069]

[0070] in, is a non-singular matrix such that There exists an orthogonal matrix Make

[0071] Make For Schur stability,

[0072] In the method for estimating the state of an aircraft system based on an adaptive interval observer of the present application, in step 3, designing an adaptive interval observer includes:

[0073] make We can get:

[0074]

[0075] in, According to the Sylvester equation, we can solve Stable and non-negative;

[0076] According to formula (3), we can get The upper and lower bounds of :

[0077]

[0078] The adaptive interval observer is designed using formula (3):

[0079]

[0080] in, and y(k) are the upper and lower bounds of the state estimate, and A y are the interval observer parameters to be designed, and t (k) is the adaptive law.

[0081] Specifically, the adaptive law and t (k) is:

[0082]

[0083] in,

[0084]

[0085] Among them, sgn is the sign function, σ i >δ i >0 is the design parameter that affects the interval width, λ i >0 is the rate of change.

[0086] The aircraft system state estimation method based on the adaptive interval observer of the present application, finally, in step 4, solves the optimization problem of the matrix inequality constraint to obtain the interval observer parameters to be designed, including:

[0087] Construct an optimization problem with linear matrix inequality constraints:

[0088] If there is a matrix:

[0089]

[0090] This solves the following problems:

[0091] minγs.t.

[0092]

[0093] Then the interval observer parameters to be determined are:

[0094]

[0095] in,

[0096]

[0097]

[0098] e=-(1-α)P 31 ,

[0099] f=-(1-α)P 32 ,

[0100] g=-(1-α)P 42 ,

[0101]

[0102] Among them, P>0 means that the matrix is ​​positive definite, and the matrix is a symmetric matrix and Indicates that the matrix is ​​negatively definite, and the symbol ≥0 means that every element is greater than or equal to 0; V 11 、V 22 ∈R n×n is a diagonal positive matrix, ∏ n2 =V 22g a gh ,g,h=1,2,…,n;V 11g Represents the matrix V 11 The gth element on the diagonal, V 22g Represents the matrix V 22 The gth element on the diagonal; and a gh The matrices to be determined are With A y The elements of the g rows and h columns, γ and μ are scalars greater than 0, 0<α<1, is a diagonal positive matrix.

[0103] The method for estimating the state of an aircraft system based on an adaptive interval observer of the present application is further described below through a specific implementation method.

[0104] Step 1:

[0105] (a) Constructing a nonlinear mathematical model of the longitudinal motion of the aircraft:

[0106]

[0107] Where, T x =Tcos(δ z )cos(δ y ), T z =Tsinδ y , T represents the engine thrust, δ y ,δ z is the lateral and longitudinal deflection angle of the thrust vector rudder; α, β, φ, θ are the angle of attack, sideslip angle, yaw angle, and pitch angle, respectively; p, q, r are the components of the angular velocity in the body coordinate system (roll angular velocity, pitch angular velocity, yaw angular velocity); V, m, g are the aircraft speed, mass, and gravitational acceleration, respectively; L, D, M are the aircraft lift, drag, and pitch moment, respectively; I xx ,I yy ,I zz I is the moment of inertia of the aircraft around the body axis; xy ,Iyz ,I zx It is the inertia product of the aircraft with respect to the body axes Ox and Oy, Oy and Oz, and Oz and Ox.

[0108] Based on the above analysis, a nonlinear mathematical model of longitudinal motion of a certain type of aircraft is established, which includes 4 state variables and 1 control variable:

[0109]

[0110] Where, column vector x is the state variable, including aircraft velocity V, angle of attack α, pitch angle θ, pitch angle velocity q, vector u represents the flight control input variable, where δ e is the rudder deflection angle.

[0111] (b) Linearize and discretize the nonlinear model of the aircraft longitudinal motion:

[0112] Taylor expansion is performed on model (1) at the equilibrium point, and only the linear part is retained, then the following relationship is obtained:

[0113]

[0114] In the formula, △x and △u are the increments of the system state variables and control variables respectively. For the convenience of writing, x and u are used to replace △x and △u respectively, and the linearized equation of the longitudinal motion of the aircraft containing four state variables is:

[0115]

[0116] make:

[0117]

[0118] Then the continuous-time linearized state equation of the aircraft longitudinal motion can be obtained in matrix form:

[0119]

[0120] In the formula, A o It is called the system state matrix, B o It is called the control matrix.

[0121] Furthermore, the sampling time is selected and the discretized linear model of the longitudinal motion equation of the aircraft is obtained using the zero-order holder method as follows:

[0122] x(k+1)=Ax(k)+Bu(k)

[0123] Where A and B are the system state matrix and control matrix after the system (2) is decentralized, and k is the time step.

[0124] In order to better fit the actual situation and consider the influence of external disturbances, a discrete time linear model of the longitudinal motion of the aircraft with external disturbances is constructed:

[0125]

[0126] Where x(k)∈R n is the state quantity, u(k)∈R m is the control input, y(k)∈R p is the measurable output of the system, A, B, C, and F are known constant matrices of appropriate dimensions, and the columns of matrices F and B are full rank, and the rows of matrix C are full rank. d(k) and v(k)∈L2[0,∞) represent disturbance and noise, respectively.

[0127] Step 2: Reduce the dimension of model (3). Using three non-singular transformations By performing state transformation on model (3), we can obtain:

[0128]

[0129] in, is a non-singular matrix such that There exists an orthogonal matrix Make

[0130] Make For Schur stability,

[0131] Step 3: Next, design an adaptive interval observer.

[0132] make Available

[0133]

[0134] in, According to the Sylvester equation, we can solve Stable and non-negative.

[0135] According to the above formula, we can get The upper and lower bounds of :

[0136]

[0137] Use formula (5) to design an adaptive interval observer:

[0138]

[0139] In the formula, and y(k) are the upper and lower bounds of the state estimate, for The same applies. e y (k) = y(k) - y(k), and A y are the interval observer parameters to be designed; and The adaptive law is designed and Specifically:

[0140]

[0141] Among them, sgn is the sign function, σ i >δ i >0 is the design parameter that affects the interval width, λ i >0 is the rate of change.

[0142] Step 4: To design the system matrix and A y , construct an optimization problem with linear matrix inequality constraints:

[0143] If there is a matrix This solves the following problems:

[0144] minγs.t.

[0145]

[0146] Among them, P>0 means that the matrix is ​​positive definite, and the matrix is a symmetric matrix and Indicates that the matrix is ​​negatively definite, and the symbol ≥0 means that every element is greater than or equal to 0; V 11 、V 22 ∈R n×n is a diagonal positive matrix, ∏ n2 =V 22g a gh ,g,h=1,2,…,n;V 11g Represents the matrix V 11 The gth element on the diagonal, V 22g Similarly; and a gh The matrices to be determined are With A y The elements of the g rows and h columns, γ and μ are scalars greater than 0, 0<α<1, is a diagonal positive matrix;

[0147]

[0148] e=-(1-α)P 31 , f = -(1-α)P 32 ,

[0149] g=-(1-α)P 42 ,

[0150]

[0151] Then the system matrix gain to be determined is

[0152] The aircraft system state estimation method based on the adaptive interval observer of the present application designs the adaptive interval observer based on the idea of ​​robust stability. For a type of aircraft longitudinal motion system, the method first constructs a discrete linear system model according to the longitudinal motion characteristics of the aircraft; reduces the dimension of the system using non-singular transformations; and further introduces the adaptive law to design an adaptive interval observer to achieve state estimation of the aircraft longitudinal motion system. The method uses the adaptive law to improve the accuracy of state estimation. In addition, the obtained system state estimation interval can be used to implement fault detection decisions and improve the system's sensitivity to sudden faults.

[0153] The aircraft system state estimation method based on adaptive interval observer in this application aims to solve the problem of high conservatism of the existing state estimation method based on interval observer, and designs adaptive law to replace the upper and lower bounds of disturbance, thereby improving the accuracy of state estimation. In addition, this method can not only realize state estimation, but also provide reference for aircraft system fault decision-making, realize the improvement of sensitivity to sudden faults, and ensure the safety of aircraft system.

[0154] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for estimating an aircraft system state based on an adaptive interval observer, characterized in that: include: Step 1: Establish a discrete linear system model based on the characteristics of the aircraft longitudinal motion system; Step 2: Using non-singular transformation to reduce the dimension of the discrete linear system model; Step 3: Introduce the adaptive law and design an adaptive interval observer to realize the estimation of the upper and lower bounds of the state; Step 4: Based on the robust stability theory, linear matrix inequality conditions are designed to solve specific observation parameters to ensure the stability and robustness of the adaptive interval observer.

2. The method for estimating an aircraft system state based on an adaptive interval observer according to claim 1, characterized in that: In step 1, a discrete linear system model is established according to the characteristics of the aircraft longitudinal motion system, including: The discrete linear system model is: x(k+1)=Ax(k)+Bu(k)+Fd(k) y(k)=Cx(k)+v(k) Among them, x(k) is the state variable, u(k) is the control input, y(k) is the measurable output of the system, A, B, C, and F are known constant matrices of appropriate dimensions, and the columns of matrices B and F are full rank, and the rows of matrix C are full rank. d(k) and v(k) represent disturbance and noise, respectively.

3. The method for estimating the state of an aircraft system based on an adaptive interval observer according to claim 2, characterized in that: In step 2, a non-singular transformation is used to reduce the dimension of the discrete linear system model, including: Using three non-singular transformations The discretized linear model is transformed into a state: in, is a non-singular matrix such that There exists an orthogonal matrix Make Make For Schur stability, 4. The method for estimating the state of an aircraft system based on an adaptive interval observer according to claim 3, characterized in that: In step 3, the adaptive law is introduced and an adaptive interval observer is designed to realize the estimation of the upper and lower bounds of the state, including: make We can get: in, According to the Sylvester equation, we can solve Stable and non-negative; According to the above formula, we can get The upper and lower bounds of : Design the adaptive interval observer as: and y (k)=y(k)-y(k) in, and y(k) are the upper and lower bounds of the state estimate, and A y are the interval observer parameters to be designed, (k) and ζ t (k) is the adaptive law.

5. The method for estimating aircraft system state based on adaptive interval observer according to claim 4, characterized in that: Adaptive Law and t (k) is: in, Among them, sgn is the sign function, σ i , δ i is the design parameter that affects the interval width, λ i is the rate of change.

6. The method for estimating aircraft system state based on adaptive interval observer according to claim 5, characterized in that: In step 4, based on the robust stability theory, linear matrix inequality conditions are designed to solve specific observation parameters to ensure the stability and robustness of the adaptive interval observer, including: Construct an optimization problem with linear matrix inequality constraints: If there is a matrix: This solves the following problems: minγs.t. Then the interval observer parameters to be determined are: in, Among them, P means that the matrix is ​​positive definite, and the matrix is a symmetric matrix and Indicates that the matrix is ​​negatively definite, and the symbol ≥0 means that every element is greater than or equal to 0; V 11 、V 22 is a diagonal positive matrix, ∏ n2 =V 22g a gh ,g,h=1,2,…,n;V 11g Represents the matrix V 11 The g-th element on the diagonal, V 22g Represents the matrix V 22 The gth element on the diagonal; and a gh The matrices to be determined are With A y The elements are in g rows and h columns, γ and μ are scalars greater than 0, 0<α<1, and T is a diagonal positive matrix.

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