CN116088312A - Multi-axis cooperative control method for dual-drive gantry platform of chip mounter - Google Patents

Abstract

The invention discloses a multi-axis cooperative control method for a double-drive gantry platform of a placement machine, and relates to the technical field of motion control of the gantry platform of a placement machine. The present invention is to solve the problem that in the existing dual-drive gantry platform control system of the placement machine, due to the inability to ensure the consistency of the motor, the coupling dynamic relationship between the synchronous movement of the mechanical beam and the positioning movement of the load, and external interference will cause errors in the control of the system, It leads to problems with high risk of system uncertainty and difficult control. The multi-axis cooperative control method of the dual-drive gantry platform of the placement machine according to the present invention, respectively designs the expected model compensation controller, the robust feedback controller and the neural network controller, and uses the sum of the designed controller outputs as the placement The general control signal of the gantry platform of the placement machine is used to perform multi-axis coordinated control of the X-axis, Y1-axis and Y2-axis of the gantry platform of the placement machine.

Description

Multi-axis collaborative control method for dual-drive gantry platform of placement machine

Technical Field

The invention belongs to the technical field of motion control of a gantry platform of a placement machine, and in particular relates to multi-axis coordinated control.

Background Art

The dual-drive gantry platform is a typical drive structure in the placement machine. The dual-drive gantry platform has the characteristics of large thrust, strong load, and high precision. It has received more and more attention and application in the field of modern industrial high-end manufacturing. In the gantry platform system of the placement machine, the mechanical beam spans across the two ends of the platform and is driven by two linear motors to realize the Y-axis feeding movement. The mobile worktable is driven by another motor to perform positioning movement along the X-axis direction where the beam is located. The complex production tasks are completed through close cooperation and coordinated movement between the two axes. It should be noted that compared with the single-drive linear motion control of the worktable, the XY multi-axis coordinated motion control is more complex and important, and its control accuracy directly affects the motion performance and processing technology of the gantry platform system of the placement machine. Therefore, it is of great practical significance to study the multi-axis coordinated control problem of the dual-drive gantry platform of the placement machine.

In the entire control system, multiple linear motor drive modes can enable the system to obtain greater thrust and speed, but at the same time it also increases the uncertainty risk and control difficulty of the system. This is mainly due to two factors. First, it is difficult to ensure that the three linear motors have exactly the same mechanical parameters and electromechanical characteristics under realistic conditions; second, the synchronous motion of the mechanical beam and the load positioning motion affect each other and have a complex coupling dynamic relationship. In addition, there will inevitably be problems of parameter uncertainty and external unknown nonlinear disturbances in the SMT gantry platform system, such as load changes, thrust fluctuations, measurement noise, etc., which can easily cause large motion errors and system oscillations. In severe cases, it may even cause damage to mechanical equipment and threaten the life safety of operators.

Summary of the invention

The present invention aims to solve the problems in the existing control system of the dual-drive gantry platform of a placement machine, in which the motor consistency cannot be guaranteed, the synchronous movement of the mechanical crossbeam and the load positioning movement have a coupled dynamic relationship, and external interference will cause errors in the control of the system, resulting in high system uncertainty risk and great control difficulty. A multi-axis collaborative control method for the dual-drive gantry platform of a placement machine is now provided.

The multi-axis cooperative control method of the dual-drive gantry platform of the placement machine is designed. The expected model compensation controller, the robust feedback controller and the neural network controller are designed respectively, and the sum of the designed controller outputs is used as the total control signal of the gantry platform of the placement machine. The total control signal is used to perform multi-axis cooperative control on the X-axis, Y1-axis and Y2-axis of the gantry platform of the placement machine.

The desired model compensation controller expression is:

为

的估计值，

为贴片机龙门平台系统耦合动力学模型中不确定参数构成的系数矩阵，Among them, υ _a is the output of the expected model compensation controller, Φ _d is the regression matrix containing the expected information,

for

The estimated value of

is the coefficient matrix of uncertain parameters in the coupled dynamics model of the SMT gantry platform system.

和

分别为归一化后贴片机龙门平台X轴和Y轴动力学中非线性扰动的常值，

为归一化后贴片机龙门平台旋转动力学中非线性扰动的常值；Among them, M _hk is the mass of the moving workbench in the SMT machine after normalization, B _xk is the viscous friction coefficient at the X-axis of the SMT gantry platform after normalization, A _xk is the Coulomb friction coefficient at the X-axis of the SMT gantry platform after normalization, _Myk is the total mass of the beam in the SMT gantry platform after normalization, _Byk is the sum of the viscous friction coefficients at the Y1-axis and Y2-axis guide rails of the SMT gantry platform after normalization, A _yk is the sum of the Coulomb friction coefficients at the Y1-axis and Y2-axis guide rails of the SMT gantry platform after normalization, J _k is the normalized moment of inertia, K _αk is the normalized equivalent rotational stiffness, B _sk is the difference in viscous friction coefficients at the Y2-axis and Y1-axis guide rails of the SMT gantry platform after normalization, A _sk is the difference in Coulomb friction coefficients at the Y2-axis and Y1-axis guide rails of the SMT gantry platform after normalization,

and

are the normalized constants of the nonlinear disturbances in the X-axis and Y-axis dynamics of the SMT gantry platform,

is the normalized constant value of the nonlinear disturbance in the rotational dynamics of the gantry platform of the placement machine;

The robust feedback controller expression is:

υ _e =-M _q Z ^-1 GK _d sK _e ε,

Where, υ _e is the output of the robust feedback controller, M _q is the normalized inertia matrix of the gantry platform of the placement machine, s is the sliding mode variable, Z = diag [z ₁ , z ₂ , z ₃ ],

_Si is the error transfer function and has:

为超调量调节系数，ε＝[ε ₁ ,ε ₂ ,ε ₃ ] is the unconstrained conversion error, the intermediate variable _ri ＝ _ei (t)/ _ρi (t), _ei (t) is the error vector at time t, _ei (0) is the initial value of the error vector,

is the overshoot adjustment coefficient,

ρ _i is the performance function and is expressed as follows:

为误差收敛速率，ρ _i0 is the initial value of the steady-state error, ρ _i∞ is the maximum value of the steady-state error,

is the error convergence rate,

λ为控制增益矩阵，K_d为比例反馈矩阵，K_e为鲁棒增益矩阵；

λ is the control gain matrix, _Kd is the proportional feedback matrix, and _Ke is the robust gain matrix;

The neural network controller expression is:

为神经网络权重矢量，χ为神经网络输入矢量，χ＝[χ₁,χ₂,...,χ_m]，

m为神经网络的神经元总层数，j＝1,2,...,m，R(χ)为神经网络多层神经元的总输出，η为鲁棒项系数，sign(·)表示符号函数；Among them, υ _nn is the output of the neural network controller,

is the neural network weight vector, χ is the neural network input vector, χ＝[χ ₁ ,χ ₂ ,...,χ _m ],

m is the total number of neuron layers in the neural network, j = 1, 2, ..., m, R(χ) is the total output of the multi-layer neurons in the neural network, η is the robust term coefficient, and sign(·) represents the sign function;

The total control signal v of the gantry platform of the placement machine is [v ₁ ,v ₂ ,v ₃ ]:

v＝υ _a +υ _e +υ _nn .

Furthermore, the total control signal of the SMT gantry platform is used to realize the coordinated control of the X-axis, Y1-axis and Y2-axis of the SMT gantry platform according to the following formula:

Among them, _Sm is the distance between the motors on both sides of the crossbeam of the gantry platform of the placement machine, α is the actual rotation angle of the crossbeam of the gantry platform of the placement machine, _Kxk is the normalized thrust constant of the X-axis motor, _Kmy = _K2 / _K1 , _K1 and _K2 are the thrust constants of the Y1-axis and Y2-axis motors of the gantry platform of the placement machine respectively, and _ux , _u1 and _u2 are the control inputs of the X-axis, Y1-axis and Y2-axis respectively.

Furthermore, the coupled dynamics model of the above-mentioned SMT machine gantry platform system is:

和

分别为贴片机龙门平台系统轴运动的速度和加速度矢量矩阵，非线性函数

和

分别为归一化后非线性扰动的常值矩阵和时变矩阵。Among them, _Cq , _Bq , _Kq and _Aq are the normalized Coriolis force matrix, viscous friction matrix, equivalent stiffness matrix and Coulomb friction matrix respectively, q is the state vector matrix of the SMT gantry platform system and q＝[x(t),y(t),α(t)], x(t) and y(t) are the actual displacements of the X-axis and Y-axis of the SMT gantry platform at time t respectively, α(t) is the actual rotation angle of the beam of the SMT gantry platform system at time t,

and

They are the velocity and acceleration vector matrices of the axis motion of the SMT gantry platform system, and the nonlinear function

and

are the constant matrix and time-varying matrix of the normalized nonlinear perturbation respectively.

Furthermore, the constraint condition of the error vector e _i (t) of the gantry platform system of the above-mentioned placement machine is:

Among them, e _i (t) = qq _d = [x (t)-x _d (t), y (t) - y _d (t), α (t)],

_qd =[ _xd (t), _yd (t), _αd (t)] is the expected trajectory signal matrix of the gantry system of the placement machine, _xd (t) and _yd (t) are the expected displacements of the X-axis and Y-axis of the gantry at time t, respectively, _αd (t) is the expected rotation angle of the crossbeam of the gantry and _αd (t)=0.

Furthermore, the above

Among them, h is the offset distance of the center of mass of the mobile worktable in the placement machine, x(t) is the actual displacement of the X-axis of the beam of the gantry platform system of the placement machine, and _Sg is the distance between the Y1-axis and Y2-axis guide rails of the gantry platform of the placement machine.

包括残差矩阵部分和含有期望信息部分，表达式如下：Furthermore, the regression quantity of the SMT gantry system

Including the residual matrix part and the part containing expected information, the expression is as follows:

为仅含有期望信息的回归量矩阵，

为回归量残差矩阵。in,

is the regressor matrix containing only the expected information,

is the residual matrix of the regressors.

Furthermore, the expression of the sliding mode variable s is:

in,

Furthermore, the output R(χ _j ) of the j-th layer neuron in the above neural network is:

Among them, _cj and _bj are the central coordinate vector and width of the neural network kernel function respectively.

的自适应率

为：Furthermore, the above neural network weight vector

Adaptive rate

for:

Where φ is the learning rate update matrix.

Beneficial effects of the present invention:

The present invention proposes a precise multi-axis collaborative control method suitable for the gantry platform of a placement machine, which solves the problems of poor anti-interference ability and inability to pre-set control performance in a complex production environment. The multi-axis collaborative control method of the dual-drive gantry platform of the placement machine described in the present invention is implemented based on the preset performance technology and the adaptive neural network control method. Among them, the preset performance function is designed in advance to plan the expected performance of the system, and the constraint problem is simplified using the error transformation technology; the parameter estimation algorithm in the adaptive link can achieve rapid convergence of the system parameters, and then the model is accurately compensated by the designed adaptive law; the robust feedback module is a controller designed based on the actual error signal, which is mainly used to stabilize the nominal system; the neural network compensator is used to approximate the interference in the unmodeled dynamics and the external environment, and further improve the stability of the system. Finally, a comparative experiment was carried out on the gantry motion test bench to verify the effectiveness and superiority of the proposed synchronous control method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a multi-axis collaborative control method for a gantry platform of a placement machine with preset performance guarantee according to the present invention;

FIG2 is a schematic diagram of the movement of the gantry platform of the chip placement machine according to the present invention;

FIG3 is a graph showing a motion position change curve when the XY axis follows a desired trajectory in an embodiment;

FIG4 is a graph showing a tracking error variation when the X-axis follows a desired trajectory in an embodiment;

FIG5 is a graph showing a tracking error variation when the Y-axis follows a desired trajectory in an embodiment;

FIG. 6 is a curve diagram showing the rotation angle variation when the Y-axis follows the desired trajectory in the embodiment.

DETAILED DESCRIPTION

The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

Most of the existing research on gantry control focuses on single-axis positioning and dual-drive synchronous tracking, and the control algorithm lacks flexibility and foresight in further improving the dynamic response and steady-state accuracy of the system. Existing research has deficiencies in improving the dynamic response and steady-state accuracy of the system, and poor control effects. This embodiment provides a precise multi-axis collaborative control method with preset performance guarantees, which can effectively handle various uncertainties and unknown interferences in the gantry system of the placement machine, while improving the transient performance and steady-state performance of each axis, ensuring the smooth and safe operation of the system. Refer to Figures 1 and 2 to explain this embodiment in detail.

Step 1: Establish a coupled dynamics model based on the geometric relationship and force analysis of the placement machine gantry platform.

各参数坐标的定义为：As shown in Figure 2, the generalized coordinate system OXY and the rotation coordinate system are defined.

The definition of each parameter coordinate is:

Define the generalized position coordinates of the center of mass G _y of the beam itself as (0, y), and the rotational position coordinates of the center of mass G _x of the mobile platform (including the load) as (x, -h). Based on the above coordinates, further define the center of mass position of the entire beam (including the mobile workbench) as G, the grating feedback coordinates of the beam on the Y1 axis side as (x ₁ , y ₁ ), and the grating feedback coordinates of the beam on the Y2 axis side as (x ₂ , y ₂ ). The distance between the left and right motors of the beam is S _m , the distance between the left and right guide rails is S _g , and the distance between the left and right gratings is _Se ; the distance from the center of mass of the entire beam to the Y1 motor is S _m1 , the distance to the Y1 guide rail is S _g1 , and the distance to the Y1 grating is _Se1 ; the distance from the center of mass of the entire beam to the Y2 motor is S _m2 , the distance to the Y2 guide rail is S _g2 , and the distance to the Y2 grating is _Se2 .

When the SMT gantry platform is working normally, it is expected that the beam is perpendicular to the left and right guide rails, that is, there is no angle between the beam and the X-axis. However, the high-speed movement of the actual working mobile platform has a certain impact on the beam shape. Once the two ends of the beam are not synchronized, they will rotate to form an angle, which is easy to cause the system to oscillate and become unstable under the constraint of large internal forces. Therefore, in order to fully consider the factors of load and beam, this implementation adds the analysis of the internal cause of beam rotation and the coupling between axes.

The actual rotation angle of the beam of the gantry platform of the placement machine is α. Considering the actual situation that α≈0, we have:

Define the state vector matrix q = [x(t), y(t), α(t)] of the entire SMT gantry system. x(t) and y(t) are the actual displacements of the X-axis and Y-axis of the SMT gantry platform at time t, respectively. α(t) is the actual rotation angle of the beam of the SMT gantry platform system at time t, which can be obtained by the feedback of the grating encoders on the Y1 and Y2 axes. Considering the kinematic relationship between the X, Y1 and Y2 axes, and combining the Lagrange equation, the dynamic modeling is as follows:

和

分别为贴片机龙门平台系统轴运动的速度和加速度矢量矩阵，

为非线性函数通常由

来替代。v＝T_qu_r表示所设计的控制输入矩阵，r＝x,1,2，u_x、u₁、u₂作为三个电机输入电压是本实施方式最终要调制输出的参数。

和

分别为归一化后非线性扰动的常值矩阵和时变矩阵，且

in,

and

They are the velocity and acceleration vector matrices of the axis motion of the SMT gantry platform system,

As a nonlinear function, it is usually

v = T _q u _r represents the designed control input matrix, r = x, 1, 2, u _x , u ₁ , u ₂ as the three motor input voltages are the parameters to be modulated and output in the present embodiment.

and

are the constant matrix and time-varying matrix of the normalized nonlinear perturbation, respectively, and

The normalized inertia matrix M _q , Coriolis force matrix C _q , viscous friction matrix B _q , Coulomb friction matrix A _q , equivalent stiffness matrix K _q and thrust coefficient matrix T _q are:

The normalized processing formula for defining the parameter "F" is expressed as F _k =F/k ₁ , where M _hk is the mass of the moving workbench in the SMT machine after normalization, B _xk is the viscous friction coefficient at the X-axis of the SMT machine gantry platform after normalization, A _xk is the Coulomb friction coefficient at the X-axis of the SMT machine gantry platform after normalization, _Myk is the total mass of the beam in the SMT machine gantry platform after normalization, Byk is the sum of the viscous friction coefficients at the Y1-axis and Y2-axis guide rails of the SMT machine gantry platform after normalization, A _yk is the sum of the Coulomb friction coefficients at the Y1-axis and Y2-axis guide rails of the SMT machine gantry platform after normalization, J _k is the normalized moment of inertia, K _αk is the normalized equivalent rotational stiffness, B _sk is the difference in the viscous friction coefficients _at the Y2-axis and Y1-axis guide rails of the SMT machine gantry platform after normalization, and A _sk is the normalized difference in Coulomb friction coefficient between the Y2-axis and Y1-axis guide rails of the SMT gantry platform.

K _my =K ₂ /K ₁ ,

_K1 and _K2 represent the thrust constants of the motors on the Y1 and Y2 axes, respectively. _Kx represents the thrust constant of the motor on the X axis, which can be obtained by looking up the manual. In addition, _By = _B1 + _B2 , _Bs = _B2 - _B1 , _Ay = _A1 + _A2 , _As = _A2 - _A1 , Bθ and _Aθ , _θ = 1, 2, represent the viscous friction coefficient and Coulomb friction coefficient at the Y1 and Y2 axis guide rails, respectively. x is the position feedback of the mobile platform, obtained by the X-axis grating encoder. h represents the displacement distance of the center of mass of the mobile platform.

Step 2: Design the performance function based on expectations and perform error transformation on complex constraints.

Set the expected trajectory signal matrix _qd to:

q _d =[x _d (t), y _d (t), α _d (t)],

Wherein, the desired beam rotation angle α _d (t)=0.

Define the systematic error as:

e _i (t) = qq _d = [x (t)-x _d (t), y (t) - y _d (t), α (t)],

Where x(t) and y(t) are the actual displacements of the X-axis and Y-axis of the SMT gantry platform at time t, respectively, and α(t) is the actual rotation angle of the beam of the SMT gantry platform system at time t. These parameters are calculated after grating feedback.

Introduce preset performance functions:

为误差收敛速率，均是待设计的常值。Among them, ρ _i0 is the initial value of the steady-state error, ρ _i∞ is the maximum value of the steady-state error,

is the error convergence rate, all of which are constants to be designed.

Set the system error to satisfy the constraints:

为超调量调节系数并决定着系统的超调量包络。Where e _i (0) is the initial value of the error vector,

It is the overshoot adjustment coefficient and determines the overshoot envelope of the system.

Introducing the error transfer function simplifies the controller design:

Preferably, the hyperbolic tangent function is the error conversion function S _i , and its inverse function is obtained as follows:

In the formula, r _i =e _i (t)/ρ _i (t).

Differentiating the above formula gives:

in,

At this time, the constrained system error e _i (t) is transformed into an unconstrained conversion error ε _i (t) for the subsequent controller design needs.

Step 3: Design an adaptive controller for the dynamic model based on the given expected signal.

为：The coefficient matrix formed by parameterizing the uncertainty vector in the system dynamics model in step 1 is

for:

For real physical systems, the parameter vector and lumped uncertainty satisfy the following bounds:

和

分别为

的上下边界，D为集总不确定性的上界，令

为参数自适应估计值，

为参数估计误差，则：In the formula,

and

They are

The upper and lower boundaries of , D is the upper bound of the lumped uncertainty, let

is the adaptive estimate of the parameter,

is the parameter estimation error, then:

Optimally design bounded discontinuous projection adaptive law:

为常见的标准投影自适应率。

是参数

的估计值，

为设计的自适应率上界，

为

的一阶导数。Among them, Γ is the adaptive learning rate matrix to be designed, τ is the adaptive function,

is the common standard projection adaptation rate.

is a parameter

The estimated value of

is the upper bound of the designed adaptation rate,

for

The first derivative of .

Design parameter estimation algorithm with forgetting factor and covariance reset as:

是滤波后的线性回归矩阵，

表示估计误差；μ代表归一化因子且δ为遗忘因子；

是设计的自适应更新率上界，tr(·)则表示求迹运算。in,

is the filtered linear regression matrix,

represents the estimation error; μ represents the normalization factor and δ is the forgetting factor;

is the upper bound of the designed adaptive update rate, and tr(·) represents the trace operation.

The regression matrix of the placement machine gantry platform system is defined as:

为回归量残差矩阵，

和

分别为期望速度和期望加速度；in,

is the residual matrix of the regression variables,

and

are the expected speed and expected acceleration respectively;

是仅含期望信息的回归量矩阵。

is the regressor matrix containing only the expected information.

Design the desired model compensation controller as:

Realize compensation of dynamic model parameters.

This step is to perform online estimation of the 13 parameters of the system dynamics model in step 1 to achieve compensation for the model.

Step 4: Design a robust feedback controller based on the acquired position/speed information;

Define the sliding mode function:

Wherein, λ=diag[λ ₁ ,λ ₂ ,λ ₃ ] is the control gain matrix, λ _i is a positive constant; the conversion error ε of the system decreases as the quasi-sliding mode variable s decreases.

Define the semi-positive definite energy function:

Wherein, Z = diag[z ₁ ,z ₂ ,z ₃ ], Ke _is the robust gain matrix.

The robust feedback controller υ _e is:

υ _e =-M _q Z ^-1 GK _d sK _e ε,

K_d为比例反馈矩阵，K_e为鲁棒增益矩阵，且同时满足：in,

_Kd is the proportional feedback matrix, _Ke is the robust gain matrix, and they both satisfy:

Among them, σ _min (·) and σ _max (·) are operations for finding the minimum and maximum eigenvalues of the matrix ·.

和

有界，得到以下合理假设：Considering

and

is bounded, and the following reasonable assumptions are obtained:

为待设计的理想神经网络最优补偿。Among them, ξ is an arbitrarily small positive number,

The optimal compensation for the ideal neural network to be designed.

Taking the derivative of V(t) and simplifying it, we get:

Among them, κ＝[||ε||,||s||] ^T , coefficient β＝2σ _min (H)/{max[σ _max (M _q Z ^-1 ),σ(K _e )]}. From Lyapunov's theorem, we know that all signals are bounded.

This step is the process of designing a robust feedback controller. The robust feedback controller is a controller designed based on the actual error signal and is mainly used to stabilize the nominal system.

Step 5: Perform neural network approximation on the unmodeled dynamics and compensation residuals.

The RBF (Radial Basis Function) neural network consists of an input layer, a hidden layer, and an output layer. The activation function of the hidden layer uses the Gaussian basis function, and the output of the j-th layer neuron is expressed as:

m为神经网络的神经元总层数，c_j和b_j分别为核函数的中心坐标矢量与宽度。Where χ is the neural network input vector, χ＝[χ ₁ ,χ ₂ ,...,χ _m ],

m is the total number of neuron layers in the neural network, c _j and b _j are the center coordinate vector and width of the kernel function respectively.

Using RBF neural network to approximate residual and unknown errors, the total output of the ideal neural network is:

F＝W ^* TR(χ)+∈，

Among them, W ^* is the optimal weight vector, ∈ represents the approximate output error, and R(χ) is the multi-layer neuron output corresponding to the input vector χ.

In the actual design process, the output of the RBF neural network is:

为权重误差矢量，其中

为所设计的权重矢量。definition

is the weight error vector, where

is the designed weight vector.

In practical systems, it is reasonable to assume that the approximation error ∈ is bounded, namely:

∈≤|∈ _M |,

Among them, ∈ _M is the upper bound of the approximation error to be designed.

The optimal design of the neural network controller is:

Where η is the robust term coefficient and sign(·) represents the sign function coefficient η ≥ |∈ _M +ξ|.

Further design the weight adaptation law of RBF neural network:

Among them, φ is the learning rate update matrix to be designed.

Redefine the Lyapunov energy function V _q (t), that is:

Here, tr(·) represents the trace operation of the matrix ·.

进行求导并简化可得：Pair

Taking the derivative and simplifying we get:

Therefore, the closed-loop system is asymptotically stable, that is, the motion trajectory of the gantry platform of the placement machine will gradually converge to the expected reference signal.

This step performs neural network approximation on the unmodeled dynamics and compensation residuals to further improve the stability of the system.

Step 6: Optimize and integrate the designed controller to control the system in real time.

Combining the controller units designed in steps 3 to 5, the collaborative controller of the placement machine gantry platform can be expressed as:

v＝υ _a +υ _e +υ _nn .

According to the total controller output matrix v and thrust coefficient described in the above formula, the linear motor control input is obtained as:

_Sm is the distance between the motors on both sides of the beam of the gantry platform of the placement machine. _Kxk and _Kmy can be obtained through offline identification. The designed control system is applied to the specific dual-drive gantry experimental platform, the controller parameters are designed and the adaptive law coefficients of each parameter are optimized and adjusted, so that the multi-axis collaborative tracking error and synchronous control accuracy of the gantry platform meet the preset performance requirements.

An embodiment is given below:

Set S _m = 0.975m, S _g = 1.095m, _Se = 1.185m, and expect input x _d (t) = 0.08*sin(πt), y _d (t) = 0.04*[1-cos(πt)], α _d (t) = 0. Use the least squares method to identify the parameters, and get the nominal value and the upper and lower limits of the parameters as follows:

设计控制器增益矩阵λ＝diag[120,100,80]。The identification results are K _xk ≈1.08, K _my ≈1.02, and the smooth function is selected

Design the controller gain matrix λ = diag[120,100,80].

The preset performance function parameters are ρ ₀ = [0.0003, 0.0005, 0.0002], ρ _∞ = [0.0001, 0.0002, 0.0001],

自适应部分参数自适应学习率为Γ(0)＝[100,100,...100,100]_13×13。set up

The adaptive learning rate of the adaptive part parameters is Γ(0)=[100,100,...100,100] _13×13 .

遗忘因子和标准化因子分别为δ＝0.02，μ＝0.1。Adaptation rate upper bound

The forgetting factor and normalization factor are δ=0.02 and μ=0.1 respectively.

The parameters of the robust feedback part are designed as: K _d = diag[30,7,2], _Ke = diag[100,200,300].

The center value and width of the Gaussian basis function of the neural network are:

c _j =[-0.3,-0.2,-0.1,0,0.1,0.2,0,3] _2×7 , b _j =[10,10,10,10,10,10,10] ^T .

The learning rate is set to φ = diag[5,5,5,5,5,5,5] and the robust gain is η = 0.05.

Optionally, an additional load of 5 kg is added to the mobile platform, and the initial starting position is located at the generalized coordinate zero point.

FIG3 shows the motion position change curve of the XY axis when following the desired trajectory.

Figures 4 and 5 show the tracking error curves of the X and Y axes when they follow the desired trajectory. Compared with the traditional nonlinear control algorithm (PID), the adaptive preset performance cooperative control method (APPC) proposed in this embodiment has better performance in tracking the desired trajectory and generates smaller errors, that is, higher control accuracy.

Figure 6 shows the curve of the rotation angle change of the beam when following the desired trajectory. From the experimental results, it can be seen that the synchronous control method of this embodiment has stronger anti-interference ability, smaller fluctuation of the beam rotation angle, and can maintain a high synchronization control accuracy even under the influence of dynamic load and beam center of mass offset, ensuring the smooth and safe operation of the placement machine gantry system.

Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It will also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims (9)

1. The multi-axis cooperative control method of the dual-drive gantry platform of the chip mounter is characterized in that a desired model compensation controller, a robust feedback controller and a neural network controller are respectively designed, the sum output by the designed controllers is used as a total control signal of the gantry platform of the chip mounter, and the total control signal is utilized to carry out multi-axis cooperative control on an X axis, a Y1 axis and a Y2 axis of the gantry platform of the chip mounter;

the desired model compensation controller expression is:

wherein ,υ_a Compensating the output of the controller for the desired model, Φ _d For a regression quantity matrix containing the desired information,

is an estimated value of theta and,θ is a coefficient matrix formed by uncertain parameters in a gantry platform system coupling dynamics model of the chip mounter,

wherein ,M_hk For normalizing the quality of the movable workbench in the chip mounter _xk For normalizing the viscous friction coefficient of the X axis of the gantry platform of the post-chip mounter, A _xk For normalizing the Coulomb friction coefficient, M, at the X axis of the gantry platform of the chip mounter _yk For normalizing the total mass of the cross beam in the gantry platform of the rear chip mounter, B _yk For normalizing the sum of viscous friction coefficients at Y1 axis and Y2 axis guide rails of the gantry platform of the post-chip mounter, A _yk For normalizing the sum of Coulomb friction coefficients at Y1 axis and Y2 axis guide rails of a gantry platform of the post-chip mounter, J _k To normalize the moment of inertia, K _αk For normalized equivalent rotational stiffness, B _sk For normalizing the difference between the viscous friction coefficients at the Y2 axis and Y1 axis guide rails of the gantry platform of the post-chip mounter, A _sk For normalizing the difference of coulomb friction coefficients at the Y2 axis and Y1 axis guide rails of the gantry platform of the chip mounter,

and

Respectively taking the non-linear disturbance constant values in X-axis and Y-axis dynamics of a gantry platform of the normalized chip mounter as +.>

The method is a constant value of nonlinear disturbance in the rotation dynamics of a gantry platform of the normalized chip mounter;

the robust feedback controller expression is:

υ _e ＝-M _q Z ^-1 G-K _d s-K _e ε，

wherein ,υ_e For robust feedback controllersOutput, M _q For the inertia matrix of the gantry platform of the normalized chip mounter, s is a sliding mode variable, and Z=diag [ Z ] ₁ ,z ₂ ,z ₃ ]，

i＝1,2,3，

S _i Is an error transfer function and has:

ε＝[ε ₁ ,ε ₂ ,ε ₃ ]as unconstrained conversion errors, the intermediate variable r _i ＝e _i (t)ρ _i (t)，e _i (t) is an error vector at time t, e _i (0) As an initial value of the error vector,

for the overshoot adjustment factor,

ρ _i is a performance function and expressed as follows:

ρ _i (t)＝(ρ _i0 -ρ _i∞ )e ^-lt +ρ _i∞ ，

ρ _i0 for the steady state error initial value ρ _i∞ Is the steady state error maximum, l is the error convergence rate,

lambda is the control gain matrix, K _d For proportional feedback matrix, K _e Is a robust gain matrix;

the neural network controller expression is:

wherein ,υ_nn As an output of the neural network controller,

is a neural network weight vector, χ is a neural network input vector, χ= [ χ ] ₁ ,χ ₂ ,...,χ _m ]，

m is the total number of layers of neurons of the neural network, j=1, 2, m, R (χ) is the total output of the multi-layer neurons of the neural network, η is the robust term coefficient, sign (·) represents a sign function;

total control signal v= [ v ] of gantry platform of chip mounter ₁ ,v ₂ ,v ₃ ]：

v＝υ _a +υ _e +υ _nn 。

2. The multi-axis cooperative control method of a dual-drive gantry platform of a chip mounter according to claim 1, wherein cooperative control of an X axis, a Y1 axis and a Y2 axis of the gantry platform of the chip mounter is realized by using a total control signal of the gantry platform of the chip mounter according to the following formula:

wherein ,S_m For the distance between motors at two sides of a gantry platform beam of the chip mounter, alpha is the actual rotation angle of the gantry platform beam of the chip mounter, K _xk K is the normalized thrust constant of the X-axis motor _my ＝K ₂ K ₁ ，K ₁ and K₂ Thrust constants, u, of motors of Y1 axis and Y2 axis of gantry platform of chip mounter respectively _x 、u ₁ and u₂ Control inputs for the X-axis, Y1-axis and Y2-axis, respectively.

3. The multi-axis cooperative control method of the dual-drive gantry platform of the chip mounter according to claim 2, wherein the coupling dynamics model of the gantry platform system of the chip mounter is as follows:

wherein ,C_q 、B _q 、K _q and A_q Respectively normalized Coriolis force matrix, viscous friction matrix, equivalent stiffness matrix and coulomb friction matrix, wherein q is a gantry platform system state vector matrix of the chip mounter and q= [ x (t), y (t), and alpha (t)]X (t) and Y (t) are respectively the actual displacement of the X axis and the Y axis of the gantry platform of the chip mounter at the moment t, alpha (t) is the actual rotation angle of the cross beam of the gantry platform system of the chip mounter at the moment t,

and

The motion speed and acceleration vector matrix of the gantry platform system shaft of the chip mounter are respectively a nonlinear function +.>

and

Respectively a constant matrix and a time-varying matrix of the nonlinear disturbance after normalization.

4. The multi-axis cooperative control method of a dual-drive gantry platform of a chip mounter according to claim 3, wherein an error vector e of the gantry platform system of the chip mounter _i The constraint of (t) is:

wherein ,e_i (t)＝q-q _d ＝[x(t)-x _d (t),y(t)-y _d (t),α(t)]，

q _d ＝[x _d (t),y _d (t),α _d (t)]Expected track signal matrix, x of gantry platform system of chip mounter _d(t) and y_d (t) the expected displacement of X axis and Y axis of gantry platform of chip mounter at t moment respectively, alpha _d (t) is the expected rotation angle of the gantry platform beam of the chip mounter and alpha _d (t)＝0。

5. The multi-axis cooperative control method of the dual-drive gantry platform of the chip mounter according to claim 3, wherein,

wherein h is the offset distance of the mass center of the movable workbench in the chip mounter, X (t) is the actual displacement of the X axis of the cross beam of the gantry platform system of the chip mounter, and S _g Is the distance between the Y1 axis guide rail and the Y2 axis guide rail of the gantry platform of the chip mounter.

6. The multi-axis cooperative control method of a dual-drive gantry platform of a chip mounter according to claim 1, wherein the regression of the gantry platform system of the chip mounter

The method comprises a residual matrix part and a part containing expected information, wherein the expression is as follows:

wherein ,

for regression matrix containing only the desired information, +.>

And the regression quantity residual error matrix.

7. The multi-axis cooperative control method of a dual-drive gantry platform of a chip mounter according to claim 1, wherein the expression of the sliding mode variable s is:

wherein ,

8. the multi-axis cooperative control method of a dual-drive gantry platform of a chip mounter according to claim 1, wherein the output R (χ _j ) The method comprises the following steps:

wherein ,c_j and b_j The percentages are the central coordinate vector and width of the neural network kernel function.

9. The multi-axis cooperative control method of a dual-drive gantry platform of a chip mounter according to claim 8, wherein the neural network weight vector is

Adaptive rate of->

The method comprises the following steps:

wherein the phi-learning rate updates the matrix.

Images