Dispersed robust H-infinity structure vibration control method, system and product

Abstract

The invention discloses a decentralized robust H-infinity structure vibration control method, system and product, and the method comprises the steps: 1) estimating the amplitude of the uncertainty influence of a structure parameter, and building an uncertain structure dynamic model of a decentralized control object with a control device; 2) on the premise of ensuring the stability of the control system and improving the calculation efficiency, establishing a state space kinetic equation of the uncertain structure decentralized control system, and establishing a control force input model of the structure decentralized control system based on a quadratic performance index; and 3) based on the robust H-infinity control basic principle, establishing a linear matrix inequality method for solving the structure decentralized control gain, obtaining a relatively optimal decentralized robust H-infinity control force in real time, inputting a calculation control force to a corresponding substructure control device, continuously performing effective vibration control on the entity structure, and obtaining the optimal decentralized robust H-infinity control force. And completing vibration control until the structural performance requirements under the action of different levels of external loads are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering structure vibration control, and particularly relates to a decentralized robust H ∞ Structural vibration control methods, systems and products. Background Art

[0002] In recent years, with the rapid development of some intelligent actuators such as electro-rheological fluids, piezoelectric materials, and shape memory alloys, active control theory has made great progress. The active control method of the structure collects the response information of the structure in real time, and applies active force to the structure or adjusts the parameters of the structure according to the preset control algorithm. It has good control adaptability and flexibility. Moreover, compared with passive control, the active control of the structure has many advantages such as good control effect, high precision, and the ability to effectively handle external interference. Moreover, the active control method is the basis of semi-active and hybrid control methods, so it has great engineering application value. In the vibration control engineering of physical structures, structural parameters such as structural stiffness and damping are difficult to accurately describe with mathematical models, and the uncertainty of the structure will lead to the instability of the control system and the deterioration of control performance. Therefore, it is an important aspect of the research on structural vibration control to study the control algorithm with good robustness to structural parameters and external disturbances and simple adjustment.

[0003] Most active controls are based on centralized control strategies, using centralized controllers to comprehensively control the entire structural system and process huge amounts of data, which will make the parallel computing capability and reliability of the structural control system insufficient. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and propose a decentralized robust H ∞ Structural vibration control method, system and product. The present invention divides a large complex structure into several subsystems or substructures, and designs a dedicated controller for each subsystem or substructure, which not only reduces the complexity and computational load of the controller, but also significantly improves the robustness and resilience of the entire control system. When a subsystem or controller fails, other subsystems or controllers can still work normally, thereby ensuring the stability and robustness of the entire structural control system.

[0005] In view of this, the present invention proposes a decentralized robust H ∞ Structural vibration control methods, including:

[0006] Step 1) estimating the magnitude of the influence of structural parameter uncertainty and establishing an uncertain structural dynamics model of a decentralized control object with a control device;

[0007] Step 2) Under the premise of ensuring the stability of the control system and improving the computational efficiency, the state space dynamic equation of the uncertain structured decentralized control system is established, and at the same time, the control force input model of the structured decentralized control system is established based on the quadratic performance index;

[0008] Step 3) Based on the robust H ∞ The basic principles of control are established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H in real time. ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

[0009] Preferably, the step 1) comprises:

[0010] Step 1-1) establishing a finite element model of the physical structure;

[0011] Step 1-2) Perform free vibration response analysis on the finite element model to obtain corresponding modal frequencies; collect data measured by an acceleration sensor, a velocity sensor or a displacement sensor on the physical structure, identify the main frequency and damping ratio of the physical structure based on a modal parameter identification method, use the first 5 to 9 order frequencies and damping ratio values ​​as main reference values, and calibrate and upgrade the finite element model of the physical structure according to the identified modal parameter values;

[0012] Steps 1-3) extract the structural mass, stiffness and damping parameter values ​​of the finite element model, and estimate the amplitudes of structural mass, stiffness, damping and control force uncertainty as Δ M , Δ K , Δ C and Establish the equation of motion for the controlled structure:

[0013]

[0014] In the formula, are the displacement vector, velocity vector and acceleration vector of the structure respectively; M is the mass matrix of the structure; B s is the control force position matrix; U(t) is the control force column vector; C and K are the structural damping and stiffness matrices respectively; is the external disturbance parameter matrix; w(t) is the external disturbance component of the structure;

[0015] Step 1-4) Divide the finite element model into N substructures, where the number of layers corresponding to the i-th substructure is n i , the corresponding number of controllers is r i .

[0016] Preferably, the step 2) comprises:

[0017] Step 2-1) The controller of the ith substructure is limited to only affect the state response of the ith substructure, and the dynamic model of the control system of each substructure is obtained:

[0018]

[0019] in, In the formula, is the ith substructure 2n i ×1The first-order differential of the state vector, X i is the ith substructure 2n i ×1 state vector, X j is the jth substructure 2n j ×1 state vector, A ii is the state parameter matrix related to the mass, stiffness and damping of the ith substructure, ΔA ii is the state parameter matrix related to the uncertainty of mass, stiffness and damping of the ith substructure, A ij is the state parameter matrix related to the mass, stiffness and damping of the i-th and j-th substructures, H i The external perturbation position matrix of the ith substructure, and U i are n of the ith substructure respectively. i ×1 displacement vector, velocity vector and r i ×1 control force vector, |ΔA ij |<R ij , |ΔB ii |<S i , R ij and S i is related to ΔA ij and ΔB ii non-negative real constant matrices with the same dimension, i = 1, 2, ..., N; j = 1, 2, ..., N; N is the number of substructures; ΔA ij and ΔB ii Used to limit the range of variation of uncertain parameters;

[0020] Step 2-2) Based on the state space theory, the dynamic model of each substructure control system obtained in step 2-1) is transformed into the following structural decentralized control system state equation:

[0021]

[0022] In the formula,

[0023] B=diag{B1,…,B i ,…,,B N}, H=diag{H1,…,H i,…,H N},A=[A ij ] N×N , ΔA=[ΔA ij ] N×N , ΔB=diag{ΔB1,…,ΔB i ,…,ΔB N},U=col{U1,…,U i ,…,U N}, Z = col{X1,…,X i ,…,X N}, w=col{w1,…,w i ,…,w N}, diag represents a diagonal matrix, col represents a column vector;

[0024] Step 2-3) Based on the quadratic performance index, the input matrix z of the structural control system is established as:

[0025] z=D d X+D f U

[0026] In the formula,

[0027] D d =diag{D d1 ,…,D di ,…,D dN},D f =diag{D f1 ,…,D fi ,…,D fN},z=col{z1,…,z N}, Q di is the semi-positive definite weight matrix of the corresponding dimension; R di is the positive definite weight matrix of the corresponding dimension,

[0028] Combined with the acceleration, velocity or displacement collected by each substructure state sensor, the state response output Y of the structural distributed control system is established s :

[0029] Y s =Z

[0030] Where Y s =col{Y s1 ,…,Y sN}, corresponding to the state response outputs of the 1st substructure, ...the Nth substructure respectively.

[0031] Preferably, the step 3) comprises:

[0032] Step 3-1) Set the system external disturbance input w(t) to the system output Y s The transfer function of (t) H ∞ Norm Where γ is a given positive number, a linear matrix inequality is constructed to solve the control force calculation method, and the feasible solution constants α>0, β>0, and the matrix and Y d :

[0033]

[0034] Where N d ∈diag{N d1 ,…,N di ,…,N dN},Y d ∈diag{Y d1 ,…,Y di ,…,Y dN}, Ω(R)=Ω([R ij ] N×N ),i,j=1,…,N,Ω(S)=diag{Ω(S1),…,Ω(S N )}; The superscript T indicates transposition;

[0035] Step 3-2) The matrix N obtained from step 3-1) d and Y d , and according to the real-time measured state response values ​​of each layer of the structure, the corresponding robust H is obtained ∞ The decentralized optimal computing control force U(t) is:

[0036]

[0037] Step 3-3) Input the structure distributed calculation control force to the corresponding sub-control device in real time, so as to realize effective vibration control of the physical structure, so that the vibration response of the structure can meet the structural performance requirements under different levels of external loads.

[0038] In a second aspect, the present invention provides a decentralized robust H ∞ Structural vibration control systems, including:

[0039] Uncertain structural dynamics model building module, used to estimate the magnitude of the influence of structural parameter uncertainty and build an uncertain structural dynamics model of a decentralized control object with a control device;

[0040] The decentralized control structure reduced-order dynamics model building module is used to establish the state space dynamics equations of the uncertain structure decentralized control system under the premise of ensuring the stability of the control system and improving the computational efficiency, and to establish the control force input model of the structure decentralized control system based on the quadratic performance index; and

[0041] Vibration control module for robust H based ∞ The basic principles of control are established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H in real time. ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

[0042] On the other hand, the present invention further provides a computer program product, comprising a computer program, which implements the steps of the above method when executed by a processor.

[0043] Compared with the prior art, the advantages of the present invention are:

[0044] The present invention uses H commonly used in engineering ∞ The optimal control is combined with the design of structured decentralized control systems, and the linear matrix inequality is applied to reduce the complexity of the solution. A decentralized robust H based on linear matrix inequality is designed to facilitate engineering applications. ∞ Structural vibration control methods.

[0045] The present invention is based on H ∞ Control and linear matrix inequality theory, a new decentralized robust H ∞ The control method effectively solves the reliability, stability and robustness problems of active, semi-active and hybrid control systems of structural vibration.

[0046] Compared with the traditional structural vibration centralized control algorithm, the control system of the present invention has simple design, good reliability, low external energy demand, and can effectively ensure the stability and robustness of the control system under the premise of structural parameter uncertainty, which is convenient for engineering application. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a control principle block diagram of the method of the present invention;

[0048] Figure 2 It is a schematic diagram of the physical structure of the present invention;

[0049] FIG3 is a comparison diagram of the peak values ​​of the structural dynamic response under different working conditions; FIG3(a) is the peak displacement of each layer of the structure relative to the ground under different working conditions, and FIG3(b) is the peak interlayer displacement of each layer of the structure under different working conditions;

[0050] Figure 4 is a comparison of dynamic responses under changes in structural parameters; Figure 4(a) is the peak displacement of each layer of the structure relative to the ground, Figure 4(b) is the peak interlayer displacement of each layer of the structure, and Figure 4(c) is the displacement response time history of the 20th layer of the structure under different working conditions;

[0051] FIG5 is a comparison of the total control force values ​​of the structure under different working conditions, wherein FIG5(a) is a comparison of the total control force of the structure between the method of the present invention and the traditional LQR control method, and FIG5(b) is a comparison of the total control force when 15 dampers are placed on the structure and when dampers are placed on each layer. DETAILED DESCRIPTION

[0052] The present invention uses H commonly used in engineering ∞ The optimal control is combined with the design of structured decentralized control systems, and the linear matrix inequality is applied to reduce the complexity of the solution. A decentralized robust H based on linear matrix inequalities (LMI) is designed to facilitate engineering applications. ∞ Structural vibration control algorithm.

[0053] H∞ control is a design method with good robustness, clear design ideas and good control effects. It is especially suitable for multi-input multi-output (MIMO) systems with model perturbations. After years of continuous development and improvement in control theory, design methods and applications, H∞ control has become a robust control theory with a relatively complete system.

[0054] The purpose of the present invention is to propose a decentralized robust control method for structural vibration which is simple in calculation and convenient for engineering application under the premise of considering the uncertainty of structural parameters.

[0055] The technical solution adopted by the present invention is based on H ∞ Control and linear matrix inequality theory, a new decentralized robust H ∞ Control methods are used to solve the reliability, stability and robustness problems of active, semi-active and hybrid control systems for structural vibration.

[0056] The specific implementation steps are:

[0057] Step 1: Estimate the magnitude of the influence of structural parameter uncertainty, and establish an uncertain structural dynamics model for decentralized control objects based on a large-scale general finite element program and computer language program platform.

[0058] Step 2: Under the premise of ensuring the stability of the control system, the state space dynamic equation of the uncertain structural decentralized control system is established, and the control force input model of the structural decentralized control system is established based on the quadratic performance index.

[0059] Step 3: Based on robust H ∞ The basic control principle is established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

[0060] In the step 1, obtaining the uncertain structure decentralized control dynamics model specifically includes the following steps:

[0061] (1) Based on the design data and large-scale general finite element programs, the corresponding modal damping ratio is assumed according to the specific characteristics of the structure (for ordinary multi-story and high-rise reinforced concrete structures and steel structures, it can be considered to be 2% to 5%), and a finite element model of the solid structure is established. The free vibration response analysis of the model is performed to obtain the corresponding modal frequency. The data measured by the acceleration sensor, velocity sensor or displacement sensor on the solid structure are collected, and then the main frequency and damping ratio of the solid structure are identified based on the structural modal parameter identification methods such as the discrete synchronous extrusion wavelet transform method and the empirical mode decoupling method. Considering the high noise and low amplitude of the measurement signal, the first 5 to 9 order frequencies and damping ratio values ​​are used as the main reference values. According to the identified modal parameter values, the finite element model of the solid structure is corrected and upgraded.

[0062] (2) Extract the numerical values ​​of the structural mass, stiffness and damping parameters of the finite element model, and estimate the amplitudes of the uncertainties of the structural mass, stiffness, damping and control force as Δ M , Δ K , Δ C and Based on the computer language program platform, the motion equations of the controlled structure are established

[0063]

[0064] In the formula, X, are the displacement vector, velocity vector and acceleration vector of the structure respectively; M is the mass matrix of the structure; B s is the control force position matrix; U(t) is the control force column vector; C and K are the structural damping and stiffness matrices respectively; External disturbance parameter matrix; w(t) is the external disturbance component to which the structure is subjected, including but not limited to earthquake, wind load, ocean wave, and shock wave.

[0065] (3) The controller of the i-th substructure is limited to only affect the state response of the i-th substructure, and the dynamic model of the control system of each substructure is obtained:

[0066]

[0067] For the left side of the equation In the formula, is the ith substructure 2n i ×1The first-order differential of the state vector, X i is the ith substructure 2n i ×1 state vector, X j is the jth substructure 2n j ×1 state vector, A ii is the state parameter matrix related to the mass, stiffness and damping of the ith substructure, ΔA ii is the state parameter matrix related to the uncertainty of mass, stiffness and damping of the ith substructure, A ij is the state parameter matrix related to the mass, stiffness and damping of the i-th and j-th substructures, H i The external perturbation position matrix of the ith substructure, and U i are n of the ith substructure respectively. i ×1 displacement vector, velocity vector and r i ×1 control force vector, |ΔA ij |<R ij , |ΔB ii |<S i , R ij and S i is related to ΔA ij and ΔB ii non-negative real constant matrices with the same dimension, i = 1, 2, ..., N; j = 1, 2, ..., N; N is the number of substructures; ΔA ij and ΔB ii Used to limit the range of variation of uncertain parameters, which can be estimated based on the actual complexity of the project;

[0068] In one embodiment, taking the structural system as an example, the number of layers corresponding to each substructure is n1, n2, and n3, and the number of controllers corresponding to each substructure is r1, r2, and r3, respectively.

[0069]

[0070] Then the dynamic equation of the decentralized structure control system can be obtained as follows

[0071]

[0072] In the formula

[0073] δ K11 =Δ K11 +δ1'K11 ,δ K12 =Δ K12 +δ1'K 12 , δ C11 =Δ C11 +δ1'C 11 ,δ C12 =Δ C12 +δ1'C 12 , δ K22 =Δ K22 +δ2'K 22 ,δ K21 =Δ K21 +δ2'K 21 , δ K23 =Δ K23 +δ2'K 23 , δ C22 =Δ C22 +δ2'C 22 ,δ C21 =Δ C21 +δ2'C 21 ,δ C23 =Δ C23 +δ2'C 23 δ K33 =Δ K33 +δ3'K 33 ,δ C33 =Δ C33 +δ3'C 33 ,δ K32 =Δ K32 +δ3'K 32 , δ C32 =Δ C32 +δ3'C 32 , (I+δ)(I+δ')=I,δ=diag[δ1,δ2,…,δ n ] and 0<Δ Mii / M ii ≤δ i <1.

[0074] Step 2: Under the premise of ensuring the stability of the control system, the state space dynamic equation of the uncertain structural decentralized control system is established, and the control force input model of the structural decentralized control system is established based on the quadratic performance index.

[0075] In the second step, obtaining the state space dynamic equation of the decentralized structure control system specifically includes the following steps:

[0076] (1) The controller of the i-th substructure is limited to only affect the state response of the i-th substructure. Then, the dynamic model of the control system of each substructure is established based on formula (3):

[0077]

[0078] Further, formula (4) can be expressed as a general form of any N substructures:

[0079]

[0080] In the formula and U i are n of the ith substructure respectively. i ×1 displacement vector and r i ×1 control force vector, |ΔA ij |<R ij ,|ΔB ii |<S i , R ij and S i is related to ΔA ij and ΔB ii Nonnegative real constant matrices of the same dimension.

[0081] (2) Based on the state space theory, the dynamic model of each substructure control system is transformed into the following structure distributed control system state equation:

[0082]

[0083] In the formula

[0084] B=diag{B1,…,B i ,…,B N}, H=diag{H1,…,H i ,…,H N},A=[A ij ] N×N ,

[0085] ΔA=[ΔA ij ] N×N , ΔB=diag{ΔB1,…,ΔB i ,…,ΔB N},U=col{U1,…,U i ,…,U N},

[0086] Z=col{X1,…,X i ,…,X N}, w=col{w1,…,w i ,…,w N},U=col{U1,…,UN}diag represents a diagonal matrix, col represents a column vector; N is the number of substructures.

[0087] (3) Based on the quadratic performance index, the input matrix of the structural control system is established as

[0088] z=D d X+D f U (7)

[0089] In the formula

[0090] D d =diag{D d1 ,…,D dN},D f =diag{D f1 ,…,D fN},z=col{z1,…,z N}

[0091] Q di is the semi-positive definite weight matrix of the corresponding dimension; R di is a positive definite weight matrix of the corresponding dimension.

[0092] Considering that the displacement and velocity of each layer of the structure can be measured, if some state responses cannot be measured in practice, they can be predicted and processed according to the state response predictor, and the state response output of the control system is formed as follows:

[0093] Y s =Z (8)

[0094] Where Y s =col{Y s1 ,…,Y sN}.

[0095] Step 3: Based on robust H ∞ The basic control principle is established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

[0096] In step 3, the calculation of the structure decentralized control force specifically includes the following steps:

[0097] (1) Set the system external disturbance input w(t) to the system output Y s The transfer function of (t) H ∞ Norm Where γ is a given positive number. For a given constant γ>0, a linear matrix inequality solution control force calculation method is constructed. By solving the linear matrix inequality (9), the feasible solution constants α>0, β>0, and the matrix and Y d .

[0098]

[0099] In the formula

[0100] N d ∈diag{N d1 ,…,N di ,…,N dN},Y d ∈diag{Y d1 ,…,Y di ,…,Y dN}, Ω(R)=Ω([R ij ] N×N ),i,j=1,…,N,Ω(S)=diag{Ω(S1),…,Ω(S N )}.

[0101] (2) The matrix N obtained by the solution d and Y d , and according to the real-time measured state response values ​​of each layer of the structure, the corresponding robust H ∞ The decentralized optimal computing control force is

[0102]

[0103] (3) The structure’s distributed computing control force is input in real time to the corresponding sub-control device, thereby achieving effective vibration control of the physical structure and enabling the vibration response of the structure to meet the performance requirements of the structure under different levels of external loads.

[0104] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0105] Example 1

[0106] Embodiment 1 of the present invention is a new decentralized robust H based on decentralized control principle and linear matrix inequality. ∞ The structural vibration control method is described in detail below with reference to the accompanying drawings and specific examples. Figure 1 The high-level entity structure is shown in Figure 2 As shown in Figure 2, a 20-story high-rise structure is taken as an example to verify the effectiveness of the proposed method.

[0107] Step 1: Obtaining the dynamic model of the decentralized structure control system The specific implementation steps are:

[0108] (1) The schematic diagram of the 20-layer physical structure is as follows Figure 2 As shown, the structure is considered to be divided into three structures, the 1st to 7th floors are substructure 1, the 8th to 14th floors are substructure 2, and the 15th to 20th floors are substructure 3. It is assumed that each layer of the structure is equipped with velocity and displacement sensors to measure the state response of the structure in real time.

[0109] (2) Assume that after finite element modeling and modal parameter identification, the structural parameters of the corrected finite element model are: the interlaminar mass of the first layer of the structure is 1.126×10 6 kg, and the interlayer mass of the 2nd to 19th layers of the structure is 1.100×10 6 kg, and the interlayer mass of the 20th layer of the structure is 1.170×10 6 kg; the lateral stiffness coefficient of the 1st to 5th floors of the structure is 8.62×10 8 N / m, and the lateral stiffness coefficient of the 6th to 11th floors of the structure is 5.54×10 8 N / m, and the lateral stiffness coefficient of the 12th to 14th floors of the structure is 4.53×10 8 N / m, and the lateral stiffness coefficient of the 15th to 17th floors of the structure is 2.91×10 8 N / m, and the lateral stiffness coefficient of the 18th-19th floors of the structure is 2.56×10 8 N / m, and the lateral stiffness coefficient of the 20th floor of the structure is 1.71×10 8 N / m; the structural damping ratio is 0.05.

[0110] (3) Considering the structural response under the El Centro earthquake, the peak value of the seismic wave acceleration is adjusted to 0.2g and the sampling period is 0.02s. The amplitude of the structural uncertainty parameter is set to ΔK = 0.2K, Δ C =0.2C, δ can be taken as 0.05. The structural parameter values ​​of the corrected finite element model are extracted, and the motion equation of the structure (1) is established based on the amplitude of the structural uncertainty parameters. According to the set three substructure division principles, the structural parameter values ​​in equation (2) are determined, thereby establishing the dynamic equation (3) of the decentralized structural control system.

[0111] Step 2: The state space dynamic equation of the decentralized structural system considering the deterministic influence of structural parameters. The specific implementation steps are:

[0112] (1) Based on equation (3), equation (4) is obtained, and then it is organized into the general form of equation (5).

[0113] (2) Further transform equation (5) into the state space equation form, namely equation (6).

[0114] (3) Option Matrix Then the control input dynamic equation (7) can be established. At the same time, the displacement and velocity of each layer of the structure can be effectively obtained by the arranged sensors or corresponding test equipment, so as to establish the state response output equation (8) of the structural control system.

[0115] Step 3: Calculate the structural dispersion robust H ∞ Optimal control force. The specific implementation steps are:

[0116] (1) Solve the linear matrix inequality (9) and obtain the feasible solution matrix N d and Y d Specific value of

[0117] (2) The obtained solution matrix N d and Y d According to formula (10), the corresponding control gain K can be calculated u The real-time measured structural state response Z(t) is multiplied by the controller gain matrix K u , the optimal decentralized control force U(t) can be calculated in real time.

[0118] (3) Extract the decentralized control force U corresponding to each substructure i (t) and input it into the corresponding substructure control device, the decentralized control of the structural vibration can be realized. Figure 3 is a comparison diagram of the peak values ​​of the dynamic response of the structure under different working conditions, wherein Figure 3 (a) is the peak displacement of each layer of the structure relative to the ground under different working conditions, and Figure 3 (b) is the peak interlayer displacement of each layer of the structure under different working conditions; Figure 4 is a comparison of the dynamic response under the change of structural parameters, wherein Figure 4 (a) is the peak displacement of each layer of the structure relative to the ground, Figure 4 (b) is the peak interlayer displacement of each layer of the structure, and Figure 4 (c) is the displacement response time history of the 20th layer of the structure under different working conditions; Figure 5 is a comparison of the total control force values ​​of the structure under different working conditions. , wherein Figure 5 (a) is a comparison of the total control force of the structure between the method of the present invention and the traditional LQR control method, and Figure 5 (b) is a comparison of the total control force under the two conditions of placing 15 dampers on the structure and placing dampers on each layer.

[0119] In Figure 3, “Uncontrolled” means there is no control device, “LQR” means the traditional LQR control algorithm is adopted, and “RH” means the decentralized robust H of the nominal structure. ∞ control, “RH(15dampers)” represents the nominal structural decentralized robust control with only 15 dampers installed. ∞ In Figure 4, “0.8kc” indicates that the structure’s stiffness and damping are reduced by 20% with the decentralized robust H ∞ control, “1.2kc” means that the structure’s stiffness and damping increase by 20% with a decentralized robust H ∞control, “0kc” indicates the decentralized robust H of the nominal structure ∞ control; "0.9kc" means that the structure's stiffness and damping are reduced by 10% of the decentralized robust H ∞ control, "1.1kc" means that the structure's stiffness and damping increase by 10% with a decentralized robust H ∞ In Figure 5, “0.8kc(15)” represents the decentralized robust H control when only 15 dampers are installed in the structure and the structural stiffness and damping are reduced by 20%. ∞ control, “1.2kc” represents the decentralized robust H when only 15 dampers are installed and the stiffness and damping of the structure are increased by 20% ∞ control, “RH(15)” represents the nominal structural decentralized robustness H with only 15 dampers installed ∞ control.

[0120] It can be seen from Figures 3, 4 and 5 that within the set parameter variation range, the present invention has good vibration control effect and robustness while ensuring the stability of the control system. Compared with the traditional LQR control algorithm, it has a smaller control input energy requirement.

[0121] Example 2

[0122] Embodiment 2 of the present invention proposes a decentralized robust H ∞ The structural vibration control system is implemented based on the method of embodiment 1, comprising:

[0123] Uncertain structural dynamics model building module, used to estimate the magnitude of the influence of structural parameter uncertainty and build an uncertain structural dynamics model of a decentralized control object with a control device;

[0124] The decentralized control structure reduced-order dynamics model building module is used to establish the state space dynamics equation of the uncertain structure decentralized control system under the premise of ensuring the stability of the control system and improving the computational efficiency, and to establish the control force input model of the structure decentralized control system based on the quadratic performance index;

[0125] Vibration control module for robust H based ∞ The basic principles of control are established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H in real time. ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

[0126] Example 3

[0127] Embodiment 3 of the present invention provides a computer program product, including a computer program. When the computer program is executed by a processor, each step in Embodiment 1 can be implemented.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A decentralized robust H ∞ Structural vibration control methods, including: Step 1) estimating the magnitude of the influence of structural parameter uncertainty and establishing an uncertain structural dynamics model of a decentralized control object with a control device; Step 2) Under the premise of ensuring the stability of the control system and improving the computational efficiency, the state space dynamic equation of the uncertain structured decentralized control system is established, and at the same time, the control force input model of the structured decentralized control system is established based on the quadratic performance index; Step 3) Based on the robust H ∞ The basic principles of control are established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H in real time. ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

2. The decentralized robust H ∞ The structural vibration control method is characterized in that: The step 1) comprises: Step 1-1) establishing a finite element model of the physical structure; Step 1-2) Perform free vibration response analysis on the finite element model to obtain corresponding modal frequencies; collect data measured by an acceleration sensor, a velocity sensor or a displacement sensor on the physical structure, identify the main frequency and damping ratio of the physical structure based on a modal parameter identification method, use the first 5 to 9 order frequencies and damping ratio values ​​as main reference values, and calibrate and upgrade the finite element model of the physical structure according to the identified modal parameter values; Steps 1-3) extract the structural mass, stiffness and damping parameter values ​​of the finite element model, and estimate the amplitudes of structural mass, stiffness, damping and control force uncertainty as Δ M , Δ K , Δ C and Δ BS , establish the motion equation of the controlled structure: In the formula, are the displacement vector, velocity vector and acceleration vector of the structure respectively; M is the mass matrix of the structure; B s is the control force position matrix; U(t) is the control force column vector; C and K are the structural damping and stiffness matrices respectively; is the external disturbance parameter matrix; w(t) is the external disturbance component of the structure; Step 1-4) Divide the finite element model into N substructures, where the number of layers corresponding to the i-th substructure is n i , the corresponding number of controllers is r i .

3. The decentralized robust H ∞ The structural vibration control method is characterized in that: The step 2) comprises: Step 2-1) The controller of the ith substructure is limited to only affect the state response of the ith substructure, and the dynamic model of the control system of each substructure is obtained: in, In the formula, is the ith substructure 2n i ×1The first-order differential of the state vector, X i is the ith substructure 2n i ×1 state vector, X j is the jth substructure 2n j ×1 state vector, A ii is the state parameter matrix related to the mass, stiffness and damping of the ith substructure, ΔA ii is the state parameter matrix related to the uncertainty of mass, stiffness and damping of the ith substructure, A ij is the state parameter matrix related to the mass, stiffness and damping of the i-th and j-th substructures, H i The external perturbation position matrix of the ith substructure, and U i are n of the ith substructure respectively. i ×1 displacement vector, velocity vector and r i ×1 control force vector, |ΔA ij |<R ij , |ΔB ii |<S i , R ij and S i is related to ΔA ij and ΔB ii non-negative real constant matrices with the same dimension, i = 1, 2, ..., N; j = 1, 2, ..., N; N is the number of substructures; ΔA ij and ΔB ii Used to limit the range of variation of uncertain parameters; Step 2-2) Based on the state space theory, the dynamic model of each substructure control system obtained in step 2-1) is transformed into the following structure distributed control system state equation: In the formula, B=diag{B1,…,B i ,…,B N }, H=diag{H1,…,H i ,…,H N },A=[A ij ] N×N , ΔA=[ΔA ij ] N×N , ΔB=diag{ΔB1,…,ΔB i ,…,ΔB N },U=col{U1,…,U i ,…,U N }, Z = col{X1,…,X i ,…,X N }, w=col{w1,…,w i ,…,w N }, diag represents a diagonal matrix, col represents a column vector; Step 2-3) Based on the quadratic performance index, the input matrix z of the structural control system is established as: z=D d X+D f U In the formula, D d =diag{D d1 ,…,D di ,…,D dN },D f =diag{D f1 ,…,D fi ,…,D fN },z=col{z1,…,z N }, Q di is the semi-positive definite weight matrix of the corresponding dimension; R di is the positive definite weight matrix of the corresponding dimension, Combined with the acceleration, velocity or displacement collected by each substructure state sensor, the state response output Y of the structural distributed control system is established s : Y s =Z Where Y s =col{Y s1 ,…,Y sN }, corresponding to the state response outputs of the 1st substructure, ...the Nth substructure respectively.

4. The decentralized robust H according to claim 2 ∞ The structural vibration control method is characterized in that: The step 3) comprises: Step 3-1) Set the system external disturbance input w(t) to the system output Y s The transfer function of (t) H ∞ Norm Where γ is a given positive number, a linear matrix inequality is constructed to solve the control force calculation method, and the feasible solution constants α>0, β>0, and the matrix and Y d : Where N d ∈diag{N d1 ,…,N di ,…,N dN },Y d ∈diag{Y d1 ,…,Y di ,…,Y dN }, Ω(S)=diag{Ω(S1),…,Ω(S N )}; The superscript T indicates transposition; Step 3-2) The matrix N obtained from step 3-1) d and Y d , and according to the real-time measured state response values ​​of each layer of the structure, the corresponding robust H is obtained ∞ The decentralized optimal computing control force U(t) is: Step 3-3) Input the structure distributed calculation control force to the corresponding sub-control device in real time, so as to realize effective vibration control of the physical structure, so that the vibration response of the structure can meet the structural performance requirements under different levels of external loads.

5. A decentralized robust H ∞ A structural vibration control system, characterized in that include: Uncertain structural dynamics model building module, used to estimate the magnitude of the influence of structural parameter uncertainty and build an uncertain structural dynamics model of a decentralized control object with a control device; The decentralized control structure reduced-order dynamics model building module is used to establish the state space dynamics equation of the uncertain structure decentralized control system under the premise of ensuring the stability of the control system and improving the computational efficiency, and to establish the control force input model of the structure decentralized control system based on the quadratic performance index; and Vibration control module for robust H based ∞ The basic principles of control are established, and the linear matrix inequality method for solving the structure decentralized control gain is established to obtain the relatively optimal decentralized robust H in real time. ∞ Control force, input the calculated control force into the corresponding substructure control device, and continuously perform effective vibration control on the physical structure until the structural performance requirements under different levels of external loads are met, thus completing the vibration control.

6. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

Images