A multi-motor collaborative control method for composite material three-dimensional braiding machine

Abstract

The present invention discloses a multi-motor collaborative control method for a composite material three-dimensional braiding machine. The method uses time delay estimation technology to estimate the lumped uncertainty of the motor closed-loop control system, so that the entire control algorithm does not depend on the system model. On this basis, a new coupling error design method and a new fractional-order non-singular terminal sliding mode hyperplane design method are proposed, and then a multi-motor collaborative control method for a composite material three-dimensional braiding machine based on time delay estimation is derived. Benefiting from the application of time delay estimation technology, the new coupling error design method and the fractional-order non-singular terminal sliding mode control method, the proposed multi-motor collaborative control method for a composite material three-dimensional braiding machine has excellent comprehensive collaborative control quality and good engineering application prospects, and is suitable for multi-motor collaborative control of large-scale composite material three-dimensional braiding machines.

Description

Technical Field

[0001] The present invention belongs to the research field of kinematics, dynamics and control of composite three-dimensional braided equipment, and in particular, is a collaborative control method for a type of composite three-dimensional braided equipment driven by a large number of motors, mainly aimed at the engineering application needs of high-quality and rapid operation of composite three-dimensional braided equipment. Background Art

[0002] Rotary 3D braiding machines are currently the most advanced equipment for 3D braiding, particularly for large, rotating preforms. Their continuous, high-efficiency design and large build size significantly improve braiding efficiency and quality, while significantly reducing costs. Preforms braided by rotary 3D braiding machines can significantly improve component performance and achieve lightweighting, which is of great significance to fields such as aerospace and rail transportation. Therefore, research on rotary 3D braiding machines has attracted considerable attention from both academia and industry.

[0003] The most important and complex chassis transmission part in the structure of the rotary braiding machine has always been the focus of research. For the chassis closed-loop gear transmission, in order to reduce the influence of tooth clearance on the position accuracy of each axis, multiple motors are used to drive, and at the same time, they can share the system inertia and torque. In order to avoid the phenomenon of overload of each drive motor, it is necessary to coordinate the speed and torque of each motor to ensure the smooth and accurate operation of the system and extend the service life of the motor. Zhuang Peican et al. [Zhuang Peican, Li Qiyang, Xi Xinfu, Sun Yize. Research on mechatronic system modeling and control strategy of radial ring braiding machine [J]. Journal of Engineering Design, 2022, 29(03): 347-357] adopt cross-coupling decoupling control to achieve speed coordination for the braiding ring main motor and the slide motor of the braiding machine. At the same time, [Zhuang Peican. Research on multi-motor coordinated control strategy of radial ring braiding machine [D]. Shanghai: Donghua University, 2022] adopt cross-coupling decoupling control based on torque balancing control strategy for the braiding ring motor group of the braiding machine to achieve torque coordination and improve the load resistance of the motor group. It has been applied to a large radial ring braiding machine. However, the above algorithms are all based on system models, which is not conducive to engineering practice. The high difficulty and poor accuracy of modeling complex actual models limit the improvement of control algorithm performance.

[0004] In order to further improve the control performance of the existing control methods, it is urgent to solve the problem of multi-motor collaborative control of closed-loop gear transmission of three-dimensional braiding machines under strong nonlinearity, complex parameter uncertainty and large unknown external interference, laying a solid foundation for improving braiding efficiency, braiding accuracy and motor service life. Summary of the Invention

[0005] The purpose of the present invention is to address the shortcomings of the existing multi-motor collaborative control method of composite material three-dimensional braiding machine and provide a collaborative control method with better comprehensive control quality and more suitable for practical engineering applications.

[0006] To effectively solve the above problems, the present invention proposes a multi-motor fractional-order non-singular terminal sliding mode collaborative control method for a composite material 3D braiding machine based on time delay estimation technology. The following technical solutions can be adopted:

[0007] A multi-motor coordinated control method for a composite material three-dimensional braiding machine includes the following steps:

[0008] (1) Establish a mathematical model of a single AC permanent magnet synchronous motor in the rotor dq axis system:

[0009]

[0010]

[0011] λ q =L q i q

[0012] λ d =L d i d +L md I df

[0013] ω f =n p ω r

[0014] where u d is the d-axis stator voltage, u q is the q-axis stator voltage; i d is the d-axis stator current, i q is the q-axis stator current; λ d is the d-axis stator flux, λ q is the q-axis stator flux; L d is the d-axis stator inductance, L q is the q-axis stator inductance; ω f is the d and q axis rotor electrical speed, ω r is the mechanical speed of d and q axes; L md is the d-axis mutual inductance, I df is the d-axis equivalent excitation current, n p is the number of pole pairs, Rs is the stator resistance;

[0015] The electromagnetic torque generated by the motor is

[0016] T e =1.5n p [L md I df i q +(L d -Lq )i q i d ]

[0017] The dynamic model of the motor is

[0018]

[0019] Where T l is the load torque of the motor, B m is the coefficient of viscous friction, J is the moment of inertia;

[0020] To simplify the system model, based on magnetic field oriented control, there is The electromagnetic torque of the motor is simplified to

[0021] T e =1.5n p L md I df i q

[0022] Combining the motor dynamics equation with the above formula, we have

[0023]

[0024] (2) The motor dynamics model given in step (1) is transformed into the following form:

[0025] Where H is the system's lumped unknown uncertainty dynamics, is the diagonal parameter matrix to be designed; H is defined as follows

[0026]

[0027] (3) Define velocity tracking error in is the desired speed of n motors, ω r ∈R n×1 is the actual speed of n motors;

[0028] The sum of the design coordination errors is e s =Te; coupling error is e c =e+γe s =(1+γT)e

[0029] Where T is the designed synergy matrix, γ is the diagonal matrix coefficient; the synergy matrix T is defined as

[0030]

[0031] Where n is the number of motors used for cooperative control;

[0032] (4) Based on the coupling error designed in step (3), the following fractional-order non-singular terminal sliding mode hyperplane is designed:

[0033]

[0034] Among them, k1, k2, α1, α2, β1, β2 are the control parameter matrices / vectors to be designed, and 0<α 1i ,α 2i <1,0<β 1i ,β 2i <1,k 1i >0,k 2i >0, i=1~n; is a fractional calculus operator;

[0035] Define the following fast terminal sliding mode reaching law

[0036]

[0037] Where μ1, μ2, γ are the control parameter matrices / vectors to be designed, and all their elements are positive values;

[0038] (5) Based on the fractional-order non-singular terminal sliding mode hyperplane and the fast terminal sliding mode reaching law proposed in step (4), the proposed control algorithm is obtained as follows:

[0039]

[0040]

[0041] in is the estimated value of H;

[0042] (6) Based on step (5), the time delay estimation technique is used to estimate H to obtain

[0043]

[0044] where x (t-L) represents the value of variable x at time (tL), where L is the delay length, which can be selected as 1 or several sampling cycles;

[0045] (7) Combining the results obtained in step (5) and step (6), the proposed multi-motor collaborative control method for composite material three-dimensional braiding machine based on time delay estimation is obtained:

[0046]

[0047] The beneficial effects of the present invention are as follows: benefiting from the adopted time delay estimation technology, the designed collaborative control method does not require a system dynamic model, which greatly improves the engineering usability and practical application value of the collaborative control method; at the same time, the designed fractional-order non-singular terminal sliding mode hyperplane and the applied fast terminal sliding mode convergence law can also ensure that the collaborative control has good control accuracy and good dynamic response quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the structure of a composite material 3D braiding machine;

[0049] Figure 2 This is a three-dimensional diagram of the gear drive mechanism and drive motor in a composite material 3D braiding machine;

[0050] Figure 3 is a schematic diagram of the gear drive mechanism and the drive motor;

[0051] Figure 4 A simulation diagram of the desired velocity trajectory for the specific implementation of the algorithm of the present invention and the conventional linear sliding mode control method based on time delay estimation;

[0052] Figure 5 A simulation diagram comparing trajectory tracking errors of the algorithm described in the present invention and a conventional linear sliding mode control method based on time delay estimation is provided;

[0053] Figure 6 A simulation diagram comparing the trajectory coupling tracking errors of the algorithm described in the present invention and the conventional linear sliding mode control method based on time delay estimation is shown. DETAILED DESCRIPTION

[0054] The present invention is further described below with reference to the accompanying drawings. The following examples are only used to describe the present invention and are not used to limit the scope of use of the present invention. Various equivalent modifications of the present invention made by engineers and technicians in various fields are included in the scope of rights claimed by the present invention.

[0055] like Figures 1 to 3 As shown, the composite material three-dimensional braiding machine used in this embodiment includes a system bracket, a driving gear mechanism, and a driving motor. Among them, four AC permanent magnet synchronous motors are used as driving motors in the three-dimensional braiding machine in this embodiment to rotate the driving gear mechanism. Among them, the gear drive mechanism includes a plurality of gears, which are adjacent to each other and mesh to form a ring-shaped gear. The four driving motors are evenly arranged at intervals of 90° in the circumferential direction. The four gears corresponding to the positions of the four driving motors serve as driving gears. The four driving gears are respectively connected to the output shafts of the four driving motors and rotated by the drive of the driving motors. The four driving motors are driven simultaneously and connected through a gear transmission closed loop to realize the closed-loop drive of the yarn carrier on the circumferential structure.

[0056] This embodiment provides a multi-motor coordinated control method for the above-mentioned composite material 3D braiding machine. The specific implementation steps are as follows:

[0057] by Figure 1 A control method for constructing a composite material three-dimensional braiding machine driven by an AC permanent magnet synchronous motor based on time delay estimation technology includes the following steps:

[0058] First, a new type of AC permanent magnet synchronous motor dynamic equation is established:

[0059] (1) Establish a mathematical model of a single AC permanent magnet synchronous motor (PMSM) in the rotor dq axis system:

[0060]

[0061]

[0062] λ q =L q i q

[0063] λ d =L d i d +L md I df

[0064] ω f =n p ω r

[0065] where u d ,u q is the d,q axis stator voltage; i d ,i q is the d,q axis stator current; d ,λ q is the d,q axis stator flux; L d ,L q is the d,q axis stator inductance; ω f ,ω r d,q axis rotor electrical speed and mechanical speed; L md is the d-axis mutual inductance, I df is the d-axis equivalent excitation current, n p is the number of pole pairs, and Rs is the stator resistance.

[0066] The electromagnetic torque generated by the motor is

[0067] T e =1.5n p [L md Idf i q +(L d -L q )i q i d ]

[0068] The dynamic model of the motor can be written as

[0069]

[0070] Where T l is the load torque of the motor, B m is the coefficient of viscous friction, and J is the moment of inertia.

[0071] To simplify the system model, based on magnetic field oriented control, there is The electromagnetic torque of the motor can be simplified as

[0072] T e =1.5n p L md I df i q

[0073] Combining the motor dynamics equation with the above formula, we have

[0074]

[0075] (2) The motor dynamics model given in step (1) is transformed into the following form:

[0076]

[0077] Where H is the system's lumped unknown uncertainty dynamics, is the diagonal parameter matrix to be designed. The definition of H is as follows

[0078]

[0079] Based on the above new form of PMSM dynamic equation, a multi-motor coordinated control method for composite 3D braiding machine based on time delay estimation is designed, which includes:

[0080] (3) Define velocity tracking error in is the desired speed of n motors, ω r ∈R n×1 is the actual speed of the n motors.

[0081] The design coordination error and coupling error are

[0082] e s =Te

[0083] e c =e+γe s =(1+γT)e

[0084] Where T is the designed synergy matrix and γ is the diagonal matrix coefficient. The synergy matrix T is defined as

[0085]

[0086] Where n is the number of motors used for coordinated control. The designed coordinated error correlates the error of the currently controlled axis with the errors of all other axes, effectively ensuring the quality of coordinated control.

[0087] (4) Based on the coupling error designed in step (3), in order to ensure high-quality multi-motor coordinated control of the composite 3D braiding machine, the following fractional-order non-singular terminal sliding mode hyperplane is designed:

[0088]

[0089] Among them, k1, k2, α1, α2, β1, β2 are the control parameter matrices / vectors to be designed, and 0<α 1i ,α 2i <1,0<β 1i ,β 2i <1,k 1i >0,k 2i >0, i=1~n. is a fractional calculus operator.

[0090] Define the following fast terminal sliding mode reaching law

[0091]

[0092] Where μ1, μ2, c are the control parameter matrices / vectors to be designed, and each element is a positive value.

[0093] (5) Based on the fractional-order non-singular terminal sliding mode hyperplane and the fast terminal sliding mode reaching law proposed in step (4), the proposed control algorithm is obtained as follows:

[0094]

[0095]

[0096] in is the estimated value of H. Since H is very complex and time-varying, the use of conventional technologies such as online identification and adaptive technology is not conducive to practical engineering applications.

[0097] (6) Based on step (5), the time delay estimation technique is used to estimate H to obtain

[0098]

[0099] where x (t-L) Represents the value of the variable x at time (tL), where L is the delay length, which is generally selected as 1 or several sampling cycles.

[0100] (7) Combining the results obtained in step (5) and step (6), the proposed multi-motor collaborative control method for composite material three-dimensional braiding machine based on time delay estimation is obtained:

[0101]

[0102]

[0103] It can be seen from the above-mentioned multi-motor collaborative control method of the composite material three-dimensional braiding machine that it is not based on the system dynamics model and is applied to engineering applications under complex working conditions.

[0104] Conduct stability analysis on the invented collaborative control method

[0105] (1) Take the Lyapunov function as V = 0.5s T s, take its derivative and substitute it into the cooperative controller to get

[0106]

[0107] in It is defined as the delay estimation error; from the delay estimation theory, we know that ε is bounded.

[0108] The above formula can be rewritten into the following two forms, namely

[0109]

[0110]

[0111] in

[0112] For the first form, using the inequality (b1 2 +…+b n 2 ) a ≤(b1 a +…+b n a ) 2 ,0<a<2,b i >0, and V=s T Substituting s / 2 into the first form, we have

[0113]

[0114] in λ min (μ2) is The minimum eigenvalue of μ2. Then the stable time of s is

[0115]

[0116] Therefore, for the first form, when λ min When (μ2)>0, the system trajectory will continue to tend towards the fractional-order non-singular terminal sliding mode hyperplane until Similarly, analyzing the second form, we can get Eventually, the system trajectory will converge to the following sphere in a finite time

[0117] ||s||≤Δ=min{Δ1,Δ2},

[0118]

[0119] (2) Prove the coupling error e c The boundedness of .

[0120] The designed fractional-order non-singular terminal sliding mode hyperplane can be rewritten as follows

[0121]

[0122] Using the analytical ideas and steps in (1), the above formula can be rewritten into the following two forms:

[0123]

[0124]

[0125] For the first form, when When it is established, it will continue to maintain the form of fractional order non-singular terminal sliding mode hyperplane, then the system trajectory will continue to tend to the equilibrium point to Then, using fractional calculus theory, we know that the system coupling error will converge to where K i and σ i is a coefficient determined by the characteristics of the calculus operator. Therefore, the coupling error e c The boundedness of has been proved.

[0126] (3) Prove the boundedness of the system tracking error e.

[0127] Rewriting the definition of system coupling error, we get Where I is the unit diagonal matrix. Then we can see Therefore, the boundedness of the system tracking error e is proved.

[0128] To verify the effectiveness of the invented collaborative control method for composite 3D braiding machines, a comparative simulation study was conducted between it and a conventional linear sliding mode controller based on time delay estimation technology. The simulation platform was Matlab 2016b under the Windows 10 64-bit operating system. The simulation object was the collaborative control of four AC permanent magnet synchronous motors. The dynamic model can be written as

[0129]

[0130] The dynamic parameters of the four motors are J=0.005, B m =0.002,n p =4,L md =0.17,I df =5.4,T l and d are the load torque and lumped external disturbance of the motor respectively, and their values are T l =A t *sin(2π / T t ),A t =[2,4,6,8] T ×10 -4 Nm,T t =[1,2,3,4]s; d = A d *sin(2π / T d ),A d =[1,2,3,4] T ×10 -4 Nm,T t =[0.5,1,1.5,2]s. The control parameters are selected as follows: k1=k2=γ=I,α1=α2=β1=β2=c=0.8*[1,1,1,1] T ,μ1=μ2=2I,ω r The initial value is set to 0, the delay L = 1ms, the simulation step size is set to 1ms, and the ode4 (Runge-Kutta) solver is used. In order to obtain the conventional linear sliding mode controller based on the delay estimation technology and ensure the fairness of the comparative simulation, α1 = α2 = β1 = β2 = c = [1, 1, 1, 1] T , other control parameters remain unchanged. The corresponding simulation comparison results are shown in Figures 4-6 , the simulation results Figure 4 is the desired velocity trajectory, Figure 5-Figure 6 They are the tracking errors and coupling errors of the four motors respectively, where the solid line represents the control method proposed in this invention, and the dotted line represents the conventional linear sliding mode.

[0131] It can be seen from the simulation results that the algorithm of the present invention can ensure faster convergence characteristics, higher control accuracy and better coordinated control effect under the same parameter conditions.

Claims

1. A multi-motor coordinated control method for a composite material three-dimensional braiding machine, characterized in that: The steps include: (1) Construct the motor dynamics model, including: (1.1) Establish the mathematical model of a single AC permanent magnet synchronous motor in the rotor dq axis system: λ d =L d and d +L md AND df oh f =n p oh r where u d is the d-axis stator voltage, u q is the q-axis stator voltage; i d is the d-axis stator current, i q is the q-axis stator current; λ d is the d-axis stator flux, λ q is the q-axis stator flux; L d is the d-axis stator inductance, L q is the q-axis stator inductance; ω f is the d and q axis rotor electrical speed, ω r is the mechanical speed of d and q axes; L md is the d-axis mutual inductance, I df is the d-axis equivalent excitation current, n p is the number of pole pairs, Rs is the stator resistance; (1.2) The electromagnetic torque generated by the motor is T e =1.5n p [THE md THE df the q +(L d -THE q )the q the d ] The dynamic model of the motor is Where T l is the load torque of the motor, B m is the coefficient of viscous friction, J is the moment of inertia; To simplify the system model, based on magnetic field oriented control, there is The electromagnetic torque of the motor is simplified to T e =1.5n p L md I df i q Combining the motor dynamics equation with the above formula gives the motor dynamics model (2) The motor dynamics model given in step (1) is transformed into the following form: Where H is the system's lumped unknown uncertainty dynamics, is the diagonal parameter matrix to be designed; H is defined as follows (3) Define velocity tracking error in is the desired speed of n motors, ω r ∈R n×1 is the actual speed of n motors; The sum of the design coordination errors is e s =Te; coupling error is e c =e+γe s =(1+γT)e Where T is the designed synergy matrix and γ is the diagonal matrix coefficient; (4) Based on the coupling error designed in step (3), the following fractional-order non-singular terminal sliding mode hyperplane is designed: Among them, k1, k2, α1, α2, β1, β2 are the control parameter matrices / vectors to be designed, and 0<α 1i ,α 2i <1,0<β 1i ,β 2i <1,k 1i >0,k 2i >0, i=1~n; is a fractional calculus operator; Define the following fast terminal sliding mode reaching law Where μ1, μ2, γ are the control parameter matrices / vectors to be designed, and all their elements are positive values; (5) Based on the fractional-order non-singular terminal sliding mode hyperplane and the fast terminal sliding mode reaching law proposed in step (4), the proposed control algorithm is obtained as follows: in is the estimated value of H; (6) Based on step (5), the time delay estimation technique is used to estimate H to obtain where x (t-L) represents the value of variable x at time (tL), where L is the delay length, which can be selected as 1 or several sampling cycles; (7) Combining the results obtained in step (5) and step (6), the proposed multi-motor collaborative control method for composite material three-dimensional braiding machine based on time delay estimation is obtained:

2. The collaborative control method according to claim 1, wherein: In step (3), the coordination matrix T is defined as Where n is the number of motors used for cooperative control.

3. The collaborative control method according to claim 1 or 2, characterized in that: In a three-dimensional braiding machine controlled by this collaborative control method, n AC permanent magnet synchronous motors are used as drive motors to drive a gear mechanism to rotate. The gear drive mechanism includes a plurality of gears that mesh with each other to form a ring-shaped gear. The n drive motors are evenly spaced in the circumferential direction. The gears corresponding to the positions of the n drive motors serve as driving gears. The driving gears are respectively connected to the output shafts of the n drive motors and are driven to rotate by the drive motors. The n drive motors are driven simultaneously.

4. The collaborative control method according to claim 3, wherein: Four AC permanent magnet synchronous motors are used as drive motors to rotate the drive gear mechanism, and the four drive motors are evenly arranged at 90° intervals in the circumferential direction.

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