A multi-axis system finite time robust cooperative control method based on disturbance compensation

Abstract

The application discloses a kind of multi-axis system finite time robust cooperative control method based on disturbance compensation, including the analysis of multi-axis system cooperative control strategy based on disturbance compensation, obtains trajectory synchronization error, trajectory disturbance compensation error and trajectory concentration error and establishes control target;Then establish the mathematical model of multi-axis system and give the state space model of multi-axis system, in second, trajectory concentration error in state space model is obtained based on disturbance compensation Multi-axis system finite time robust cooperative controller. The controller of each motor uses the input sensor information combined with the multi-axis system finite time robust cooperative controller based on disturbance compensation to calculate and process, obtain the PWM signal required for motor speed control and send to motor driver, realize the finite time robust cooperative control of multi-axis system. The present application uses external disturbance information to compensate for disturbance error, improves the cooperative control precision of multi-axis system while having strong robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multi-axis cooperative control, and particularly relates to a multi-axis system finite time robust cooperative control method based on disturbance compensation. BACKGROUND

[0002] In many industrial applications, such as textile dyeing and finishing machines, continuous rolling mills in steel plants, and industrial robot manufacturing and assembly, the load is usually driven by two or more axes simultaneously. In practical applications, each axis is required to track the desired trajectory and maintain its trajectory unchanged during operation; at the same time, the multi-axis presents a consistent synchronous control or a variable proportion cooperative control. In addition, factors such as system parameter changes and external load disturbances will reduce the synchronization performance of the system, and the synchronization error will affect the quality of the workpiece, and even cause the product to be unusable. Therefore, in the presence of system parameter changes and external load disturbances, for the multi-axis variable proportion robust cooperative control problem in engineering applications, how to design a finite time robust cooperative control method so that the multi-axis variable proportion cooperative control system can obtain good synchronization performance has become a challenge for the increasing demand for fast response and high-precision manufacturing and detection.

[0003] Regarding the cooperative control method, the cooperative control methods applied to multi-axis systems mainly include master-slave control, parallel control, deviation coupling synchronization control, and the like. However, the above methods have many problems, such as in master-slave control, when the slave axis is subjected to complex disturbance, it will not be fed back to the master axis, which is not conducive to the cooperative control of the multi-axis system; in parallel control, when a certain axis is subjected to load disturbance, it will not be fed back to other axes, which is also not conducive to the cooperative stable control of the multi-axis system; and in the deviation coupling synchronization control method, when the number of multi-axes in the system increases, the control system faces the problem of high complexity. In addition, when the multi-axis cooperative control system is subjected to external load disturbance, the above cooperative control methods cannot utilize the external disturbance to compensate for the disturbance error to improve the cooperative control precision. Therefore, in order to improve the cooperative control precision of the multi-axis system, it is of great practical significance to design a multi-axis system finite time cooperative control method based on disturbance compensation. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a multi-axis system finite time robust cooperative control method based on disturbance compensation, so as to solve the problems of poor multi-axis variable proportion cooperative control performance of the existing system and the inability to utilize external disturbance to improve the cooperative control precision, so that each axis in the multi-axis system tracks its desired trajectory while realizing the finite time robust cooperative control based on disturbance compensation.

[0005] In order to solve the above technical problems, the application provides a multi-axis system finite time robust cooperative control method based on disturbance compensation, which comprises the following specific process: the motor comprises a controller, a motor driver and a sensor, the controller of each motor uses the input sensor information to combine the multi-axis system finite time robust cooperative controller based on disturbance compensation to perform calculation and processing, obtains the PWM pulse width modulation signal required for motor speed control and sends the signal to the motor driver, drives and controls the speed of the motor, and realizes the finite time robust cooperative control of the multi-axis servo system.

[0006] As an improvement of the multi-axis system finite time robust cooperative control method based on disturbance compensation of the application:

[0007] The establishment process of the multi-axis system finite time robust cooperative controller based on disturbance compensation is specifically as follows:

[0008] Firstly, the multi-axis system cooperative control strategy based on disturbance compensation is analyzed to obtain the trajectory synchronization error, the trajectory disturbance compensation error and the trajectory concentration error, and the control target of the multi-axis system finite time robust cooperative control based on disturbance compensation is obtained; then, the mathematical model of the multi-axis system is established and the state space model of the multi-axis system after disturbance compensation is given, and then the multi-axis system finite time robust cooperative controller based on disturbance compensation is obtained in combination with the trajectory concentration error in the state space model.

[0009] As a further improvement of the multi-axis system finite time robust cooperative control method based on disturbance compensation of the application:

[0010] The target of the multi-axis system finite time robust cooperative control based on disturbance compensation is to design the multi-axis system finite time robust cooperative controller based on disturbance compensation under the condition that the system has parameter variation and external load disturbance, so as to ensure that the trajectory concentration error ||ξ(t)|| of the multi-axis system converges to 0 within a limited time T, so as to ensure that the trajectory tracking error ||e ref (t)||, the trajectory synchronization error |e i,i+1 (t)| and the trajectory disturbance compensation error ||ρ(t)|| of the multi-axis system all converge to 0 within a limited time T.

[0011] As a further improvement of the multi-axis system finite time robust cooperative control method based on disturbance compensation of the application:

[0012] The specific analysis of the multi-axis system cooperative control strategy based on disturbance compensation is as follows:

[0013] 1) the trajectory tracking error of the multi-axis system is defined as:

[0014] e ref (t)=η d ωref (t) - ω(t) (2)

[0015] wherein e ref (t) = [e ref,1 (t), e ref,2 (t), …, e ref,n (t)] T , η d = diag{η d,1 , η d,2 , …, η d,n}, ω(t) = [ω1(t), ω2(t), …, ω n (t)] T , is the system desired trajectory, ω i (t) is the real trajectory of the i-th axis, and η d,i is the proportional coefficient of the desired trajectory of the i-th axis to the system desired trajectory;

[0016] 2) defining the trajectory synchronization error as:

[0017] e i,i+1 (t) = η d,i+1 ω i (t) / η d,i - ω i+1 (t) (3)

[0018] 3) defining the trajectory disturbance compensation error as:

[0019]

[0020] wherein d j represents the external load disturbance applied to the j-th axis; l j is a constant and ensures that |d j + l j |≠0; d k is the external load disturbance applied to the k-th axis; l k is a constant; and e ref,j (t) is the trajectory tracking error of the j-th axis;

[0021] 4) defining the trajectory centralized error of the multi-axis system as:

[0022] ξ(t) = e ref (t) + αp(t) (6)

[0023] wherein α i is a small positive number, and ξ(t) = [ξ1(t), ξ2(t), …, ξ n (t)] T , α = diag{α1, α2, …, αn},e ref (t) = [e ref,1 (t), e ref,2 (t), …, e ref,n (t)] T and ρ(t) = [ρ 1,∑ (t), ρ 2,∑ (t), …, ρ n,∑ (t)] T .

[0024] As a further improvement of the multi-axis system finite time robust cooperative control method based on disturbance compensation of the application:

[0025] The establishment process of the target of the multi-axis system finite time robust cooperative control based on disturbance compensation is:

[0026] Equation (4) is expanded and written in matrix form:

[0027]

[0028] wherein ρ i,∑ (t) is a trajectory disturbance compensation error; e ref,i (t) is a trajectory tracking error of the i-th axis;

[0029] Equation (7) can be described as:

[0030] wherein,

[0031] then:

[0032]

[0033] wherein, I n is an n-dimensional unit matrix;

[0034] By selecting a proper diagonal matrix α, the inverse matrix of matrix exists, then when ||ξ(t)||→0 in a finite time T, ||e ref (t)||→0, so that ||ρ(t)||→0; since , so when t→T, the trajectory synchronization error can also be guaranteed to converge to 0, i.e. |e i,i+1 (t)|→0.

[0035] As a further improvement of the multi-axis system finite time robust cooperative control method based on disturbance compensation of the application:

[0036] The mathematical model of the multi-axis system is:

[0037] The torque and kinematic equations of the i-axis permanent magnet synchronous motor are:

[0038]

[0039]

[0040] where T e,i (t) is the electromagnetic torque, p i is the number of motor pole pairs, ψ f,i is the rotor flux, i q,i (t) is the q-axis stator current, J i is the rotational inertia, d i (t) is the external load torque, ω i (t) is the mechanical angular velocity of the rotor.

[0041] The mathematical model of the multi-axis system with external load disturbance is:

[0042]

[0043] where, i q (t) = [i q,1 (t), i q,2 (t), …, i q,n (t)] T , a = diag{a1, a2, …, a n},

[0044] The state space model of the multi-axis system after disturbance compensation is:

[0045] The state variables of the multi-axis system are defined as:

[0046]

[0047] where X1(t) = [X 1,1 (t), X 1,2 (t), …, X 1,n (t)] T , X2(t) = [X 2,1 (t), X 2,2 (t), …, X 2,n (t)] T ;

[0048] The state space model of the multi-axis system is:

[0049]

[0050] where V(t) = i q (t).

[0051] As a further improvement to the finite-time robust cooperative control method for multi-axis systems based on disturbance compensation of the present invention:

[0052] The process of obtaining the finite-time robust cooperative controller for the multi-axis system based on disturbance compensation by combining the trajectory set error in the state-space model is as follows:

[0053] Choosing γ(t) to integrate states X1(t) and X2(t) into

[0054] γ(t)=bX1(t)+X2(t) (14)

[0055] Among them, γ(t)=[γ1(t), γ2(t),…,γ n (t)] T b = diag{b1, b2, ..., b n}, b i It is a positive number;

[0056] Differentiating (14), we have

[0057]

[0058] make

[0059]

[0060] Where c = diag{c1,c2,…,c n}, f = diag{f1, f2, ..., f n}, c i and f i It is a positive number;

[0061] Combining equations (15) and (16), we obtain the finite-time robust cooperative controller for the multi-axis system based on disturbance compensation:

[0062]

[0063] The beneficial effects of this invention compared to the prior art are mainly reflected in:

[0064] This invention proposes a finite-time robust cooperative control method for multi-axis systems based on disturbance compensation. This method utilizes external load disturbances experienced by the multi-axis system to compensate for the errors caused by the disturbances, thereby improving the cooperative control accuracy of the multi-axis system. Furthermore, this invention introduces a finite-time robust control algorithm, combining the designed disturbance-compensated multi-axis system cooperative control method with finite-time robust control to handle uncertainties in the multi-axis system. This enables each axis in the multi-axis system to track its desired trajectory within a finite time while simultaneously achieving fast, high-precision, robust cooperative control based on disturbance compensation. Attached Figure Description

[0065] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0066] Figure 1 This is a flowchart illustrating a finite-time robust cooperative control method for multi-axis systems based on disturbance compensation according to the present invention.

[0067] Figure 2 The rotational speed curves of the multi-axis system using parallel cooperative control in the experiment are shown.

[0068] Figure 3 This is a speed curve of a multi-axis system using the control method of this invention in the experiment;

[0069] Figure 4 The graph shows the speed synchronization error of the multi-axis system using parallel cooperative control in the experiment.

[0070] Figure 5 The figure shows the speed synchronization error curve of the multi-axis system using the control method of this invention in the experiment. Detailed Implementation

[0071] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto:

[0072] Example 1: A finite-time robust cooperative control method for multi-axis systems based on disturbance compensation. This method uses external disturbance information to compensate for disturbance errors, improving the cooperative control accuracy of the multi-axis system. Simultaneously, a robust control algorithm is introduced into the multi-axis system, exhibiting strong robustness in handling system parameter changes and external load disturbances during operation. Figure 1 As shown, it includes the following steps:

[0073] Step S101: Analysis of the cooperative control strategy for multi-axis systems based on disturbance compensation, including:

[0074] 1) The trajectory tracking error of the i-th axis in a multi-axis system is defined as follows:

[0075]

[0076] in, For the system's desired trajectory, ω i (t) represents the true trajectory along the i-th axis, η d,i is the ratio coefficient between the expected trajectory on the i-th axis and the expected trajectory of the system.

[0077] Considering the multi-axis system as a whole, equation (1) can be modified as follows:

[0078] e ref (t)=ηd ω ref (t)-ω(t) (2)

[0079] wherein: e ref (t)=[e ref,1 (t),e ref,2 (t),…,e ref,n (t)] T ,η d =diag{η d,1 ,η d,2 ,…,η d,n}, ω(t)=[ω1(t),ω2(t),…,ω n (t)] T .

[0080] 2) The trajectory synchronization error is defined as:

[0081] e i,i+1 (t) = η d,i+1 ω i (t) / η d,i -ω i+1 (t) (3)

[0082] 3) The trajectory disturbance compensation error is defined as:

[0083]

[0084] wherein d j represents the external load disturbance applied to the jth axis; l j is a constant, which can ensure that |d j +l j |≠0; d k represents the external load disturbance applied to the kth axis; l k is a constant; and e ref,j (t) is the trajectory tracking error of the jth axis.

[0085] 4) The trajectory centralized error of the multi-axis system is defined as:

[0086] ξ i (t) = e ref,i (t) + α i ρ i,∑ (t) (5)

[0087] wherein α i is a small positive number.

[0088] Rewrite equation (5) in the following form

[0089] ξ(t) = e ref (t) + αρ(t) (6)

[0090] Among them, ξ(t)=[ξ1(t),ξ2(t),…,ξ n (t)] T e ref (t)=[e ref,1 (t),e ref,2 (t),…,e ref,n (t)] T α = diag{α1, α2, ..., α n} and ρ(t)=[ρ 1,∑ (t),ρ 2,∑ (t),…,ρ n,∑ (t)] T .

[0091] Step S102: Based on the above cooperative control strategy, analyze the objective of finite-time robust cooperative control of a multi-axis system based on disturbance compensation, specifically as follows:

[0092] Expanding equation (4) and writing it in matrix form, we have:

[0093]

[0094] Where, ρ i,∑ (t) represents the trajectory disturbance compensation error; e ref,i (t) represents the trajectory tracking error on the i-th axis.

[0095] Equation (7) can be described as

[0096] in,

[0097] Then we have:

[0098]

[0099] Among them, I n It is an n-dimensional identity matrix.

[0100] By selecting an appropriate diagonal matrix α, the matrix is ​​made... If the inverse matrix exists, then in a finite time T when ||ξ(t)||→0, then ||e ref Since |ρ(t)||→0, we get |ρ(t)||→0. but Therefore, as t→T, the trajectory synchronization error can be guaranteed to converge to 0, i.e., |e i,i+1 (t)|→0.

[0101] According to the above description, the goal of the multi-axis system finite time robust cooperative control based on disturbance compensation is to design a multi-axis system finite time robust cooperative controller based on disturbance compensation to ensure that the trajectory centralized error ||ξ(t)|| of the multi-axis system converges to 0 within a finite time T, so as to ensure that the trajectory tracking error ||e ref (t)||, the trajectory synchronization error |e i,i+1 (t)| and the trajectory disturbance compensation error ||ρ(t)|| of the multi-axis system all converge to 0 within a finite time T.

[0102] Step S103: Establish a mathematical model of the multi-axis system and give a state space model of the multi-axis system after disturbance compensation:

[0103] The torque and kinematics equation of the ith permanent magnet synchronous motor is

[0104]

[0105]

[0106] where T e,i (t) is the electromagnetic torque, p i is the number of motor pole pairs, ψ f,i is the rotor flux, i q,i (t) is the q-axis stator current, J i is the moment of inertia, d i (t) is the external load torque, ω i (t) is the mechanical angular velocity of the rotor.

[0107] The mathematical model of the multi-axis system with external load disturbance is

[0108]

[0109] where, i q (t) = [i q,1 (t), i q,2 (t), …, i q,n (t)] T , a = diag{a1, a2, …, a n},

[0110] The state variable of the multi-axis system is defined as:

[0111]

[0112] where X1(t) = [X 1,1 (t), X 1,2 (t), …, X1,n (t)] T , X2(t) = [X 2,1 (t), X 2,2 (t), …, X 2,n (t)] T .

[0113] The state space model of the multi-axis system can be arranged as

[0114]

[0115] wherein V(t) = i q (t).

[0116] Step S104: Design a finite time robust controller for the multi-axis system in combination with the error in the trajectory set in the state space model:

[0117] Select γ(t) to integrate the states X1(t), X2(t) as

[0118] γ(t) = bX1(t) + X2(t) (14)

[0119] wherein γ(t) = [γ1(t), γ2(t), …, g n (t)] T , b = diag{b1, b2, …, b n}, b i is a normal number.

[0120] Derivation of (14) has

[0121]

[0122] Let

[0123]

[0124] wherein c = diag{c1, c2, …, c n}, f = diag{f1, f2, …, f n}, c i and f i are normal numbers.

[0125] Combine equations (15) and (16), and after arrangement, the finite time robust controller for the multi-axis system based on disturbance compensation is:

[0126]

[0127] Step S105: Analyze the finite time stability of the multi-axis system in combination with the state space model and the robust control:

[0128] 1) The designed Lyapunov candidate function is

[0129]

[0130] Taking the derivative of W(t), we have

[0131]

[0132] 2) According to inequality (19), we have Since W(t) is a continuous positive definite function, and 2||f||>0, it can be concluded that the designed multi-axis system robust cooperative control method based on disturbance compensation can drive the variable g(t) and the trajectory concentration error ξ(t) of the multi-axis system to converge to 0 in a finite time T, i.e. and

[0133] 3) From the stability of the system, we have and That is, when there are parameter variations and external load disturbances in the multi-axis system, the multi-axis system robust cooperative control system based on disturbance compensation can ensure that the trajectory concentration error, the trajectory tracking error, the trajectory synchronization error, and the trajectory disturbance compensation error of the multi-axis system converge to 0 in a finite time T.

[0134] Step S106: Finite-time robust cooperative control based on disturbance compensation in the presence of uncertain terms in the multi-axis system.

[0135] The finite-time robust cooperative control method of the multi-axis system based on disturbance compensation is applied to the variable proportion cooperative control of the multi-motor system. The existing motor collects sensor information and control commands through the control unit (controller) and processes them, and then transmits the control signal to the motor driver, which in turn drives the motor to control the motor speed. The controller, motor driver and sensor used are usually powered after voltage conversion; the controller outputs PWM wave; the sensor mainly includes encoder, Hall voltage and current sensor, etc.; the motor driver outputs three-phase alternating current which can directly drive the rotation of the motor. The motor body, controller, motor driver and sensor components are mature products that can be easily obtained by purchasing, for example, selecting the servo motor body and motor driver of Yaskawa Electric Corporation, the motor driver model is SGDV-7R6A21A, the controller selects the TMS C320F2812 DSP of TI Corporation, the encoder is E40S6-5000, and the Hall current sensor AHBC-LTA series, etc.

[0136] The controller (TMSC320F2812 DSP) uses the input sensor information to combine the disturbance compensation-based multi-axis system finite time robust controller (formula (17)) obtained in step S104 to perform calculation processing, and sends a PWM wave to a motor driver to drive and control the speed of the motor, thereby achieving collaborative control of the multi-motor system.

[0137] Experiment 1:

[0138] A disturbance compensation-based multi-axis system finite time robust collaborative control method described in Example 1 is used to simulate and verify the collaborative control of a multi-axis system composed of four motors. The model parameters of the four motors used in the study are slightly different, which can reflect the parameter changes in the system. The expected speed of the four-motor system is 1000r / min, and the proportional coefficients of the first motor, the second motor, the third motor and the fourth motor to the system expected speed are 1, 0.9, 0.8 and 0.7, respectively. The parameters of the disturbance compensation-based multi-motor system finite time robust collaborative controller are b i = 700, c i = 30, f i = 110, where i = 1, 2, 3, 4. In order to verify the feasibility and effectiveness of the disturbance compensation-based multi-axis system finite time robust collaborative control method of the present application, the parallel collaborative control method of the multi-axis system (《Pan Liang. Research on multi-motor synchronization control method based on fuzzy control[D]. Donghua University, 2016. 》) is used as a benchmark for comparison. The external load disturbance acting on the multi-axis collaborative control system in the simulation is shown in Table 1. The simulation results include the speed curves of the four motors and the speed synchronization error curves. The simulation results are shown in Figures 2 to 5 .

[0139] In addition, in order to illustrate the robustness of the control method of the present application, when 0.1≤t≤0.2s, different external load disturbances are added to the multi-axis system based on the collaborative control method of the present application, and the control performance of the control method of the present application in resisting disturbances is investigated. In order to compare the quantitative performance, the root mean square error of the speed synchronization error of the multi-axis system based on the control method of the present application is given, as shown in Table 2.

[0140] Table 1 External load disturbance acting on the multi-axis collaborative control system

[0141] d (N-m) 1st axis 2nd axis 3rd axis 4th axis 0.1 ≤ t ≤ 0.2 s 0 0 0 10

[0142] Table 2 Root mean square error of speed synchronization error of multi-axis system based on control method of the present application (r / min)

[0143]

[0144] By Figures 2-5The comparison results show that the speed synchronization error of the multi-axis system based on the control method of the present invention is significantly smaller than that of the parallel cooperative control method. Furthermore, the speed synchronization error of the multi-axis system based on the control method of the present invention converges to 0 rapidly within a finite time. This indicates that the multi-axis system constructed by the disturbance-compensated finite-time robust cooperative control method of the present invention has high cooperative control accuracy and fast response speed.

[0145] As can be seen from the comparison results in Table 2, the root mean square error of the speed synchronization error of the multi-axis system controlled by the present invention varies very little under different external load disturbances. This indicates that the multi-axis cooperative control system constructed by the finite-time robust cooperative control method for multi-axis systems based on disturbance compensation described in the present invention has strong robustness in dealing with system parameter changes and external load disturbances.

[0146] Finally, it should be noted that the above examples are merely some specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A finite-time robust cooperative control method for a multi-axis system based on disturbance compensation, wherein the motor includes a controller, a motor driver, and sensors, characterized in that: Each motor's controller uses the input sensor information in conjunction with a disturbance-compensated multi-axis system finite-time robust cooperative controller to perform calculations, obtain the PWM pulse width modulation signal required for motor speed control, and send it to the motor driver to drive and control the motor speed, thereby realizing the finite-time robust cooperative control of the multi-axis servo system. The specific process for establishing the finite-time robust cooperative controller for the multi-axis system based on disturbance compensation is as follows: First, the cooperative control strategy of the multi-axis system based on disturbance compensation is analyzed to obtain the trajectory synchronization error, trajectory disturbance compensation error, and trajectory concentration error, and the control objective of the finite-time robust cooperative control of the multi-axis system based on disturbance compensation is obtained. Then, a mathematical model of the multi-axis system is established and the state-space model of the multi-axis system after disturbance compensation is given. Next, the finite-time robust cooperative controller of the multi-axis system based on disturbance compensation is obtained by combining the trajectory concentration error in the state-space model. The objective of the disturbance-compensated finite-time robust cooperative control for multi-axis systems is to design a disturbance-compensated finite-time robust cooperative controller for multi-axis systems to ensure that the trajectory concentration error ||ξ(t)|| of the multi-axis system converges to 0 within a finite time T, thereby guaranteeing the trajectory tracking error ||e|| of the multi-axis system under the conditions of parameter changes and external load disturbances. ref (t)||、The trajectory synchronization error|e i,i+1 The trajectory disturbance compensation error ||ρ(t)|| converges to 0 within a finite time T; The finite-time robust cooperative controller for multi-axis systems based on disturbance compensation: Where a = diag{a1, a2, ..., a n }, p i ψ is the number of pole pairs of the motor. f,i For rotor flux linkage, J i Let d be the moment of inertia. k External load disturbance applied to the k-th axis; l k α is a constant; α = diag{α1, α2, ..., α n }, α i For small positive constants; b = diag{b1, b2, ..., b n }, b i It is a positive constant; c = diag{c1,c2,…,c n }, f = diag{f1, f2, ..., f n }, c i and f i y is a positive constant; sat() is a saturation function; γ(t) = bX1(t) + X2(t); where X1(t) and X2(t) represent two states of the multi-axis system; Among them, I n Let d be an n-dimensional identity matrix. j L represents the external load disturbance applied to the j-th axis. j It is a constant and guarantees |d j +l j |≠0.

2. The finite-time robust cooperative control method for multi-axis systems based on disturbance compensation according to claim 1, characterized in that: The specific analysis of the multi-axis system cooperative control strategy based on disturbance compensation is as follows: 1) Define the trajectory tracking error of the multi-axis system as: e ref (t)=η d oh ref (t)-ω(t) (2) Among them, e ref (t)=[e ref,1 (t),e ref,2 (t),…,e ref,n (t)] T η d =diag{η d,1 ,η d,2 ,…,η d,n }, ω(t)=[ω1(t),ω2(t),…,ω n (t)] T , For the system's desired trajectory, ω i (t) represents the true trajectory along the i-th axis, η d,i is the ratio coefficient between the expected trajectory on the i-th axis and the expected trajectory of the system; 2) Define the trajectory synchronization error as: e i,i+1 (t)=η d,i+1 oh i (t) / h d,i -oh i+1 (t) (3) 3) Define the trajectory disturbance compensation error as: Among them, e ref,j (t) represents the trajectory tracking error along the j-th axis; 4) Define the trajectory concentration error of the multi-axis system as: ξ(t)=e ref (t)+ar(t) (6) Where, ξ(t)=[ξ1(t),ξ2(t),…,ξ n (t)] T ,e ref (t)=[e ref,1 (t),e ref,2 (t),…,e ref,n (t)] T and ρ(t)=[ρ 1,∑ (t),p 2,∑ (t),…,ρ n,∑ (t)] T 。 3. The finite-time robust cooperative control method for multi-axis systems based on disturbance compensation according to claim 2, characterized in that: The process for establishing the objective of the finite-time robust cooperative control of the multi-axis system based on disturbance compensation is as follows: Expanding equation (4) and writing it in matrix form gives: Where, ρ i,∑ (t) represents the trajectory disturbance compensation error; e ref,i (t) represents the trajectory tracking error along the i-th axis; Equation (7) can be described as: Then we have: By selecting an appropriate diagonal matrix α, the matrix is ​​made... If the inverse matrix exists, then in a finite time T when ||ξ(t)||→0, then ||e ref (t)||→0, thus we get ||ρ(t)||→0; since but Therefore, as t→T, the trajectory synchronization error can be guaranteed to converge to 0, i.e., |e i,i+1 (t)|→0.

4. The finite-time robust cooperative control method for multi-axis systems based on disturbance compensation according to claim 3, characterized in that: The mathematical model of the multi-axis system is as follows: The torque and kinematic equations of the i-th axis permanent magnet synchronous motor are: Among them, T e,i (t) represents the electromagnetic torque, i q,i (t) represents the q-axis stator current, d i (t) represents the external load torque, ω i (t) represents the mechanical angular velocity of the rotor; The mathematical model of a multi-axis system with external load disturbance is as follows: wherein, i q (t) = [i q,1 (t), i q,2 (t), …, i q,n (t)] T , The state-space model of the multi-axis system after disturbance compensation is as follows: Define the state variables of a multi-axis system as follows: where, X1(t) = [X 1,1 (t), X 1,2 (t), …, X 1,n (t)] T , X2(t) = [X 2,1 (t), X 2,2 (t), …, X 2,n (t)] T ; The state-space model of a multi-axis system is as follows: Where V(t)=i q (t).

5. The finite-time robust cooperative control method for multi-axis systems based on disturbance compensation according to claim 4, characterized in that: The process of obtaining the finite-time robust cooperative controller for the multi-axis system based on disturbance compensation by combining the trajectory set error in the state-space model is as follows: Choosing γ(t) to integrate states X1(t) and X2(t) into γ(t)=bX1(t)+X2(t) (14) Where, γ(t)=[γ1(t),γ2(t),…,γ n (t)] T ; Differentiating (14), we have make Combining equations (15) and (16) yields the finite-time robust cooperative controller for multi-axis systems based on disturbance compensation.

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