A method for collaboratively suppressing multi-modal vibration of wind tunnel model support system

Abstract

The present invention belongs to the field of active control of aircraft model vibration, and provides a method for collaborative suppression of multi-modal vibration of a wind tunnel model support system. First, the wind tunnel model support system is subjected to force hammer pulse excitation to obtain the system frequency response function and identify the modal parameters of each order; secondly, the system modal rate decoupling matrix is ​​obtained and the modal filter is designed; then the state space equations of each order of the system are identified and the modal observer is designed; finally, the control gain of each order is calculated, and the modal control force and physical control force of each order are obtained to achieve collaborative suppression of multi-modal vibration of the model support system. The present invention performs decoupling observation in the modal space on the multi-modal complex vibration system, solves the optimal controller gain, introduces the vibration control closed loop of the model support system, and realizes active collaborative suppression of multi-modal vibration; the suppression effect on the complex vibration system is obvious, the wind tunnel test data is accurately obtained, and the reliable evaluation of the dynamic stability of high-maneuverability aircraft can be guaranteed, and it is suitable for many types of wind tunnel tests and model support systems.

Description

Technical Field

[0001] The invention relates to the field of active control of aircraft model vibration, and in particular to a method for collaboratively suppressing multi-modal vibration of a wind tunnel model support system. Background Art

[0002] High-speed wind tunnel dynamic derivative test is the main means to evaluate the dynamic stability of highly maneuverable aircraft. Its core is to measure the aerodynamic force of the model with high reliability and high precision under the excitation state of the scaled model. However, the exciting aircraft model under the high angle of attack test condition forms a complex and strong flow field, which causes the model support system to produce multi-modal random and large vibration interference, resulting in the failure of aerodynamic data and difficulty in accurately evaluating the dynamic stability of the aircraft. Therefore, it is necessary to suppress the vibration of the model support system to ensure the accuracy of the wind tunnel test data. The existing active vibration suppression technology is mainly aimed at the suppression of low-order modal vibrations in conventional high angle of attack force measurement of aircraft models. The vibration suppression mechanism is single, the vibration suppression order is low, and the vibration suppression control method is not adaptable enough, and it cannot effectively suppress the multi-modal random vibration of the model support system. Therefore, in order to ensure the accurate evaluation of the dynamic stability of highly maneuverable aircraft, it is of great significance to study the collaborative suppression method of multi-modal vibration interference of the wind tunnel model support system.

[0003] In the paper "Active damping ofsting vibrations in transonic wind tunnel testing" (Balakrishna S, ViGYAN Transonic Wind Tunnel Testing Support System Active Damping Design, AIAA 2008:840) published in 2008, Balakrishna S et al. from ViGYAN proposed a post-active vibration suppression system based on piezoelectric ceramics to control the output of reverse torque of two sets of actuators in the pitch and yaw planes to achieve the suppression of first-order vibrations in the pitch and yaw planes. The proposed method has a significant effect on the suppression of multi-dimensional low-order vibrations of the model support system, but does not have the ability to suppress high-order vibrations of the model support system. In the paper "Active Control Technology of Model Vibration in Low-Speed ​​Wind Tunnel Tests" published in 2021, Chen Lujun et al. from Northwestern Polytechnical University proposed an active vibration suppression control system based on an adaptive internal model algorithm. The active vibration suppression system can effectively suppress low-order vibrations of various types of model support systems, but cannot suppress multi-modal random vibrations of the model support system.

[0004] At present, the active vibration suppression method is mainly aimed at suppressing low-order modal vibrations in conventional high-angle force measurement of aircraft models. The vibration suppression mechanism is single, the vibration suppression order is low, and the vibration suppression control method is not adaptable enough to meet the multi-modal random vibration suppression requirements of the model support system in the dynamic derivative test. Therefore, based on the independent modal space control theory, converting the physical space multi-input and multi-output system into a modal space single-input and single-output system, and performing multi-modal decoupling observation and collaborative control is an effective method to achieve multi-modal vibration suppression of the model support system. Summary of the invention

[0005] The present invention overcomes the shortcomings of the existing methods and proposes a method for cooperatively suppressing multi-modal vibration of a wind tunnel model support system. The method first performs a force hammer pulse excitation on the wind tunnel model support system, and identifies the system's modal parameters, namely the natural frequency and damping ratio, by obtaining the system frequency response function; secondly, based on the modal expansion of the frequency response function, the system modal rate decoupling matrix is ​​solved, and the modal filter is designed to realize the conversion from physical space mutual coupling to modal space mutual decoupling; then, the state space equations of each order in the system modal space are identified, and the modal observer is designed to estimate the vibration information in the modal space; finally, the control gain matrix of each order is solved, and the control force of each order mode is obtained and then converted into the physical control force, and the physical control force required for each order mode is outputted respectively through a multi-stage vibration suppressor, so as to realize the cooperative suppression of multi-modal vibration of the model support system. This method can ensure the high reliability and high precision measurement of the model aerodynamic force in the high-speed wind tunnel dynamic derivative test, and accurately evaluate the dynamic stability of high maneuverable aircraft.

[0006] The technical solution of the present invention is: a method for collaboratively suppressing multi-modal vibration of a wind tunnel model support system, and the specific steps are as follows:

[0007] 1) The wind tunnel model support system is subjected to hammer pulse excitation, the hammer input signal x(t) is recorded, the multi-point time domain vibration response signal y(t) of the wind tunnel model support system is measured, and the open-loop frequency response H(ω) of each point of the wind tunnel model support system is obtained;

[0008] The steps to determine the frequency response function H(ω) of each point of the wind tunnel model support system are as follows:

[0009] 1.1) Perform windowing function processing on the hammer input signal x(t) and the output wind tunnel model support system multi-point time domain vibration response signal y(t);

[0010] 1.2) Calculate the power spectrum density function S of the windowed data xx (ω) and the cross power spectral density function S xy (ω);

[0011] 1.3) S xy (ω) and S xx(ω) is used as the ratio to obtain the system frequency response function H(ω), and the amplitude-frequency response curve and phase-frequency response curve of the system are plotted with frequency as the horizontal coordinate and amplitude ratio and phase difference as the vertical coordinate;

[0012]

[0013] 2) Combine the amplitude-frequency response curve in the system frequency response function to identify the modal parameters of each order of the system, including the natural frequency ω r and modal damping ratio ζ r ;

[0014] The steps for identifying the modal parameters of each order are as follows:

[0015] 2.1) Obtain the open-loop frequency response function of the system, where the abscissas corresponding to the first r peak points of the amplitude-frequency response curve are the first-order, second-order, ... r-order natural frequencies of the system respectively;

[0016] 2.2) Record the peak values ​​A of the amplitude-frequency response curve n , based on the half-power bandwidth method to determine 0.707A n The frequency values ​​on both sides of ω r1 ,ω r2 ;

[0017] 2.3) Calculate the damping ratio ζ of each modal according to formula (2): r :

[0018]

[0019] 3) Based on the principle of modal superposition, the system modal filter decoupling matrix is ​​obtained, and the modal filter is designed to realize the conversion from mutual coupling in physical space to mutual decoupling in modal space;

[0020] The steps to solve the modal filter decoupling matrix are as follows:

[0021] 3.1) Based on modal orthogonality and normalization, define the modal filter decoupling matrix Ψ T , the conversion from physical space to modal space is realized through formula (3);

[0022] η=Φ T Mδ=Ψ T δ (3)

[0023] Among them, η is the modal coordinate, δ is the physical coordinate, M is the system mass matrix, and Φ is the natural vibration matrix;

[0024] 3.2) Apply excitation X to the j point of the wind tunnel model support system j , record the acceleration response Y at point i j According to step (1), we can get the acceleration response function W ij(w), derive the acceleration frequency response modal expansion (4);

[0025]

[0026] in, is the rth column vector of the vibration matrix, ω is the frequency, m r is the modal mass coefficient of each order, ω r is the natural frequency of each order, ξ r is the damping ratio of each mode;

[0027] 3.3) Based on the normalization condition of vibration mode, we get m r =1, multiply the left side of equation (4) by the column vector of the decoupling matrix r because Orthogonal to all vibration modes except the rth vibration mode, we get equation (5);

[0028]

[0029] Among them, single point incentive is a constant;

[0030] 3.4) Due to is a constant, and is defined To find the r-th order decoupling vector, according to formula (6), select the appropriate observation point frequency and establish For the unknown quantity equations, solve the decoupling vectors of each order to form the modal filter decoupling matrix Ψ T ;

[0031]

[0032] 4) Identify the state space equations of each order in the system modal space, design the modal observer, and estimate the modal space vibration information as control feedback;

[0033] The steps of modal observer design are as follows:

[0034] 4.1) Combining the natural frequencies and damping ratios of each order, identify the state space equations (7) of each order in the modal space;

[0035]

[0036] in, η r is the modal displacement, is the modal velocity, f r is the modal control force;

[0037] 4.2) Acceleration is taken as the system output, and the state observation equation (8) based on Luenberger's improved form is derived;

[0038]

[0039] in, is the estimated value of the modal displacement, is the estimated modal velocity, is the estimated value of modal acceleration, K r is the modal observer gain, y is the system output, and E is the unit matrix;

[0040] 4.3) Configuration based on Lyapunov criterion (E+K r C r ) -1 A r The pole is located in the left plane, solving the modal observer gain K r ;

[0041] (4.4) Combining the observation equation (8) with the modal observer gain K r , to estimate the modal velocity and modal displacement;

[0042] (5) Calculate the optimal controller gain coefficient K based on the control algorithm and obtain the control force f required for each mode r , combined with the natural vibration matrix Φ, converted into the physical control force F required for each mode r ;

[0043] Physical control force F at each level r The solution steps are as follows:

[0044] (5.1) Based on LQR, LQG, H ∞ The control algorithm obtains the optimal control gain matrix K;

[0045] (5.2) Combining the observed modal displacement and modal velocity, the control force f required for each mode is calculated by formula (9): r ;

[0046]

[0047] (5.3) Combined with the intrinsic matrix Φ, the physical control force F required for each mode is obtained through formula (10): r ;

[0048] F r =Φf r (10)

[0049] (6) Combined with the piezoelectric ceramic electromechanical coupling matrix, calculate the input electrical signal U required for each section of the vibration suppressor r , and then provide the physical control force F required for each mode r , achieving multi-modal collaborative active suppression.

[0050] The modal observer gain K in 4.3) r When considering system noise and measurement noise, based on the Kalman filter principle, the Riccati equation (11) is solved to obtain the modal observer gain K r =PC r T V -1 ;

[0051] PA r T +A r P-PC r T V -1 C r P+W=0 (11)

[0052] Where P is the solution of the Riccati equation, W is the system noise covariance matrix, and V is the system measurement noise covariance matrix.

[0053] Figure 2 This is a closed-loop control schematic diagram of the multi-modal collaborative vibration active suppression method provided by the present invention. When multi-modal random vibration occurs in the model support system, the method performs multi-modal mutual decoupling observation based on a modal filter and a modal observer, and realizes multi-modal collaborative control through a multi-stage vibration suppressor.

[0054] The beneficial effect of the present invention is to provide a method for cooperatively suppressing multi-modal vibrations of a wind tunnel model support system. Compared with the traditional method, which has the disadvantages of a single vibration suppression mechanism and a low vibration suppression order, the method proposed by the present invention can perform decoupling observations in the modal space for multi-modal complex vibration systems, solve the optimal controller gain, and introduce a vibration control closed loop of the model support system, thereby realizing cooperative active suppression of multi-modal vibrations. The method has an obvious suppression effect on complex vibration systems, and the wind tunnel test data is accurately obtained, which can ensure reliable evaluation of the dynamic stability of highly maneuverable aircraft, and can be applied to many types of wind tunnel tests and model support systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The present invention is a flowchart of a method for collaboratively suppressing multi-modal vibrations of a wind tunnel model support system.

[0056] Figure 2 It is a closed-loop control principle diagram of the multi-modal vibration collaborative suppression method of the wind tunnel model support system of the present invention.

[0057] Figure 3 This is a simulation diagram of the pitch first-order modal control effect using the method of the present invention.

[0058] Figure 4 This is a simulation diagram of the pitch second-order modal control effect using the method of the present invention. DETAILED DESCRIPTION

[0059] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments and drawings.

[0060] According to previous wind tunnel test experience and modal analysis results, the vibration of the model support system is mainly first-order and second-order vibration. Therefore, this embodiment considers the first two modes in the pitch plane of the wind tunnel model support system, uses an acceleration sensor to monitor the system vibration information, and realizes multi-modal collaborative suppression based on the front and rear vibration suppression devices. The specific steps are as follows:

[0061] 1) Use a hammer to perform pulse excitation x(t) on the model support system, arrange acceleration sensors at the center of mass of the aircraft model and the key nodes of the support rods, and collect the time domain vibration signal y(t) of the model support system.

[0062] 2) Perform windowing on x(t) and y(t) respectively, and then obtain the cross power spectrum density function S xy (ω) and the auto-power spectral density function S xx (ω).

[0063] 3) The S obtained in the previous step xy (ω) and S xx Substitute (ω) into formula (1) to obtain the frequency response function H(ω) of the system, and draw the amplitude-frequency and phase-frequency curves.

[0064] 4) Combine the system amplitude-frequency response curve and phase-frequency response curve, and use the horizontal coordinates corresponding to the peak values ​​of the curves to obtain the first two natural frequencies ω1 and ω2 of the system.

[0065] 5) Based on the half-power bandwidth method, the damping ratios ζ1 and ζ2 of the first two modes are calculated according to formula (2).

[0066] 6) Measurement system two-point acceleration frequency response H 11 (ω), H 21 (ω), according to formula (6), select the appropriate observation point frequency and establish The first two order decoupling vectors are obtained as the set of equations with unknown quantities. Then form the modal filter decoupling matrix Ψ T .

[0067] 7) Considering only the first two modes in the pitch plane, the acceleration signals at two points form a one-dimensional column vector, combined with the second-order modal filter decoupling matrix Ψ T , and obtain the modal acceleration signals that are decoupled from each other in the modal space Complete the design of the modal filter.

[0068] 8) Combining the first two order natural frequencies and damping ratios, identify the first two order state space equations in the modal space;

[0069]

[0070] in η r is the modal displacement, is the modal velocity, f r is the modal control force.

[0071] (9) Since acceleration is the system output, the state observation equation based on Luenberger's improved form is derived.

[0072]

[0073] in is the estimated value of the modal displacement, is the estimated modal velocity, is the estimated value of modal acceleration, K r is the observer gain, and y is the system output.

[0074] (10) Taking into account the system noise and measurement noise, the Riccati equation (9) is solved based on the Kalman filter principle to obtain the observation gain K r .

[0075] K r =PC r T V -1 (r=1,2);

[0076] (11) The estimated modal displacement and modal velocity As the feedback of the control system, the controller is designed.

[0077] (12) Considering the high-frequency noise disturbance problem, select H ∞ The robust control algorithm solves the controller gain matrix K and combines the control feedback information to obtain the first two order modal control forces f r .

[0078]

[0079] (13) Combined with the intrinsic matrix Φ, the physical control force F required for the first two modes is obtained r ;

[0080] F r =Φf r (r=1,2)

[0081] (14) Combined with the piezoelectric ceramic electromechanical coupling matrix, the first-order modal electrical signal is controlled by the post-vibration suppressor input, and the second-order modal electrical signal is controlled by the pre-vibration suppressor input, thereby providing the physical control force F required for the two modes respectively.r , to achieve coordinated control of the first two vibration modes in the pitch plane.

[0082] A simulation model is established based on the Matlab / Simulink platform to simulate the above method. Figure 3 This is the simulation diagram of the first-order modal control effect in the pitch plane. Figure 4 This is a simulation diagram of the second-order modal control effect in the pitch plane. It can be seen that when multi-modal vibration coordinated control is not performed, the first-order vibration still has residual vibration at 20s, the first-order damping ratio is 0.011, and the second-order vibration is completely attenuated at about 14s, and the second-order damping ratio is 0.006; after applying multi-modal vibration coordinated control, the first-order vibration is completely attenuated at about 4s, the first-order damping ratio is 0.097, which is about 8.818 times higher than when it is not turned on, and the second-order vibration is completely attenuated at about 6s, the second-order damping ratio is 0.041, which is about 6.667 times higher than when it is not turned on. The multi-modal vibration of the model support system is effectively suppressed.

[0083] Compared with traditional methods, this vibration suppression method improves the shortcomings of a single vibration suppression mechanism and low vibration suppression order. It can decouple and observe the multi-modal complex vibration of the wind tunnel model support system in the modal space, and solve the optimal controller gain through the control algorithm, thereby realizing the coordinated active suppression of multi-modal vibration. The suppression effect on the multi-modal complex vibration system is obvious, and the wind tunnel test data is accurately obtained, which can ensure the reliable evaluation of the dynamic stability of high-maneuverability aircraft, and can be applied to various types of wind tunnel tests and model support systems.

Claims

1. A method for collaboratively suppressing multi-modal vibration of a wind tunnel model support system, characterized in that: This method firstly obtains the system frequency response function and identifies the modal parameters of each order by applying hammer pulse excitation to the wind tunnel model support system; secondly, it obtains the system modal filter decoupling matrix and designs the modal filter; Then, the state space equations of each order of the system are identified and the modal observer is designed. Finally, the control gain matrix of each order is calculated to obtain the modal control force and physical control force of each order, so as to realize the coordinated suppression of multi-modal vibration of the model support system. The specific steps are as follows: 1) The wind tunnel model support system is subjected to hammer pulse excitation, the hammer input signal x(t) is recorded, the multi-point time domain vibration response signal y(t) of the wind tunnel model support system is measured, and the open-loop frequency response H(ω) of each point of the wind tunnel model support system is obtained; The steps to determine the frequency response function H(ω) of each point of the wind tunnel model support system are as follows: 1.1) Perform windowing function processing on the hammer input signal x(t) and the output wind tunnel model support system multi-point time domain vibration response signal y(t); 1.2) Calculate the power spectrum density function S of the windowed data xx (ω) and the cross power spectral density function S xy (ω); 1.3) S xy (ω) and S xx (ω) is used as the ratio to obtain the system frequency response function H(ω), and the amplitude-frequency response curve and phase-frequency response curve of the system are plotted with frequency as the horizontal coordinate and amplitude ratio and phase difference as the vertical coordinate; 2) Combine the amplitude-frequency response curve in the system frequency response function to identify the modal parameters of each order of the system, including the natural frequency ω r and modal damping ratio ζ r ; The steps for identifying the modal parameters of each order are as follows: 2.1) Obtain the open-loop frequency response function of the system, where the abscissas corresponding to the first r peak points of the amplitude-frequency response curve are the first-order, second-order, ... r-order natural frequencies of the system respectively; 2.2) Record the peak values ​​A of the amplitude-frequency response curve n , based on the half-power bandwidth method to determine 0.707A n The frequency values ​​on both sides of ω r1 ,ω r2 ; 2.3) Calculate the damping ratio ζ of each modal according to formula (2): r : 3) Based on the principle of modal superposition, the system modal filter decoupling matrix is ​​obtained, and the modal filter is designed to realize the conversion from mutual coupling in physical space to mutual decoupling in modal space; The steps to solve the modal filter decoupling matrix are as follows: 3.1) Based on modal orthogonality and normalization, define the modal filter decoupling matrix Ψ T , the conversion from physical space to modal space is realized through formula (3); η=Φ T Mδ=Ψ T d (3) Among them, η is the modal coordinate, δ is the physical coordinate, M is the system mass matrix, and Φ is the natural vibration matrix; 3.2) Apply excitation X to the j point of the wind tunnel model support system j , record the acceleration response Y at point i j According to step (1), we can get the acceleration response function W ij (w), derive the acceleration frequency response modal expansion (4); in, is the rth column vector of the vibration matrix, ω is the frequency, m r is the modal mass coefficient of each order, ω r is the natural frequency of each order, ξ r is the damping ratio of each mode; 3.3) Based on the normalization condition of vibration mode, we get m r =1, multiply the left side of equation (4) by the column vector of the decoupling matrix r because Orthogonal to all vibration modes except the rth vibration mode, we get equation (5); Among them, single point incentive is a constant; 3.4) Due to is a constant, and is defined To find the r-th order decoupling vector, according to formula (6), select the appropriate observation point frequency and establish For the unknown quantity equations, solve the decoupling vectors of each order to form the modal filter decoupling matrix Ψ T ; 4) Identify the state space equations of each order in the system modal space, design the modal observer, and estimate the modal space vibration information as control feedback; The steps of modal observer design are as follows: 4.1) Combining the natural frequencies and damping ratios of each order, identify the state space equations (7) of each order in the modal space; in, η r is the modal displacement, is the modal velocity, f r is the modal control force; 4.2) Acceleration is taken as the system output, and the state observation equation (8) based on Luenberger's improved form is derived; in, is the estimated value of the modal displacement, is the estimated modal velocity, is the estimated value of modal acceleration, K r is the modal observer gain, y is the system output, and E is the unit matrix; 4.3) Configuration based on Lyapunov criterion (E+K r C r ) -1 A r The pole is located in the left plane, solving the modal observer gain K r ; (4.4) Combining the observation equation (8) with the modal observer gain K r , to estimate the modal velocity and modal displacement; (5) Calculate the optimal controller gain coefficient K based on the control algorithm and obtain the control force f required for each mode r , combined with the natural vibration matrix Φ, converted into the physical control force F required for each mode r ; Physical control force F at each level r The solution steps are as follows: (5.1) Based on LQR, LQG, H ∞ The control algorithm obtains the optimal control gain matrix K; (5.2) Combining the observed modal displacement and modal velocity, the required control force f for each mode is calculated using formula (9): r ; (5.3) Combined with the intrinsic matrix Φ, the physical control force F required for each mode is obtained through formula (10): r ; F r =Φf r (10) (6) Combined with the piezoelectric ceramic electromechanical coupling matrix, calculate the input electrical signal U required for each section of the vibration suppressor r , and then provide the physical control force F required for each mode r , achieving multi-modal collaborative active suppression.

2. The method for collaboratively suppressing multi-modal vibration of a wind tunnel model support system according to claim 1 is characterized in that: The modal observer gain K in 4.3) r When considering system noise and measurement noise, based on the Kalman filter principle, the Riccati equation (11) is solved to obtain the modal observer gain K r =PC r T V -1 ; PA r T +A r P-PC r T V -1 C r P+W=0 (11) Where P is the solution of the Riccati equation, W is the system noise covariance matrix, and V is the system measurement noise covariance matrix.

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