CN108415247B - Time scale separation aircraft elastomer robust control method based on nominal information - Google Patents

Abstract

The invention discloses a time scale separation aircraft elastomer robust control method based on nominal information, belongs to the field of aircraft control, and is used for solving the control problem that a slow time scale has uncertain time varying information when the rigid-flexible mode separation control of the conventional elastic hypersonic aircraft is carried out. Firstly, defining a fast and slow time scale coupling form of an object dynamic model, completing time scale separation based on a singular perturbation algorithm, and separating a rigid mode and an elastic mode in the dynamic model; secondly, designing a robust control strategy based on nominal information aiming at a slow time scale part representing a rigid mode of the system, and finishing compensation control by estimating an upper bound of uncertain time-varying information to realize height instruction tracking; designing a sliding mode control strategy aiming at a fast time scale part representing the elastic mode of a system, and aiming at realizing elastic mode suppression; and finally, combining the two control inputs into one to be used as an overall rudder deflection to realize the effective control of the height and the elastic mode of the aircraft.

Description

Time scale separation aircraft elastomer robust control method based on nominal information

Technical Field

The invention relates to a hypersonic aircraft elastomer robust control technology, in particular to a time scale separation hypersonic aircraft elastomer robust control strategy based on nominal information, and belongs to the field of aircraft control.

Background

At present, most scholars regard an object model as a pure rigid body to carry out algorithm design when carrying out control algorithm research on a hypersonic aircraft, the processing idea can simplify the object model and grasp main contradictions so as to verify a control algorithm, however, the influence of an elastic mode becomes more important along with the lightening of hypersonic aircraft materials and the faster development of speed, and the control algorithm designed aiming at a rigid body cannot meet engineering requirements. The hypersonic aircraft elastomer is a typical control object with a multi-time scale phenomenon, so that a singular perturbation algorithm can be adopted to perform model fast and slow time scale separation to complete decoupling of a rigid mode and a flexible mode.

In the hypersonic aircraft dynamic characteristic analysis and control law design with model parameter uncertainty (Sun Chong, Square cluster, Yuanjian, Ming Jian, Hei's university of northwest's university, vol. 30, No. 4, 2012), uncertainty in an elastomer model of the hypersonic aircraft is considered, and a control algorithm based on feedback linearization is designed.

Disclosure of Invention

In order to solve the problem that the existing control algorithm designed for a rigid body object cannot meet the engineering application of the existing hypersonic aircraft under the influence of elastic deformation, the invention provides a time scale separation hypersonic aircraft elastomer robust control strategy based on nominal information. Firstly, performing fast and slow time scale separation on hypersonic aircraft elastomer dynamics, and processing a basic idea of a multi-time scale problem according to a singular perturbation theory; secondly, respectively designing a control algorithm for the dynamic model after time scale separation, designing an uncertain upper bound estimation strategy by considering the uncertainty of the slow time scale part, realizing compensation control, and designing a sliding mode control strategy for the elastic vibration problem of the fast time scale part; and finally, combining control input as a rudder deflection command to realize height tracking and elastic mode suppression.

A time scale separation aircraft elastomer robust control method based on nominal information is particularly suitable for hypersonic aircraft elastomers, and is realized through the following steps:

(a) consider the following hypersonic aircraft elastomer model:

wherein,

in the above formula, V represents velocity, γ represents track pitch, h represents altitude, α represents angle of attack, q represents pitch angle velocity, δ_eIs the rudder deflection angle, and delta_e＝δ_es+δ_ef，δ_esFor slow-varying time-scale control input, delta_efFor the control input of the fast time scale, subsequent design is carried out, wherein phi is the opening of the throttle valve, and eta is the elastic mode;it is shown that the dynamic pressure, C_Tare all the pneumatic parameters, and the pneumatic parameters,representing the mean aerodynamic chord, S representing the aerodynamic reference area, z_TIs a thrust moment; t, D, L and M_yyRespectively representing thrust, resistance, lift and pitching rotation moment; m, I_yyRepresenting the moment of inertia of the mass, pitch axis, N^(·)Is a modal parameter, N is a generalized force, ζ is a damping ratio, and ω is a natural frequency;

defining a height tracking error e_h＝h-h_dDesign track angle command gamma_d：

In the formula, h_dFor the height instructions, given by the designer,being height-orderedFirst order differential, k_h>0，k_i>0 is given by the designer; considering that the track angle change of the cruise section is small and the first-order differential of the track angle instructionTaking the value as zero;

get x₁＝γ，x₂＝θ，x₃Q, θ + γ represents a pitch angle; equations (3) to (5) are written as follows:

wherein,

(b) defining:ρσ＝η，ρB₆＝β₁then equations (12), (14), (6) are further modified as:

when ρ is 0, expressions (15), (16), and (17) are expressed as follows:

wherein's' represents a slow-change subsystem;

is shown by the formula (20)

When formula (21) is substituted for formula (19), formulae (18), (13), and (19) are as follows:

the product of the thrust term and the sine of the angle of attack is very small compared to the lift term, and neglecting this, equations (22), (24) are expanded to

Wherein,

wherein, X_s＝[x_1s,x_2s,x_3s]^T；

defining: psi₁＝σ-σ_s，Then formula (6) is converted into:

substituting equation (21) into equation (28) yields:

equations (29), (30) are written as:

wherein psi ═ psi₁,ψ₂]^T，

(c) Defining the velocity tracking error:

in the formula, V_dThe speed command is given by the designer. The throttle opening is designed as follows:

in the formula, k_pV＞0、k_iV＞0、k_dV> 0 is given by the designer.

(d) Equations (25), (23), (26) are written as follows:

wherein f is₁₀，g₁₀，f₃₀，g₃₀Respectively, nominal values of the non-linear terms, i.e. f₁＝f₁₀+Δf₁，g₁＝g₁₀+Δg₁，f₃＝f₃₀+Δf₃，g₃＝g₃₀+Δg₃；

Let D₁＝Δf₁+Δg₁x_2s，D₃＝Δf₃+Δg₃δ_esThen equation (34) is written as follows:

definition e₁＝x_1s-x_1dAnd calculating the error differential:

designing virtual control quantities

In the formula, k₁The normal number is designed for the man-made,as an uncertainty term D₁Upper bound D_1mEstimate of, ω₀Design the normal number for humanThe update law form is as follows:

where ρ is₁And delta₁Designing a normal number for people; designing a first order filter

In the formula, epsilon₁For artificially designing a normal number, further defining the pitch angle tracking error as:

e₂＝x_2s-x_2c (40)

is differentiated by

Designing virtual control quantities

In the formula, k₂Designing a first-order filter for artificially designing the normal number

In the formula, epsilon₃For design normality, defining pitch angle speed tracking error:

e₃＝x_3s-x_3c (44)

in differential form of

Design of slowly time-varying rudder deflection control law

In the formula, k₃The normal number is designed for the man-made,as an uncertainty term D₃Upper bound D_3mAn estimated value of (d); design ofThe adaptive update law is as follows:

where ρ is₃And delta₃Designing a normal number for people;

(e) the sliding mode switching function is chosen as follows:

c＝Gψ (48)

in the formula, G is belonged to R^2*2To design a positive definite matrix, equation (31) is combined to obtain a differential form of equation (48)

Designing fast-varying subsystem rudder deflection control input

δ_ef＝-(GQ_f)⁺(GP_fψ+z_nsgn(c)) (50)

Wherein x is⁺Represents the molar penrose inverse of x, z_n∈R^2*2For the positive definite matrix to be designed,

(f) system rudder deflection control input

(g) From the resulting rudder deflection angle delta_eAnd the throttle opening phi returns to the dynamic models (1) to (6) of the hypersonic aircraft to control the height, the elastic mode and the speed.

And the control comprises adjusting an input value to be optimized to enable the altitude to approach the acquired aircraft altitude instruction, the speed to approach the acquired aircraft speed instruction and the elastic mode to tend to be stable.

Compared with the prior art, the invention has the beneficial effects that:

(1) rigid-flexible mode decoupling of a hypersonic aircraft elastomer dynamic model is realized by adopting a singular perturbation algorithm, so that rigid-flexible modes are respectively controlled;

(2) and the upper bound of the uncertain information is estimated to carry out compensation control strategy design, so that the robustness of the control algorithm is improved.

Drawings

FIG. 1 is a flow chart of a preferred embodiment of the time scale isolated aircraft elastomer robust control method based on nominal information of the present invention.

Detailed Description

In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

The invention discloses a time scale separation hypersonic aircraft elastomer robust control strategy based on nominal information, and the specific embodiment analysis is as follows by combining with a figure 1:

(a) consider the following hypersonic aircraft elastomer model:

wherein,C_T(α)＝-2421.6α-100.9，

in the above formula, V represents velocity, γ represents track pitch, h represents altitude, α represents angle of attack, q represents pitch angle velocity, δ_eIs the rudder deflection angle, and delta_e＝δ_es+δ_ef，δ_esFor slow-varying time-scale control input, delta_efFor the control input of the fast time scale, subsequent design is carried out, wherein phi is the opening of the throttle valve, and eta is the elastic mode;it is shown that the dynamic pressure, C_Tare all the pneumatic parameters, and the pneumatic parameters,denotes the mean aerodynamic chord length, S-17 denotes the aerodynamic reference area, z_TThe thrust moment is 8.36; t, D, L and M_yyRespectively representing thrust, resistance, lift and pitching rotation moment; m is 300, I_yy＝500000，N^α＝4573.7，N⁰117.52, N is generalized force, ζ is 0.05, ω is 16.0214;

defining a height tracking error e_h＝h-h_dDesign track angle command gamma_d：

In the formula, h_dFor the height instructions, given by the designer,is the first differential of the height command, k_h＝0.5，k_i0.05; considering that the track angle change of the cruise section is small and the first-order differential of the track angle instructionTaking the value as zero;

get x₁＝γ，x₂＝θ，x₃Q, θ + γ represents a pitch angle; equations (3) to (5) are written as follows:

wherein,

(b) defining:ρσ＝η，ρB₆＝β₁then equations (12), (14), (6) are further modified as:

when ρ is 0, expressions (15), (16), and (17) are expressed as follows:

wherein's' represents a slow-change subsystem;

is shown by the formula (20)

When formula (21) is substituted for formula (19), formulae (18), (13), and (19) are as follows:

the product of the thrust term and the sine of the angle of attack is very small compared to the lift term, and neglecting this, equations (22), (24) are expanded to

Wherein,

wherein, X_s＝[x_1s,x_2s,x_3s]^T；

defining: psi₁＝σ-σ_s，Then formula (6) is converted into:

substituting equation (21) into equation (28) yields:

equations (29), (30) are written as:

wherein psi ═ psi₁,ψ₂]^T，

(c) Defining the velocity tracking error:

in the formula, V_dThe speed command is given by the designer. The throttle opening is designed as follows:

in the formula, k_pV＝0.5、k_iV＝0.001、k_dV＝0.01。

(d) Equations (25), (23), (26) are written as follows:

wherein f is₁₀＝-0.0036，g₁₀＝0.0535，f₃₀＝0.1835，g₃₀-1.2044 is the nominal value of each non-linear term, respectively, i.e., f₁＝f₁₀+Δf₁，g₁＝g₁₀+Δg₁，f₃＝f₃₀+Δf₃，g₃＝g₃₀+Δg₃；

Let D₁＝Δf₁+Δg₁x_2s，D₃＝Δf₃+Δg₃δ_esThen equation (34) is written as follows:

definition e₁＝x_1s-x_1dAnd calculating the error differential:

designing virtual control quantities

In the formula, k₁＝0.8，As an uncertainty term D₁Upper bound D_1mEstimate of, ω₀1, design asThe update law form is as follows:

where ρ is₁＝15，δ₁Design the first order filter at 0.1

In the formula, epsilon₁The pitch tracking error is further defined as 0.05:

e₂＝x_2s-x_2c (40)

is differentiated by

Designing virtual control quantities

In the formula, k₂0.8, design the first order filter

In the formula, epsilon₃Define the pitch rate tracking error as 0.05:

e₃＝x_3s-x_3c (44)

in differential form of

Design of slowly time-varying rudder deflection control law

In the formula, k₃＝10，As an uncertainty term D₃Upper bound D_3mAn estimated value of (d); design ofThe adaptive update law is as follows:

where ρ is₃＝15，δ₃＝0.1；

(e) The sliding mode switching function is chosen as follows:

c＝Gψ (48)

in the formula,combining equation (31) to obtain a differential form of equation (48)

Designing fast-varying subsystem rudder deflection control input

δ_ef＝-(GQ_f)⁺(GP_fψ+z_nsgn(c)) (50)

Wherein x is⁺Represents the molar penrose inverse of x,

(f) system rudder deflection control input

(g) From the resulting rudder deflection angle delta_eAnd the throttle opening phi returns to the dynamic models (1) to (6) of the hypersonic aircraft to control the height, the elastic mode and the speed.

It should be noted that the aircraft altitude command and the aircraft speed command given by the designer in the above description of the present invention are target values, such as the specification "k₂Artificially designed normal number and k_pV＞0、k_iV＞0、k_dVThe designer gives other parameters to be optimized, such as '0' and the like, and the invention aims to adjust the parameter values to be optimized so that in the final dynamic model, the altitude approaches the acquired aircraft altitude command, the speed approaches the acquired aircraft speed command, and the elastic mode tends to be stable, namely the result tends to be equal to or equal to a target value, and the parameter values given in the specific embodiment of the specification are actually the final result/optimal result obtained through calculation.

Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (3)

1. A time scale separation aircraft elastomer robust control method based on nominal information is characterized by comprising the following steps:

step one, constructing the dynamic model of the aircraft elastomer:

wherein,

in the above formula, V represents velocity, γ represents track pitch, h represents altitude, α represents angle of attack, q represents pitch angle velocity, δ_eIs the rudder deflection angle, and delta_e＝δ_es+δ_ef，δ_esFor slow-varying time-scale control input, delta_efThe method comprises the following steps of inputting control for a fast time scale, wherein phi is the opening degree of a throttle valve, and eta is an elastic mode;it is shown that the dynamic pressure,C_Tare all the pneumatic parameters, and the pneumatic parameters,representing the mean aerodynamic chord, S representing the aerodynamic reference area, z_TIs a thrust moment; t, D, L and M_yyRespectively representing thrust, resistance, lift and pitching rotation moment; m, I_yyRepresenting the moment of inertia of the mass, pitch axis, respectively, N^(·)Is a modal parameter, N is a generalized force, ζ is a damping ratio, and ω is a natural frequency;

step two, acquiring an aircraft height instruction, dividing the aircraft rudder deflection input into a slow-change subsystem rudder deflection control input and a fast-change subsystem rudder deflection control input according to a singular perturbation theory, setting a sliding mode control function aiming at the fast-change subsystem rudder deflection control input, and determining the input of the sliding mode control function; designing a robust control strategy based on nominal information for the rudder deflection control input of the slowly-varying subsystem, and specifically comprising the following steps:

defining a height tracking error e_h＝h-h_dDesign track angle command gamma_d：

In the formula, h_dIn order to obtain the aircraft altitude instruction,is the first differential of the height command, k_h>0，k_i>0 is the input value to be optimized; considering that the track angle change of the cruise section is small and the first-order differential of the track angle instructionTaking the value as zero;

get x₁＝γ，x₂＝θ，x₃Q, θ + γ represents a pitch angle; equations (3) to (5) are written as follows:

wherein,

(b) defining:ρσ＝η，ρB₆＝β₁then equations (12), (14), (6) are modified as:

when ρ is 0, expressions (15), (16), and (17) are expressed as follows:

wherein's' represents a slow-change subsystem;

is shown by the formula (20)

When formula (21) is substituted for formula (19), formulae (12) to (14) are as follows:

the product of the thrust term and the sine of the angle of attack is very small compared to the lift term, and neglecting this, equations (22), (24) are expanded to

Wherein,

wherein, X_s＝[x_1s,x_2s,x_3s]^T；

defining: psi₁＝σ-σ_s，Then formula (6) is converted into:

substituting equation (21) into equation (28) yields:

equations (29), (30) are written as:

wherein psi ═ psi₁,ψ₂]^T，

Equations (25), (23), (26) are written as follows:

wherein f is₁₀，g₁₀，f₃₀，g₃₀Respectively, nominal values of the non-linear terms, i.e. f₁＝f₁₀+Δf₁，g₁＝g₁₀+Δg₁，f₃＝f₃₀+Δf₃，g₃＝g₃₀+Δg₃；

Let D₁＝Δf₁+Δg₁x_2s，D₃＝Δf₃+Δg₃δ_esThen equation (34) is written in the form:

definition e₁＝x_1s-x_1dAnd calculating the error differential:

the design virtual control quantity is as follows:

in the formula, k₁For the design input to be optimized, a normal number,as an uncertainty term D₁Upper bound D_1mEstimate of, ω₀For the design input to be optimized, for the normal number, designThe update law form is as follows:

where ρ is₁And delta₁Inputting the design to be optimized as a normal number; designing a first order filter

In the formula, epsilon₁For the design input to be optimized, for the normal number, the pitch angle tracking error is defined as:

e₂＝x_2s-x_2c (40)

is differentiated by

The design virtual control quantity is as follows:

in the formula, k₂Designing a first order filter for the design input to be optimized, for the normal number

In the formula, epsilon₃For the design input to be optimized, the pitch angle velocity tracking error is defined for the normal number:

e₃＝x_3s-x_3c (44)

is differentiated by

Therefore, the slowly-varying time scale rudder deflection control law is designed

In the formula, k₃For the design input to be optimized, a normal number,as an uncertainty term D₃Upper bound D_3mAn estimated value of (d); design ofThe adaptive update law is as follows:

where ρ is₃And delta₃Inputting the design to be optimized as a normal number;

determining the rudder deflection control input of the fast-changing subsystem according to the sliding mode control function comprises the following steps:

the sliding mode switching function is chosen as follows:

c＝Gψ (48)

in the formula, G is belonged to R^2*2To design the positive definite matrix 1, equation (31) is combined to obtain a differential form of equation (48)

Designing fast-varying subsystem rudder deflection control input

δ_ef＝-(GQ_f)⁺(GP_fψ+z_nsgn(c)) (50)

Wherein x is⁺Represents the molar penrose inverse of x, z_n∈R^2*2A positive definite matrix 2 is to be designed;

determining the system rudder deflection control input as the sum of the slow-change subsystem rudder deflection control input and the fast-change subsystem rudder deflection control input;

step four, acquiring an aircraft speed instruction, defining a speed tracking error according to the aircraft speed instruction, and determining the opening of a throttle valve;

step five, according to the obtained rudder deflection angle delta_eAnd the throttle opening phi returns to the dynamic model formulas (1) to (6) of the hypersonic aircraft to control the altitude, the elastic mode and the speed, wherein the control comprises the adjustment of an input value to be optimized to enable the altitude to approach the acquired aircraft altitude instruction, the speed to approach the acquired aircraft speed instruction and the elastic mode to tend to be stable.

2. The time scale isolated aircraft elastomer robust control method based on nominal information of claim 1, wherein in step four, said determining a throttle opening comprises:

defining the velocity tracking error:

in the formula, V_dFor the speed command, given by the designer, the throttle opening is designed as follows:

in the formula, k_pV＞0、k_iV＞0、k_dV> 0 is the input value to be optimized.

3. The time scale separation aircraft elastomer robust control method based on nominal information as claimed in claim 1, wherein in step three, the system rudder deflection control input is: