CN106773782A - A kind of aeroelastic divergence hybrid modeling method - Google Patents

Abstract

The invention belongs to the field of pneumatic servo elasticity and relates to a modeling method of pneumatic servo elasticity. The structural model is established through the test data, and the aeroelastic motion model and control model are established by calculation, which objectively reduces the degree of freedom of the model and improves the calculation efficiency.

Description

A Hybrid Modeling Method for Aeroservoelasticity

technical field

The invention belongs to the field of pneumatic servo elasticity and relates to a modeling method of pneumatic servo elasticity.

Background technique

For aircraft with servo control systems, the aeroservoelastic stability problem is an unavoidable problem. Aeroservoelastic stability analysis is required for both the first flight of an aircraft and major aircraft modifications.

At present, the problem of aerodynamic servo elastic stability is mainly analyzed through computer simulation, and the computer simulation modeling is quite different from the actual situation of the aircraft. Therefore, the simulation model is mainly corrected through the test method, but the model correction is relatively difficult, and the correction The results are also difficult to fully match.

Contents of the invention

Purpose of the present invention: in order to solve the problem that the simulation model is quite different from the real aircraft and the simulation model is difficult to correct, by analyzing the test data, the test model is established, and then the aeroservoelasticity analysis is carried out through the mixed model of test and simulation.

The technical solution of the present invention: an aeroservoelastic hybrid modeling method, characterized in that the method includes the following steps:

(1) Select n test points as structural degrees of freedom, establish a structural model, conduct a ground resonance test of the whole machine, and measure the modal frequency ω, modal vibration shape Φ _h , modal damping C _hh , and modal mass M _hh ;

(2) Calculate the modal stiffness K _hh according to the measured modal mass M _hh and the modal frequency ω;

K _hh = ω ² M _hh

(3) Establish the control surface mode Φ _c on its structural degrees of freedom according to the test model;

(4) Calculate the mass M _g on the structural degree of freedom according to the mode shape Φ _h and the mode mass M _hh ;

(5) According to the structural mode Φ _h , the control surface mode Φ _c and the mass M _g , the structural mode and

Coupling mass M _hc between control surface modes;

(6) Establish the structural motion equation:

where ξ and δ represent the generalized structural displacement and control surface deflection, respectively;

(7) According to the modal data obtained from the test, use the flow field solver or other numerical calculation methods to calculate the unsteady aerodynamic force, and identify the generalized aerodynamic force matrix Q _h (s);

In the formula, Q _h =[Q _hh Q _hc ], A _n =[A _hhn A _hcn ](n=0,1,2), E=[E _h E _c ]. L is the reference length, V is the air velocity, and _s is the Laplace variable;

(8) Using the fitted generalized aerodynamic matrix Q _h (s) to obtain the generalized aerodynamic force f _a ;

where q _∞ represents the incoming flow pressure, q is the generalized displacement, q=[ξ δ] ^T , including generalized structural displacement ξ and rudder surface deflection δ;

(9) Get the state variable of aerodynamic force:

Convert to time domain space:

The generalized aerodynamic force in time domain can be written as:

(10) Establish the aeroelastic motion equation:

(11) Write the aeroelastic equation in state space form:

In the formula

(12) According to the frequency response function of the steering gear measured by the test, the state equation of the steering gear is obtained:

(13) Since x _act =u _ae , the state equation of the controlled object (plant) can be expressed by the following formula:

In the formula

C _p =[C _ae D _ae ], D _p =0;

(14) Considering the state equation of the control system, it can be obtained from the simulation model:

(15) Establish the open-loop transfer function between the controlled object and the control system:

In the formula C _o = [D _c C _p C _c ], D _o = D _c D _p ;

(16) Transform the state space equation into a frequency response function:

H(s)＝C _o (sI-A _o ) ^-1 B _o +D _o

Drawing Bode diagram and Nyquist diagram can be used for stability analysis and stability margin analysis.

The beneficial effect of the present invention is that the structure model is established through test data, and the aeroelastic motion model and control model are established through calculation, which objectively reduces the degree of freedom of the model and improves the calculation efficiency.

detailed description

(1) Select n test points as structural degrees of freedom, establish a structural model, conduct a ground resonance test of the whole machine, and measure the modal frequency ω, modal vibration shape Φ _h , modal damping C _hh , and modal mass M _hh .

(2) Calculate the modal stiffness K _hh according to the measured modal mass M _hh and modal frequency ω.

K _hh = ω ² M _hh

(3) Establish the mode Φ _c of the control surface on its structural degrees of freedom according to the test model.

(4) According to the relationship between mass M _g and modal matrix Φ _h and modal mass matrix M _hh :

can get:

Then, the following coupling mass matrix between the structural mode and the control surface mode can be obtained:

(5) According to the modal data obtained from the test, solve the generalized aerodynamic force and fit the generalized aerodynamic force matrix:

Q _h (p)＝A ₀ +A ₁ p+A ₂ p ² +D(Ip-R) ^-1 Ep

In the formula, Q _h =[Q _hh Q _hc ], A _n =[A _hhn A _hcn ](n=0,1,2), E=[E _h E _c ]. L is the reference length, V is the air velocity, the dimensionless Laplace variable p=sL/V, and s is the Laplace variable. Therefore, the generalized aerodynamic matrix can be written as:

Then, the generalized aerodynamic force can be written as:

where q _∞ represents the incoming flow pressure, q is the generalized displacement, including generalized structural displacement ξ and rudder surface deflection δ, q=[ξ δ] ^T .

Pneumatic power state variables:

Convert to time domain space:

Then, the aerodynamic force can be written as:

(6) The aeroservoelastic motion equation can be written as:

Then, the aeroservoelasticity equation can be written in the state space form:

In the formula

(7) According to the frequency response function of the steering gear measured by the test, the state equation of the steering gear is obtained:

(8) Since x _act =u _ae , the state equation of the controlled object (plant) can be expressed by the following formula:

In the formula

C _p =[C _ae D _ae ], D _p =0.

(9) Consider the state equation of the control system, which can be obtained from the simulation model or measured by the test:

(10) Establish the open-loop transfer function between the controlled object and the control system

In the formula C _o = [D _c C _p C _c ], D _o = D _c D _p

(11) Transform the state space equation into a frequency response function:

H(s)＝C _o (sI-A _o ) ^-1 B _o +D _o

Draw Bode diagrams and Nyquist diagrams. Stability analysis and stability margin analysis can be performed.

Claims (1)

1. a kind of aeroelastic divergence hybrid modeling method, it is characterised in that described method comprises the following steps：

(1) n test point is chosen as the Degree of Structure Freedom, structural model is set up, and carries out full machine ground resonance test, measurement mode Frequencies omega, Mode Shape Φ_h, modal damping C_hh, modal mass M_hh；

(2) according to the modal mass M for measuring_hhModal stiffness K is obtained with modal frequency ω_hh；

K_hh=ω²M_hh

(3) chain of command mode Φ is set up on its Degree of Structure Freedom according to test model_c；

(4) according to Mode Shape Φ_hWith modal mass M_hhMass M in the computation structure free degree_g；

$M_g={\mathrm{\Φ}}_k{M}_{kk}{\mathrm{\Φ}}_k^T$

(5) according to structural modal Φ_hWith chain of command mode Φ_cAnd mass M_gSolve between structural modal and chain of command mode Coupling mass M_hc；

$M_{kc}={\mathrm{\Φ}}_k^T{M}_g{\mathrm{\Φ}}_c$

(6) structure motion equation is set up：

$M_{kk}\stackrel{\·\·}{\mathrm{\ξ}}+C_{kk}\stackrel{\·}{\mathrm{\ξ}}+K_{kk}\mathrm{\ξ}+M_{kc}\stackrel{\·\·}{\mathrm{\δ}}=0$

In formulaRepresent generalized structure displacement with control deflecting facet respectively；

(7) modal data obtained according to experiment, calculates unsteady pneumatic using flow field calculation device or other numerical computation methods Power, and identify broad sense aerodynamic force matrix Q_h(s)；

$Q_k\left(s\right)=A_0+\frac{L}{V}{A}_{1}s+\frac{L^2}{V^2}{A}_2{s}^2+D{(sI-\frac{V}{L}R)}^{-1}Es$

Q in formula_h=[Q_hh Q_hc], A_n=[A_hhn A_hcn] (n=0,1,2), E=[E_h E_c].L is reference length, and V is gas velocity Degree, s is Laplace variable；

(8) using the broad sense aerodynamic force matrix Q of fitting_hS () obtains broad sense aerodynamic force f_a；

$f_a=q_{\mathrm{\∞}}{Q}_{h}q=q_{\mathrm{\∞}}(A_0+\frac{L}{V}{A}_{1}s+\frac{L^2}{V^2}{A}_2{s}^2+D{(Is-\frac{V}{L}R)}^{-1}Es)q$

Q in formula_∞Represent to flow pressure, q is generalized displacement, q=[ξ δ]^T, including generalized structure displacement ξ and control surface deflection δ；

(9) aerodynamic force state variable is taken：

$x_a\left(s\right)={(Is-\frac{V}{L}R)}^{-1}Eqs$

${\mathrm{sx}}_a\left(s\right)=\frac{V}{L}{\mathrm{Rx}}_a\left(s\right)+Eqs$

It is transformed into time domain space：

${\stackrel{\·}{x}}_a=\frac{V}{L}{\mathrm{Rx}}_a+E\stackrel{\·}{q}$

Time domain broad sense aerodynamic force can be write as：

$f_a=q_{\mathrm{\∞}}{Q}_{h}q=q_{\mathrm{\∞}}(A_{0}q+\frac{L}{V}{A}_1\stackrel{\·}{q}+\frac{L^2}{V^2}{A}_2\stackrel{\·\·}{q}+{\mathrm{Dx}}_a)$

(10) the aeroelasticity equation of motion is set up：

$\begin{array}{c}(M_{hh}+q_{\mathrm{\∞}}\frac{L^2}{V^2}{A}_{hh2})\stackrel{\·\·}{\mathrm{\ξ}}+(C_{hh}+q_{\mathrm{\∞}}\frac{L}{V}{A}_{hh1})\stackrel{\·}{\mathrm{\ξ}}+(K_{hh}+q_{\mathrm{\∞}}{A}_{hh0})\mathrm{\ξ}+\\ (M_{hc}+q_{\mathrm{\∞}}\frac{L^2}{V^2}{A}_{hc2})\stackrel{\·\·}{\mathrm{\δ}}+q_{\mathrm{\∞}}\frac{L}{V}{A}_{hc1}\stackrel{\·}{\mathrm{\δ}}+q_{\mathrm{\∞}}{A}_{kc0}\mathrm{\δ}+{\mathrm{Dx}}_a=0\end{array}$

(11) aeroelasticity equation is write as state space form：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{ae}\left(t\right)=A_{ae}{x}_{ae}\left(t\right)+B_{ae}{u}_{ae}\left(t\right)\\ y_{ae}\left(t\right)=C_{ae}{x}_{ae}\left(t\right)+D_{ae}{u}_{ae}\left(t\right)\end{array}\right.$

In formula

(12) frequency response function of steering wheel is measured according to experiment, steering wheel state equation is obtained：

${\stackrel{\·}{x}}_{act}\left(t\right)=A_{act}{x}_{act}\left(t\right)+B_{act}{u}_{act}\left(t\right)$

(13) due to x_act=u_ae, the state equation of controlled device (plant) can represent with following formula：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_p\left(t\right)=A_p{x}_p\left(t\right)+B_p{u}_p\left(t\right)\\ y_p\left(t\right)=C_p{x}_p\left(t\right)+D_p{u}_p\left(t\right)\end{array}\right.$

In formula

C_p=[C_ae D_ae], D_p=0；

(14) consider control system state equation, can be obtained by simulation model：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)=A_c{x}_c\left(t\right)+B_c{u}_c\left(t\right)\\ y_c\left(t\right)=C_c{x}_c\left(t\right)+D_c{u}_c\left(t\right)\end{array}\right.$

(15) open-loop transfer function of controlled device and control system is set up：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_o\left(t\right)=A_o{x}_o\left(t\right)+B_o{u}_o\left(t\right)\\ y_o\left(t\right)=C_o{x}_o\left(t\right)+D_o{u}_o\left(t\right)\end{array}\right.$

In formulaC_o=[D_cC_p C_c], D_o=D_cD_p；

(16) state space equation is converted into frequency response function：

H (s)=C_o(sI-A_o)^-1B_o+D_o

Bode figures and Nyquist figures are drawn, stability analysis can be carried out and analyzed with stability margin.