Disturbance estimation method for linear motor system based on fusion of multiple extended state observers

Abstract

A method for estimating disturbances of a linear motor system based on the fusion of multiple extended state observers belongs to the fields of precision machining, electromechanical servo and motion control. The present invention solves the problem that the peak value of disturbance estimation of a linear motor system by a traditional linear extended state observer is relatively large. The present invention comprises: step one, establishing a transfer function model of the control quantity output to the running position of the linear motor, and writing the transfer function model in the form of a state space equation; step two, designing an extended state observer based on an n-order state space equation, establishing an observer model based on the extended state observer, and selecting the initial state value of the extended state observer according to the rules; step three, using the recursive least squares method with a forgetting factor and the initial state value of the extended state observer, calculating the weights of each extended state observer, and performing weighted summation on the disturbance estimates of each extended state observer according to the weights to obtain the disturbance estimation result. The method of the present invention can be applied to disturbance estimation of a linear motor servo control system.

Description

Technical Field

[0001] The invention belongs to the fields of precision machining, electromechanical servo and motion control, and in particular relates to a linear motor system disturbance estimation method based on multi-extended state observer fusion. Background Art

[0002] In the precision electromechanical equipment commonly used in industrial automation, the linear motor drive system plays an important role and is the development direction of future technology upgrades. In the fields involving linear motion such as precision CNC machine tools, placement machines, 3D printers, and lithography machines, traditional solutions such as rotary motors combined with ball screw drive solutions are far inferior to linear motor drive solutions.

[0003] At present, the control technology applied to linear motors is becoming more and more mature. During the operation of linear motors, they are often affected by various disturbances, including friction disturbances, thrust fluctuations of the system, model nonlinearity and uncertainty of the system, elastic deformation, mechanical resonance and other complex internal disturbances and external disturbances. In order to overcome these complex disturbances, the engineering community has tried a variety of disturbance observation and compensation methods. Among them, the extended state observer considers the total disturbance as an extended state, and reliably estimates and compensates the sum of the unmodeled dynamics of the system and various disturbances. Since the observation accuracy and robustness of the linear extended state observer are affected by the observer gain, a large gain can obtain a more accurate disturbance estimate, but if the observer gain is too high, it will lead to the peak phenomenon. When the system starts or some variables suddenly change, the process of the linear extended state observer's estimate approaching the initial value to the steady-state value will produce a large overshoot, resulting in a large error peak. If the error peak estimated by the linear extended state observer is directly compensated into the system without processing, on the one hand, it may give the system an impact on the control quantity and damage the system, and on the other hand, it may make the originally stable system unstable. In addition, when the speed suddenly changes (such as the motor tracking the triangular wave signal, the speed suddenly changes at the corner point), the speed value to be observed by the system will jump, and the state estimated by the linear expansion state observer will enter the transient process, which will also cause large errors in speed and disturbance observation. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of large peak value of disturbance estimation error of linear motor system by traditional linear extended state observer, and propose a disturbance estimation method of linear motor system based on fusion of multiple extended state observers.

[0005] The technical solution adopted by the present invention to solve the above technical problems is:

[0006] A linear motor system disturbance estimation method based on multi-extended state observer fusion, the method specifically comprises the following steps:

[0007] Step 1: Establish a transfer function model from the control quantity output to the running position of the linear motor, and then write the established transfer function model in the form of a state space equation;

[0008] Step 2: Design an extended state observer based on the n-order state space equation, then establish an observer model including n+1 extended state observers, and select the initial value of the state of the extended state observer according to the selection rule;

[0009] Step 3: Calculate the weight corresponding to each extended state observer in the observer model by using the recursive least squares method with forgetting factor and the initial value of the extended state observer state, and perform weighted summation on the disturbance estimates of each extended state observer according to the weight to obtain the disturbance estimation result.

[0010] The beneficial effects of the present invention are:

[0011] 1. The present invention proposes an extended state observer based on speed observation error feedback, which uses position observation error and speed observation error simultaneously in speed estimation and disturbance estimation, so that the observer can estimate the state and disturbance more accurately while reducing the error peak and overshoot.

[0012] 2. The present invention proposes a multi-extended state observer fusion technology to solve the error peak problem of state estimation and disturbance estimation of the motor system, which has definite research significance and practical value.

[0013] 3. The multi-expanded state observer fusion technology of the present invention fuses multiple expanded state observers with different initial values ​​through a linear weighted combination method, and can eliminate overshoot peaks in the observation process through convex combination, thereby achieving overshoot-free observation results and significantly increasing the reliability of the observer.

[0014] 4. The present invention uses the recursive least squares method based on the forgetting factor to realize the parameter estimation of multiple extended state observers, which solves the data accumulation problem caused by the increase in the number of recursive steps of the general least squares method, so that the latest data fed back by the motor sensor can play a sufficient correction role in the parameter estimation, thereby improving the parameter estimation effect of the extended state observer. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram for selecting initial values ​​of second-order multi-extended state observer;

[0016] Figure 2 Schematic diagram for initial value selection of third-order multi-extended state observer;

[0017] Figure 3 It is the flow chart of multi-extended state observer fusion algorithm;

[0018] Figure 4A comparison diagram of velocity estimation between the present invention and the traditional observer;

[0019] Figure 5 A comparison diagram of the speed observation error between the present invention and the traditional observer;

[0020] Figure 6 Schematic diagram of the third-order multi-extended state observer fusion for disturbance observation peak suppression;

[0021] Figure 7 It is the velocity observation result of the third-order multi-extended state observer;

[0022] Figure 8 Estimation of weight parameters for third-order multi-extended state observer fusion;

[0023] Fig. 9 is the disturbance fusion result of the second-order extended state observer (γ=100);

[0024] Fig.10 is the velocity fusion result of the second-order extended state observer (γ=10 5 );

[0025] Fig.11 is the disturbance fusion result of the second-order extended state observer (γ=10 5 ). DETAILED DESCRIPTION

[0026] The present application is further described in detail below through specific implementations in combination with the accompanying drawings. Obviously, the described implementations are only part of the implementations of the present invention, not all of the implementations. Based on the implementations in the present invention, other implementations obtained by ordinary technicians in the field without making creative work are all within the scope of protection of the present invention.

[0027] Specific implementation method 1: The linear motor system disturbance estimation method based on multi-extended state observer fusion described in this implementation method specifically includes the following steps:

[0028] Step 1: Establish a transfer function model from the actual control quantity output to the running position of the linear motor, and then write the established transfer function model into the form of a state space equation;

[0029] Step 2: Design multiple extended state observers based on the n-order state space equation, then establish an observer model containing n+1 extended state observers, and select the initial value of the extended state observer state according to a certain selection rule (the selection rule is to make the actual state initial value x(0) of the system within the observer state initial value z (i) (0))

[0030] Step 3: Establish an observer model containing n+1 extended state observers, and then use the recursive least squares method with forgetting factor and the initial value of the extended state observer state to calculate the weight corresponding to each extended state observer in the observer model, and perform weighted summation on the disturbance estimates of each extended state observer according to the weights to obtain the disturbance estimation result.

[0031] For two observed variables, an observer model containing three extended state observers needs to be designed; for three observed variables, an observer model containing four extended state observers needs to be designed.

[0032] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the transfer function model is:

[0033]

[0034] Where, K is the open-loop gain of the second-order system, T is the mechanical time constant, s is the Laplace differential operator, F(s) is the Laplace transform of the control quantity, and P(s) is the Laplace transform of the position quantity;

[0035] The state space equation is:

[0036]

[0037] Where x is the position of the linear motor, is the first-order derivative of x, v is the speed of the linear motor, is the first-order derivative of v, g v is the motor Coulomb friction coefficient, sgn(·) is the sign function, d is the system model uncertainty and external disturbance, and u is the control input of the system.

[0038] Specific implementation method three: This implementation method is different from the specific implementation method two in that the order of the state space equation n=3, and the extended state observer designed based on the state space equation is:

[0039]

[0040] Among them, z 1 is an estimate of the motor position, For z 1 The first derivative of 2 is an estimate of the motor speed, For z 2 The first derivative of 3 is an estimate of the total motor disturbance, For z 3 The first derivative of 1 , α 2 and α 3is the position observation error coefficient, β 2 and β 3 is the velocity observation error coefficient;

[0041] Position estimation error e 1 and the velocity estimation error e 2 They are:

[0042]

[0043] In this implementation, the number of state variables that the extended state observer needs to observe is three, namely, the motor position, the motor speed, and the motor total disturbance.

[0044] The third-order extended state observer in this embodiment is constructed based on the speed observation error feedback, and uses both position information and speed information. The observation effect of the designed third-order extended state observer is better and more accurate. 2 It is equivalent to the speed negative feedback of the observer, so it can effectively reduce the system overshoot and error peak.

[0045] Specific implementation method 4: This implementation method is different from the specific implementation method 2 in that the order of the state space equation n=2, and the extended state observer designed based on the state space equation is:

[0046]

[0047] Among them, z 1 is an estimate of the motor speed, For z 1 The first derivative of 2 is an estimate of the total motor disturbance, For z 2 The first derivative of o2 and β o3 represents the speed observation error coefficient of the observer;

[0048] Speed ​​estimation error e 1 for:

[0049] e 1 =vz 1 (6).

[0050] In this embodiment, the number of state variables that the extended state observer needs to observe is 2, namely, the motor speed and the motor total disturbance. Figure 1 shown.

[0051] Specific implementation mode 5: This implementation mode is different from specific implementation mode 3 or 4 in that the initial value of the state of the extended state observer is selected according to the selection rule; specifically:

[0052] Select a set of initial weight parameters a 1 (0),a 2 (0),...,a n+1 (0), so that the actual state initial value x(0) of the linear motor system is within the state initial value z of the extended state observer (i) (0) is in the convex hull, that is, z (i) (0) is the initial value of the state of the i-th extended state observer, z (i) (0) = [z 1(i) (0),z 2(i) (0),....,z n(i) (0)] T , z 1(i) (0),z 2(i) (0),....,z n(i) (0) are the first, second, ..., nth state variables observed by the i-th extended state observer at the initial moment.

[0053] like Figure 1 The convex hull and initial value selection relationship of the two-state system in the phase plane are shown as follows: Figure 2 Shown is the convex hull and initial value selection relationship of the three-state system in the phase plane.

[0054] Specific implementation method 6: This implementation method is different from the specific implementation method 5 in that the specific process of step 3 is as follows:

[0055] Step 3. Calculate the weight parameter a corresponding to each extended state observer at time t 1 (t),a 2 (t),...,a n+1 (t), so that the actual state For any t ≥ 0, z (i) (t) represents the vector of all state variables observed by the i-th extended state observer at time t, z (i) (t) = [z 1(i) (t),z 2(i) (t),...,z n(i) (t)] T , z 1(i) (t),z 2(i) (t),...,z n(i) (t) are the first, second, ..., nth state variables observed by the i-th extended state observer at time t, respectively. The superscript T represents the transpose.

[0056] Step 32: According to the weight parameter a 1 (t),a 2(t),...,a n+1 (t) Perform a weighted summation on the state vectors observed by each extended state observer to obtain the state estimation result at time t, that is, the estimation result of the disturbance is obtained.

[0057] Specific implementation method seven: This implementation method is different from specific implementation method six in that the specific process of step three-one is:

[0058] Step 3: Establish the estimated error expression:

[0059]

[0060] According to formula (7), we get:

[0061]

[0062]

[0063]

[0064] Rewrite equation (10) into the form of equation (11):

[0065]

[0066] Since only part of the state can be measured, a feedback signal can be formed, such as the following control system:

[0067]

[0068] Then multiply both sides of equation (11) by the system output matrix C to obtain the estimation equation of the actual measured state of the system:

[0069]

[0070] Among them, y(t) is the actual measurement state at time t;

[0071] Step 3.12: Use the recursive least squares method with forgetting factor to calculate the weight a in equation (13): 1 (t),a 2 (t),...,a n (t) performing fusion estimation;

[0072] Step 3: According to the weight a 1 (t),a 2 (t),...,a n (t) Calculate the weight of the n+1th extended state observer as

[0073] The present invention uses the recursive least squares method with a forgetting factor to estimate the parameters of the multi-extended state observer on the linear motor. The memory length of the recursive least squares method is infinite. Therefore, as the number of recursive steps increases, the accumulated old data will gradually increase, making it difficult for the latest data fed back by the motor sensor to correct the parameter estimation of the observer, resulting in a weakening of the estimation effect and affecting the subsequent parameter estimation effect. The introduction of the forgetting factor can avoid the above situation.

[0074] Specific implementation eight: This implementation is different from specific implementation seven in that the specific process of step three to two is as follows:

[0075] Rearrange formula (13) into formula (14):

[0076] Y(t)=Φ(t) T Θ(t) (14)

[0077] Where: Φ(t) T is the transpose of Φ(t);

[0078]

[0079] Initialize P(t 0 )=γI, I is the identity matrix, γ is a positive constant, and is randomly initialized According to the recursive least squares method with forgetting factor, the recursive formula of formula (16) is obtained:

[0080]

[0081] Among them, t k is the time corresponding to the kth sampling, t k-1 is the time corresponding to the k-1th sampling, P and K are intermediate variables, λ is the forgetting factor, and the selected initial value of the extended state observer is expressed as Φ(t 0 ), Φ(t k )According to Φ(t k-1 ) calculation (usually implemented using the Euler method or the Runge-Kutta method);

[0082] Φ(t k )=[z (n+1) (t k )-z (1) (t k ) (n+1) (t k )-z (2) (t k )...z (n+1) (t k )-z (n) (t k )]T C T ;

[0083] according to Get the weights corresponding to each extended state observer at each sampling time.

[0084] Taking the observer of two variables as an example, the variables in the definition are:

[0085]

[0086] P(t k ) is a second-order reversible matrix, and we define is the matrix P(t k-1 )’s i-th row and j-th column element, K(t k )The two factors of the vector are

[0087] Expand the recursion into discrete form:

[0088]

[0089]

[0090]

[0091] At this time, the expression of recursive least squares method is obtained. i =θ i (i=1,2), a 3 =1-a 1 -a 2 .

[0092] Taking the three-variable observer as an example, the variables in the definition are:

[0093]

[0094] x is the position value fed back by the sensor. Set the initial value P(0) = γI 3 , P(t k ) is a third-order reversible matrix, I 3 is the third-order identity matrix, defined is the matrix P(t k-1 )'s i-th row and j-th column element, the vector K(t k ) are y(t k ) is t k The time is calculated according to formula (21).

[0095]

[0096] Use matrix multiplication to expand the recursion into discrete form:

[0097]

[0098] K(t k )=P(t k )Φ(t k ) (twenty four)

[0099]

[0100] At this time, the expression of the recursive least squares method is obtained.

[0101]

[0102] Specific implementation method 9: This implementation method is different from specific implementation method 8 in that the value of the forgetting factor λ is 0.95≤λ≤1.

[0103] Specific implementation method ten: This implementation method is different from specific implementation method nine in that the specific process of step three-two is as follows:

[0104]

[0105] Where z(t)=[z 1 (t),z 2 (t),...,z n (t)] T , z n (t) is the disturbance fusion estimation result.

[0106] In this implementation, a fusion method of weighted average of multiple extended state observers is used for processing, which can effectively avoid the error peak of the traditional observer for disturbance estimation.

[0107] Embodiment 1

[0108] Combination Figure 3 This embodiment describes a linear motor disturbance estimation algorithm based on multi-extended state observer fusion, which can be used for disturbance observation and control compensation of a linear motor system. If the position and speed of the linear motor can be measured, the linear motor is considered as a second-order system model, and the extended state observer is set to third order, then four observers are required for data fusion.

[0109] Step 1: Establishment of linear motor model

[0110]

[0111] In the formula, x 1 ,x 2are the position and speed of the motor respectively, K and T are the open-loop gain and time constant of the motor respectively, g v is the motor Coulomb friction coefficient, K = 5.2, T = 0.15, g v =1.13, d is the motor model uncertainty and external disturbance.

[0112] Step 2: Design of the third-order linear state observer

[0113] First, define the state observation error as:

[0114]

[0115] In the formula, e i is the observation error, x i is the actual state variable, z i To observe the state variables, an extended state observer is designed using the proposed observer structure.

[0116]

[0117] Secondly, select the initial value according to the following rules:

[0118] Since this is an estimation of three state variables, four extended state observers need to be established. From the perspective of linear space theory, the actual initial state value of the system must be constrained to be in the convex hull formed by the initial state values ​​of these four observers. That is, the initial values ​​of these four state observers form a geometric body (triangular pyramid) in three-dimensional space, as shown in Figure 2 As shown in , the actual initial state of the system needs to be in this geometry. For example, the actual state of the system is The three states of the four state observers are [100 0 0], [-50 -200 0], [0 200 0], and [10 50 1000], which can satisfy the convex combination constraint. The selection of the initial value depends on the actual operating state of the system, that is, it is necessary to know the values ​​of each state of the current system a priori.

[0119] Step 3: Least Squares Parameter Estimation with Forgetting Factor

[0120] After the above steps, the extended state observer is established, and the appropriate initial value is selected, and numerical calculations are performed to obtain the system state observed by each observer. Then, the state observation problem needs to be transformed into a parameter estimation problem, that is,

[0121]

[0122] In the formula, x 1 is the position state of the system, z j(i) is the j-th observation value of the i-th observer.

[0123] Let y = -(x 1 -z 1(4) ), Φ=[z 1(4) -z 1(1) z 1(4) -z 1(2) z 1(4) -z 1(3) ] T , Θ T =[a 1 ,a 2 ,a 3 ], then the estimation problem is equivalent to the following form

[0124] y=Φ T Θ (32)

[0125] According to the recursive least squares method with forgetting factor, the following recursive formula can be obtained:

[0126]

[0127] Among them, k is the number of iterations, λ is the forgetting factor, which is generally 0.95≤λ≤1. After several iterations of the sampling cycle, the parameter a can be estimated. 1 ,a 2 ,a 3 , the weight of the fourth observer is

[0128] Using the estimated parameter a i The states observed by the four extended state observers are weighted averaged to obtain the final observation value:

[0129]

[0130] Control system The estimated value of d is:

[0131]

[0132] Compensated to the controller in the form of control quantity u

[0133]

[0134] Among them, u b For the basic controller.

[0135] In order to verify the estimation effect of the method of the present invention, from the perspective of state observation and disturbance observation of the linear motor platform, a third-order linear extended state observer (bandwidth ω = 200 rad / s, that is, three position gains are α 1 =600,α 2 =120000,α3 =8000000, the two speed gains are β 2 =400,β 3 =40000). Comparing the observation effects of the third-order expanded observation method of the present invention and the traditional third-order expanded state observer, the results are shown as follows: Figure 4 and Figure 5 As shown, Figure 4 The results of speed estimation of the linear motor using the traditional third-order extended state observer and the extended state observer of the invention are shown. Figure 5 is the speed estimation error. The speed estimation result can reflect the estimation of the disturbance to a certain extent. It can be seen that the observer of the method of the present invention not only has a more accurate estimation, but also has a smaller estimation noise. Due to the use of speed estimation negative feedback, the method of the present invention has a greater advantage over the traditional method, which is mainly manifested in lower estimation error peak, smaller overshoot and shorter convergence time.

[0136] Figure 6 to Figure 8 The figure shows the fusion of four third-order linear extended state observers using the method of the present invention (bandwidth ω = 200 rad / s, i.e., three position gains are α 1 =600,α 2 =120000,α 3 =8000000, the two speed negative feedback gains are β 2 =400,β 3 =40000), select P k Matrix initial value parameter γ = 10 5 , the initial value of Θ is selected as Θ = [0.3, 0.3, 0.2, 0.2], the forgetting factor λ = 0.98, and the initial state values ​​of the four observers are selected as: [100 0 -2000], [-100 -1002000], [200 0 2000], [-100 100 2000].

[0137] like Figure 6 , Figure 7 As shown, the multi-ESO fusion estimation method of the present invention significantly reduces the transient peak value of a single ESO and shortens the time for the estimated state to reach a steady state. Figure 8 It is the estimated value of the weight parameters of the four observers generated by the least squares method. The method of the present invention solves the problem of large overshoot caused by large initial error when the extended state observer of the linear motor observes disturbances under the condition of uncertain initial values, and verifies the good practical value of the method of the present invention. In the case of linear motor tracking with speed mutation points (such as triangular wave signals), large overshoot will also occur. The method of the present invention can also be used to specify the initial value of each extended state observer, perform observation value fusion, and achieve better speed observation and disturbance observation effects.

[0138] Embodiment 2

[0139] The difference between this embodiment and the first embodiment is that this embodiment is for the data fusion of three second-order linear extended state observers, the system parameters K = 5.2, T = 0.15, β o2 =600,β o3 =90000,

[0140]

[0141] P k The matrix initial value parameters are γ = 10 2 ,γ=10 5 , select the initial value of Θ as Θ = [0.4, 0.4, 0.2]. The final observation fusion result is as follows Figures 9 to 11 As shown, Fig. 9 is at γ = 10 2 In this case, the fusion result under an arbitrary initial state value is Fig.10 The speed observation error comparison between the fused observer and the three observers is shown. The initial speed values ​​of the three observers and the initial value of the total disturbance are selected according to the rules. The speed error graphs of the extended state observers with three different initial values ​​and the fused observer are compared. The observer of the method of the present invention has a significant improvement in the convergence speed of the speed observation error. Fig.11 The fused observation value representing the total disturbance has a smaller transient peak value of the multi-extended state observer method of the present invention, that is, after the disturbance estimate is compensated into the system, the impulse response generated by the system is smaller than that of a single observer.

[0142] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. Disturbance estimation method of linear motor system based on fusion of multiple extended state observers, It is characterized in that The method specifically comprises the following steps: Step 1: Establish a transfer function model from the control quantity output to the running position of the linear motor, and then write the established transfer function model in the form of a state space equation; The transfer function model is: Where, K is the open-loop gain of the second-order system, T is the mechanical time constant, s is the Laplace differential operator, F(s) is the Laplace transform of the control quantity, and P(s) is the Laplace transform of the position quantity; The state space equation is: Where x is the position of the linear motor, is the first-order derivative of x, v is the speed of the linear motor, is the first-order derivative of v, g v is the motor Coulomb friction coefficient, sgn(·) is the sign function, d is the system model uncertainty and external disturbance, and u is the control input of the system; Step 2: Design an extended state observer based on the n-order state space equation, then establish an observer model including n+1 extended state observers, and select the initial value of the state of the extended state observer according to the selection rule; Step 3: Calculate the weight corresponding to each extended state observer in the observer model by using the recursive least squares method with forgetting factor and the initial value of the extended state observer state, and perform weighted summation on the disturbance estimates of each extended state observer according to the weight to obtain the disturbance estimation result.

2. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 1, It is characterized in that The order of the state space equation is n=3, and the extended state observer designed based on the state space equation is: Among them, z 1 is an estimate of the motor position, For z 1 The first derivative of 2 is an estimate of the motor speed, For z 2 The first derivative of 3 is an estimate of the total motor disturbance, For z 3 The first derivative of 1 , α 2 and α 3 is the position observation error coefficient, β 2 and β 3 is the velocity observation error coefficient; Position estimation error e 1 and the velocity estimation error e 2 They are:

3. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 1, It is characterized in that The order of the state space equation is n=2, and the extended state observer designed based on the state space equation is: Among them, z 1 is an estimate of the motor speed, For z 1 The first derivative of 2 is an estimate of the total motor disturbance, For z 2 The first derivative of o2 and β o3 represents the speed observation error coefficient of the observer; Speed ​​estimation error e 1 for: yes 1 =with 1 (6).

4. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 2 or 3, It is characterized in that The initial value of the state of the extended state observer is selected according to the selection rule; specifically: Select a set of initial weight parameters a 1 (0),a 2 (0),...,a n+1 (0), so that the actual state initial value x(0) of the linear motor system is within the state initial value z of the extended state observer (i) (0) is in the convex hull, that is, z (i) (0) is the initial value of the state of the i-th extended state observer, z (i) (0) = [z 1(i) (0),z 2(i) (0),....,z n(i) (0)] T , z 1(i) (0),z 2(i) (0),....,z n(i) (0) are the first, second, ..., nth state variables observed by the i-th extended state observer at the initial moment.

5. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 4, It is characterized in that The specific process of step three is: Step 3. Calculate the weight parameter a corresponding to each extended state observer at time t 1 (t),a 2 (t),...,a n+1 (t), so that the actual state For any t ≥ 0, z (i) (t) represents the vector of all state variables observed by the i-th extended state observer at time t, z (i) (t) = [z 1(i) (t),z 2(i) (t),...,z n(i) (t)] T , z 1(i) (t),z 2(i) (t),...,z n(i) (t) are the first, second, ..., nth state variables observed by the i-th extended state observer at time t, respectively. The superscript T represents the transpose. Step 32: According to the weight parameter a 1 (t),a 2 (t),...,a n+1 (t) Perform a weighted summation on the state vectors observed by each extended state observer to obtain the state estimation result at time t, that is, the estimation result of the disturbance is obtained.

6. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 5, It is characterized in that The specific process of step three is as follows: Step 3: Establish the estimated error expression: According to formula (7), we get: Rewrite equation (10) into the form of equation (11): Then multiply both sides of equation (11) by the system output matrix C to obtain the estimation equation of the actual measured state of the system: Among them, y(t) is the actual measurement state at time t; Step 3.12: Use the recursive least squares method with forgetting factor to calculate the weight a in equation (13): 1 (t),a 2 (t),...,a n (t) make estimates; Step 3: According to the weight a 1 (t),a 2 (t),...,a n (t) Calculate the weight of the n+1th extended state observer as 7. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 6, It is characterized in that The specific process of step 312 is as follows: Rearrange formula (13) into formula (14): Y(t)=Φ(t) T Θ(t) (14) Where: Φ(t) T is the transpose of Φ(t); Initialize P(t 0 )=γI, I is the identity matrix, γ is a constant, and is randomly initialized According to the recursive least squares method with forgetting factor, the recursive formula of formula (16) is obtained: Among them, t k is the time corresponding to the kth sampling, t k-1 is the time corresponding to the k-1th sampling, P and K are intermediate variables, λ is the forgetting factor, and the selected initial value of the extended state observer is expressed as Φ(t 0 ), Φ(t k ) According to Φ(t k-1 )calculate; Φ(t k )=[z (n+1) (t k )-z (1) (t k )z (n+1) (t k )-z (2) (t k )...z (n+1) (t k )-z (n) (t k )] T C T ; according to Get the weights corresponding to each extended state observer at each sampling time.

8. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 7, It is characterized in that The value of the forgetting factor λ is 0.95≤λ≤1.

9. The linear motor system disturbance estimation method based on multi-extended state observer fusion according to claim 8, It is characterized in that The specific process of step 32 is as follows: Where z(t)=[z 1 (t),z 2 (t),...,z n (t)] T , z n (t) is the disturbance estimation result.

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