WO2024037394A1 - 一种龙门机床动梁交叉耦合控制方法 - Google Patents

一种龙门机床动梁交叉耦合控制方法 Download PDF

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WO2024037394A1
WO2024037394A1 PCT/CN2023/111894 CN2023111894W WO2024037394A1 WO 2024037394 A1 WO2024037394 A1 WO 2024037394A1 CN 2023111894 W CN2023111894 W CN 2023111894W WO 2024037394 A1 WO2024037394 A1 WO 2024037394A1
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machine tool
gantry
control
model
loop
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PCT/CN2023/111894
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English (en)
French (fr)
Inventor
陈传海
刘志峰
郭劲言
金桐彤
贺鑫元
赵硕
齐宝宝
刘春时
杨兆军
黎志杰
化春雷
张亮
严昊明
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吉林大学
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Priority to US18/508,333 priority Critical patent/US20240082966A1/en
Publication of WO2024037394A1 publication Critical patent/WO2024037394A1/zh

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q1/00—Members which are comprised in the general build-up of a form of machine, particularly relatively large fixed members
    • B23Q1/25—Movable or adjustable work or tool supports
    • B23Q1/44—Movable or adjustable work or tool supports using particular mechanisms
    • B23Q1/56—Movable or adjustable work or tool supports using particular mechanisms with sliding pairs only, the sliding pairs being the first two elements of the mechanism
    • B23Q1/60—Movable or adjustable work or tool supports using particular mechanisms with sliding pairs only, the sliding pairs being the first two elements of the mechanism two sliding pairs only, the sliding pairs being the first two elements of the mechanism
    • B23Q1/62—Movable or adjustable work or tool supports using particular mechanisms with sliding pairs only, the sliding pairs being the first two elements of the mechanism two sliding pairs only, the sliding pairs being the first two elements of the mechanism with perpendicular axes, e.g. cross-slides
    • B23Q1/621—Movable or adjustable work or tool supports using particular mechanisms with sliding pairs only, the sliding pairs being the first two elements of the mechanism two sliding pairs only, the sliding pairs being the first two elements of the mechanism with perpendicular axes, e.g. cross-slides a single sliding pair followed perpendicularly by a single sliding pair
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/408—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by data handling or data format, e.g. reading, buffering or conversion of data
    • G05B19/4086—Coordinate conversions; Other special calculations
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B6/00—Internal feedback arrangements for obtaining particular characteristics, e.g. proportional, integral or differential
    • G05B6/02—Internal feedback arrangements for obtaining particular characteristics, e.g. proportional, integral or differential electric
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35356—Data handling
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

Definitions

  • the invention relates to the field of CNC machine tool control, specifically a cross-coupling control method for moving beams of gantry machine tools.
  • High-end CNC machine tools are the core of "industrial mother machines". Their structure and control accuracy are key factors affecting their reliability. Research on common key technologies of high-end CNC machine tools plays an important role in promoting the development of my country's manufacturing industry.
  • the gantry machining center has a moving beam structure that can process large-mass, large-volume, and irregular-shaped components through beam movement, such as large submarines at sea and key components of large ships.
  • the moving beam gantry machining center is more widely used in practical applications. Ensuring synchronous driving accuracy during beam movement is the key to ensuring processing quality. Therefore, it is of great significance to study the synchronous driving strategy when the beam moves.
  • the synchronization algorithm of the existing CNC system rarely considers the change of the center of mass of the beam caused by the movement of the moving parts on the beam, resulting in large synchronization errors.
  • the synchronization error on both sides when the crossbeam moves will affect the machining accuracy of the gantry machine tool and reduce the dynamic response of the system, which needs to be improved.
  • the purpose of the present invention is to provide a cross-coupling control method for the moving beam of a gantry machine tool to solve the problems raised in the above background technology.
  • a cross-coupling control method for moving beams of gantry machine tools including:
  • Step 1 Establish a dynamic model of the beam considering the ram on the beam, and simplify the model for the design of the observer;
  • Step 2 Follow the method of parameter tuning of the single-sided servo control system to achieve PID control parameter tuning of the motors at both ends.
  • Step 3 Use cross-coupled synchronous control to feedback the mutual influence between the two axes, and design an interference observer to compensate the output to the corresponding axis to form another closed loop;
  • Step 4 Design an interference observer and compensate for the interference to improve the robustness of the system while reducing synchronization errors.
  • step 1 includes:
  • Step 11 Use the generalized three-degree-of-freedom coordinate system (Z, ⁇ , Y) or the position coordinate system (Z1, Z2, Y) to establish the three-degree-of-freedom kinematic model of the beam assembly;
  • Step 12 Obtain the differential equation during the movement of the beam of the gantry beam mechanism
  • Step 13 Simplify the differential equation during the movement of the beam.
  • step 11 use the position coordinate system (Z1, Z2, Y) or the generalized three-degree-of-freedom coordinate system (Z, ⁇ , Y) to establish the kinematic model of the beam assembly:
  • the two models can be converted to each other, where: ⁇ is the deflection angle of the beam, L is the span of the beam, z is the translational displacement of the beam, y is the displacement of the moving part from the center of gravity of the beam, z1 and z2 are the translational displacements of the two axes. .
  • step 12 the moment of inertia J of the gantry beam can be expressed as:
  • k 1 and k 2 are the friction coefficients between both sides of the beam and the sliding seat respectively, k bh is the friction coefficient between the beam and the moving parts;
  • the potential energy can be considered unchanged, that is:
  • M, C, and K are the mass matrix, damping coefficient matrix, and stiffness coefficient matrix respectively; H is the Coriolis centripetal moment.
  • step 13 during the actual movement of the gantry beam, the torsion angle ⁇ is very small ( ⁇ 0.0001rad), so it can be simplified to cos ⁇ 1; sin ⁇ 0, then in (7)
  • the elements in the mass matrix M can be approximated as:
  • M s , C s , and K s are the simplified mass matrix, damping coefficient matrix, and stiffness coefficient matrix respectively;
  • q s (Z, ⁇ , Y) T ;
  • F s (F z ,F ⁇ ,F y ) T .
  • Equation (9) The matrix forms in equation (9) are as follows:
  • step 2 includes:
  • Step 21 Build the control model of the servo motor
  • Step 22 Build the three-loop modeling of the servo system
  • Step 23 Complete the three-loop parameter tuning of the servo system.
  • step 22 In step 22: Based on the permanent magnet synchronous motor control model, the servo control system is designed. The current loop, speed loop and position loop are three interrelated and based on the PID controller. Closed-loop negative feedback regulation system, the servo control system controls the current loop, speed loop, and position loop to achieve the purpose of controlling the motor's output torque, operating speed, and output position.
  • step 23 the same motor is selected on both sides of the double drive of the gantry machine tool beam, and the three-loop parameters of the single-side servo system are first adjusted through the three-loop servo system modeling, and then the three-loop parameters of the single-side servo system are adjusted using the same control parameters.
  • the two servo systems jointly drive the beam of the gantry machine tool to achieve synchronous control.
  • DOB disurbance observer
  • P(s) of the object includes the transfer function P(s) of the object, the nominal model P n -1 (s) of the object, and the interference observation value Control input r, measurement noise ⁇ , low-pass filter Q(s), equivalent interference d (external interference, modeling error reduction of nominal model);
  • the design of low-pass filter Q(s) affects the actual performance of DOB, so the design problem of DOB is transformed into the design problem of low-pass filter Q(s).
  • the model of Q(s) is described as:
  • ⁇ is the time constant (the reciprocal of the cutoff frequency); N is the denominator order; M is the numerator order; N-M is the relative order;
  • the order of Q(s) will affect the stability of the system.
  • High-order Q(s) will have phase lag, which weakens the compensation effect for interference; increasing the order of the numerator will offset it.
  • the phase lag phenomenon improves the system's anti-interference ability, but will destroy the system stability;
  • the nominal model P n (s) of the synchronous control system of the gantry beam can be obtained through the parameter identification principle based on the least square method.
  • the driving torque signal is collected as the input signal and the displacement signal of the beam end is used as the output signal to identify the parameters of the control object.
  • the obtained nominal model P n (s) is shown in (13):
  • model (14) As the nominal model of the two axes, considering the control accuracy, system robustness and stability, among all the formulas that satisfy (12), the performance of model (14) is the best, and its relative order When it is 2, better anti-interference performance and noise suppression performance can be obtained.
  • the beneficial effects of the present invention are: when the present invention is actually applied to a large moving beam gantry machining center, it not only reduces the synchronization error caused by the torsion of the crossbeam due to differences in mechanical structure, but also solves the problem of the crossbeam moving parts being The synchronization error caused by the asymmetry of the loads on both sides caused during the movement process also improves the system robustness and stability.
  • Figure 1 is a flow chart of a cross-coupling control method for the moving beam of a gantry machine tool.
  • Figure 2 is the schematic diagram of cross-coupling control.
  • Figure 3 is a schematic diagram of the gantry beam synchronous drive structure.
  • Figure 4 is the control structure diagram of the permanent magnet synchronous motor in the d-q coordinate system.
  • Figure 5 is the control block diagram of the servo system.
  • Figure 6 is a schematic diagram of the three-loop parameters of the motor.
  • Figure 7 is a schematic diagram of the cross-coupled synchronous control structure of a gantry machine tool.
  • Figure 8 is the internal structure diagram of DOB.
  • Figure 9 is a schematic diagram of the synchronization error during the movement of the moving parts on the beam.
  • Figure 10 is a schematic diagram of the synchronization error of the PID controller under step interference.
  • Figure 11 is a schematic diagram of the synchronization error of the DOB observer under step interference.
  • a cross-coupling control method for the moving beam of a gantry machine tool including:
  • Step 1 Establish a dynamic model of the beam considering the ram on the beam, and simplify the model for the design of the observer;
  • Step 2 Follow the method of parameter tuning of the single-sided servo control system to achieve PID control parameter tuning of the motors at both ends.
  • Step 3 Use cross-coupling synchronous control to feedback the mutual influence between the two axes, and design an interference observer to compensate the output to the corresponding axis to form another closed loop;
  • Step 4 Design an interference observer and compensate for the interference to improve the robustness of the system while reducing synchronization errors.
  • the changes in the two axes (beam changes) in the beam dynamic model are compensated for the output to the corresponding axes through the interference observer, thereby improving the robustness of the system while reducing the synchronization error of the two axes.
  • the cross-coupling is shown in Figure 2.
  • the servo control system mainly includes the motor and the required designed observer.
  • the drive system is controlled through the three-loop parameter setting of the motor and the observation results of the observer.
  • the drive system includes a gantry driven by two ball screws.
  • the position signals at both ends of the beam can be measured by grating scales and encoders, and the position signals are fed back to the servo control system to build a feedback compensation closed loop.
  • step 1 includes:
  • Step 11 Use the generalized three-degree-of-freedom coordinate system (Z, ⁇ , Y) or the position coordinate system (Z1, Z2, Y) to establish the three-degree-of-freedom kinematic model of the beam assembly;
  • Step 12 Obtain the differential equation during the movement of the beam of the gantry beam mechanism
  • Step 13 Simplify the differential equation during the movement of the beam.
  • step 11 use the position coordinate system (Z1, Z2, Y) or the generalized three-degree-of-freedom coordinate system (Z, ⁇ , Y) to establish the kinematic model of the beam assembly:
  • the two models can be converted to each other, where: ⁇ is the deflection angle of the beam, L is the span of the beam, z is the translational displacement of the beam, y is the displacement of the moving part from the center of gravity of the beam, z1 and z2 are the translational displacements of the two axes. , M is the mass of the beam, and m is the mass of the moving parts.
  • the gantry beam synchronous drive structure generally uses two identical servo motors to drive the ball screws of the Z1 and Z2 axes respectively to drive the beam to move up and down.
  • the ram and tool holder (hereinafter collectively referred to as moving parts) on the beam move on the Y axis.
  • moving parts it is regarded as a concentrated mass block, and the final result caused by the unsynchronized movement of both sides of the beam is that the beam will twist at a small angle.
  • step 12 the moment of inertia J of the gantry beam can be expressed as:
  • k 1 and k 2 are the friction coefficients between both sides of the beam and the sliding seat respectively, k bh is the friction coefficient between the beam and the moving parts;
  • the potential energy can be considered unchanged, that is:
  • M, C, and K are the mass matrix, damping coefficient matrix, and stiffness coefficient matrix respectively;
  • H is the Coriolis centripetal matrix;
  • generalized coordinate vector: q (Z, ⁇ ,Y) T ;
  • generalized force vector: F (F z ,F ⁇ ,F y ) T .
  • step 13 During the actual movement of the gantry beam, the torsion angle ⁇ is very small ( ⁇ 0.0001rad), so it can be simplified to cos ⁇ 1; sin ⁇ 0, then ( 7)
  • the elements in the medium mass matrix M can be approximated as:
  • M s , C s , and K s are the simplified mass matrix, damping coefficient matrix, and stiffness coefficient matrix respectively;
  • q s (Z, ⁇ , Y) T ;
  • F s (F z ,F ⁇ ,F y ) T .
  • Equation (9) The matrix forms in equation (9) are as follows:
  • step 2 includes:
  • Step 21 Build the control model of the servo motor
  • Step 22 Build the three-loop modeling of the servo system
  • Step 23 Complete the three-loop parameter tuning of the servo system.
  • K E n p ⁇ f , which is called the motor back electromotive force coefficient.
  • K T 1.5n p ⁇ f , which is called the motor torque constant (n p is the number of magnetic pole pairs; ⁇ f is the permanent magnet flux linkage).
  • step 22 Based on the permanent magnet synchronous motor control model, the servo control system is designed.
  • the current loop, speed loop and position loop are three interrelated closed loops based on the PID controller.
  • Negative feedback adjustment system, servo control system controls the current loop, speed loop, and position loop to achieve the purpose of controlling the motor's output torque, operating speed, and output position.
  • the current loop and speed loop use PI controllers, and the position loop uses P controller.
  • Kp, Kv, and Ki are the feedback coefficients of the position loop, speed loop, and current loop respectively. Therefore, the current loop and speed loop need to set the proportional coefficient and integral time constant, and the position loop only needs to set the proportional coefficient.
  • step 23 the same motors are selected on both sides of the double drive of the beam of the gantry machine tool.
  • the three-loop servo system modeling the three-loop parameters of the single-side servo system are first adjusted, and then the three-loop parameters of the single-side servo system are adjusted using Two servo systems with the same control parameters jointly drive the beam of the gantry machine tool to achieve synchronous control.
  • step 3 the schematic diagram of the gantry machine tool beam synchronous drive cross-coupling synchronous control structure is shown in Figure 7.
  • the servo control system mainly includes the motor and the required designed observer.
  • the drive system is controlled through the three-loop parameter setting of the motor and the observation results of the observer.
  • the drive system mainly includes a gantry beam driven by two ball screws.
  • the position signals at both ends can be measured by grating scales and encoders, and the position signals are fed back to the servo control system.
  • DOB disurbance observer
  • P(s) of the object includes the transfer function P(s) of the object, the nominal model P n -1 (s) of the object, and the interference observation value Control input r, measurement noise ⁇ , low-pass filter Q(s), equivalent interference d (external interference, modeling error reduction of nominal model);
  • the design of low-pass filter Q(s) affects the actual performance of DOB, so the design problem of DOB is transformed into the design problem of low-pass filter Q(s).
  • the model of Q(s) is described as:
  • ⁇ is the time constant (the reciprocal of the cutoff frequency); N is the denominator order; M is the numerator order; N-M is the relative order;
  • the order of Q(s) will affect the stability of the system.
  • High-order Q(s) will have phase lag, which weakens the compensation effect for interference; increasing the order of the numerator will offset it.
  • the phase lag phenomenon improves the system's anti-interference ability, but will destroy the system stability;
  • the nominal model P n (s) of the synchronous control system of the gantry beam can be obtained through the parameter identification principle based on the least square method.
  • the driving torque signal is collected as the input signal and the displacement signal of the beam end is used as the output signal to identify the parameters of the control object.
  • the obtained nominal model P n (s) is shown in (13):
  • model (14) As the nominal model of the two axes, considering the control accuracy, system robustness and stability, among all the formulas that satisfy (12), the performance of model (14) is the best, and its relative order When it is 2, better anti-interference performance and noise suppression performance can be obtained.

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Abstract

本发明公开了一种龙门机床动梁交叉耦合控制方法，涉及数控机床控制领域，该龙门机床动梁交叉耦合控制方法包括：步骤1：建立考虑横梁上滑枕的横梁动力学模型，同时将该模型进行化简用于观测器的设计；步骤2：按照单边伺服控制系统参数整定的方法进行，使用相同控制参数的伺服系统共同驱动横梁上下移动，实现同步控制，实现两端电机PID控制参数整定；与现有技术相比，本发明的有益效果是：本发明在实际应用于大型动梁式龙门加工中心不仅减小了横梁因机械结构差异而扭转产生的同步误差，并且解决了横梁移动部件在运动过程中造成的两侧负载不对称造成的同步误差，而且提高了系统鲁棒性和稳定性。

Description

一种龙门机床动梁交叉耦合控制方法 技术领域
本发明涉及数控机床控制领域，具体是一种龙门机床动梁交叉耦合控制方法。
背景技术
高端数控机床作为“工业母机”的核心，其结构和控制精度是影响其可靠性的关键一环，研究高端数控机床的共性关键技术，对推动我国制造业的发展有着重要作用。龙门加工中心作为一种常见的高端数控机床，其动梁式结构可以通过横梁移动完成大质量、大体积、形状不规则部件的加工，例如海上的大型潜艇、大型船舶的关键零部件等。
而动梁式龙门加工中心在实际应用中更加广泛，保证横梁运动时同步驱动精度是保证加工质量的关键。因此，研究横梁运动时同步驱动策略有着重要意义。
现有数控系统的同步算法很少考虑横梁上移动部件运动过程中引起的横梁质心改变的问题，导致同步误差较大。横梁运动时两侧的同步误差会影响龙门机床的加工精度并降低系统动态响应，需要改进。
发明内容
本发明的目的在于提供一种龙门机床动梁交叉耦合控制方法，以解决上述背景技术中提出的问题。
为实现上述目的，本发明提供如下技术方案：
一种龙门机床动梁交叉耦合控制方法，包括：
步骤1：建立考虑横梁上滑枕的横梁动力学模型，同时将该模型进行化简用于观测器的设计；
步骤2：按照单边伺服控制系统参数整定的方法进行，实现两端电机PID控制参数整定，使用相同控制参数的伺服系统共同驱动横梁上下移动(两侧的结构对称)，实现同步控制；
步骤3：采用交叉耦合同步控制来反馈两轴之间的相互影响，并设计干扰观测器将输出补偿到相应的轴，构成另外一个闭环回路；
步骤4：设计干扰观测器，并对干扰进行补偿，提高系统的鲁棒性的同时减小同步误差。
作为本发明再进一步的方案：步骤1包括：
步骤11：采用广义三自由度坐标系(Z,θ,Y)或位置坐标系(Z1,Z2,Y)建立横梁组合体的三自由度运动学模型；
步骤12：获取龙门横梁机构的横梁移动过程中的微分方程；
步骤13：对横梁移动过程中的微分方程进行化简。
作为本发明再进一步的方案：步骤11中：采用位置坐标系(Z1,Z2,Y)或广义三自由度坐标系(Z,θ,Y)建立横梁组合体的运动学模型：
两个模型可互相转换，其中：θ为横梁的偏转角度、L为横梁跨度、z为横梁平动位移量、y为移动部件距离横梁重心的位移量、z1和z2为两轴平动位移量。
作为本发明再进一步的方案：步骤12中：龙门横梁转动惯量J可以表示为：
根据拉格朗日方程建立横梁移动过程中的微分方程需要提前定义与其动态性相关的能量表达式，包括动能T、弹性势能V、瑞利耗散函数D、横梁质量M；移动部件质量m，表达式如下：

瑞利耗散函数D中：k1、k2分别为横梁两侧与滑座之间的摩擦系数、kbh为横梁与移动部件之间的摩擦系数；
由于龙门横梁为刚体结构，可认为势能不变，即：
V＝0；(4)
对于广义三自由度坐标系(Z,θ,Y)，其对应的广义力为：
其中，Fi和fi(i＝1,2,3)是伺服电机驱动力和摩擦力(i＝1,2,3分别代表沿Z,θ,Y方向)。
联合(2)～(5)，代入到带耗散的拉格朗日方程(6)中：
其中：广义坐标qj＝(Z,θ,Y)；广义力Fj＝(Fz,Fθ,Fy)；L＝T-V。；
龙门横梁机构的横梁移动过程中的微分方程可以表示为：
其中，M、C、K分别为质量矩阵、阻尼系数矩阵、刚度系数矩阵；H为科里奥利向心矩 阵；广义坐标向量：q＝(Z,θ,Y)T；广义力向量：F＝(Fz,Fθ,Fy)T。
作为本发明再进一步的方案：步骤13中：龙门横梁在实际运动过程中，扭转角度θ很小(θ<0.0001rad),故可化简为cosθ≈1；sinθ≈0，则(7)中质量矩阵M中元素可近似为：
同理，科里奥利向心矩阵中所有元素可以忽略不计，即H≈0；取系统动力学方程中关于z和θ两式进行分析，可以将(7)化简为：
Ms、Cs、Ks分别为化简后的质量矩阵、阻尼系数矩阵、刚度系数矩阵；化简后的广义坐标向量：qs＝(Z,θ,Y)T；化简后的广义力向量：Fs＝(Fz,Fθ,Fy)T。
(9)式中各矩阵形式如下：
对于y轴，其独立的运动学微分方程为：
作为本发明再进一步的方案：步骤2包括：
步骤21：构建伺服电机的控制模型；
步骤22：构建伺服系统三环建模；
步骤23：完成伺服系统三环参数整定。
作为本发明再进一步的方案：步骤21中：根据永磁电机在d-q坐标系下的数学模型，并选用id＝0的控制方法实现d、q两轴解耦，得到在id＝0控制方式下的永磁同步电机控制模型。
作为本发明再进一步的方案：步骤22中：步骤22中：基于永磁同步电机控制模型，对伺服控制系统进行设计，电流环、速度环以及位置环是三个相互关联且基于PID控制器的闭环负反馈调节系统，伺服控制系统对电流环、速度环、位置环三环进行控制，达到控制电机的输出转矩、运行速度、输出位置的目的。
作为本发明再进一步的方案：步骤23中：龙门机床横梁双驱动两侧选用相同的电机，通过伺服系统三环建模先进行单侧的伺服系统的三环参数整定，然后用具有相同控制参数的两伺服系统共同驱动龙门机床横梁，实现同步控制。
作为本发明再进一步的方案：步骤4中：DOB(干扰观测器)包括对象的传递函数P(s)、对象的名义模型Pn -1(s)、干扰观测值控制输入r、测量噪声ζ、低通滤波器Q(s)，等效干扰d(外界干扰、名义模型的建模误差折合)；
低通滤波器Q(s)的设计影响DOB的实际性能，故DOB的设计问题转化为低通滤波器Q(s)的设计问题，Q(s)的模型描述为：
其中，τ是时间常数(截止频率的倒数)；N是分母阶数；M是分子阶数；N-M是相对阶；
Q(s)的阶次会影响系统的稳定性，分母阶次越大，系统越稳定，高阶次的Q(s)出现相位滞后现象，削弱对干扰的补偿作用；分子阶次增大会抵消相位滞后现象，提高系统抗干扰能力，但会破坏系统稳定性；
龙门横梁的同步控制系统的名义模型Pn(s)可以通过基于最小二乘法的参数辨识原理获得，采集驱动力矩信号作为输入信号和横梁端的位移信号作为输出信号来对控制对象进行参数辨识。得到的名义模型Pn(s)如(13)所示：
以模型(13)作为两轴的名义模型，考虑控制精度、系统鲁棒性和稳定性，在满足(12)的所有式子中，模型(14)的性能是最好的，其相对阶次为2，可以获得较好的抗干扰性能和噪音抑制性能。
模型(14)为Q31(s)型低通滤波器，时间常数选为τ＝0.005s，可得：
与现有技术相比，本发明的有益效果是：本发明在实际应用于大型动梁式龙门加工中心不仅减小了横梁因机械结构差异而扭转产生的同步误差，并且解决了横梁移动部件在运动过程中造成的两侧负载不对称造成的同步误差，而且提高了系统鲁棒性和稳定性。
附图说明
图1为一种龙门机床动梁交叉耦合控制方法的流程图。
图2为交叉耦合控制的原理图。
图3为龙门横梁同步驱动结构的示意图。
图4为永磁同步电机d-q坐标系下的控制结构图。
图5为伺服系统的控制框图。
图6为电机三环参数的示意图。
图7为龙门机床交叉耦合同步控制结构示意图。
图8为DOB的内部结构图。
图9为横梁上移动部件运动过程中的同步误差示意图。
图10为阶跃干扰下PID控制器的同步误差示意图。
图11为阶跃干扰下DOB观测器的同步误差示意图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例，基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
请参阅图1，一种龙门机床动梁交叉耦合控制方法，包括：
步骤1：建立考虑横梁上滑枕的横梁动力学模型，同时将该模型进行化简用于观测器的设计；
步骤2：按照单边伺服控制系统参数整定的方法进行，实现两端电机PID控制参数整定，使用相同控制参数的伺服系统共同驱动横梁上下移动(两侧的结构对称)，实现同步控制；
步骤3：采用交叉耦合同步控制来反馈两轴之间的相互影响，并设计干扰观测器将输出补偿到相应的轴，构成另外一个闭环回路；
步骤4：设计干扰观测器，并对干扰进行补偿，提高系统的鲁棒性的同时减小同步误差。
在具体实施例中：横梁动力学模型中的两轴(横梁变化)变化通过干扰观测器将输出补偿到相应的轴，以此高系统的鲁棒性的同时减小两轴的同步误差。其中交叉耦合如图2所示。
在步骤3中：伺服控制系统主要包括电机以及所需设计的观测器，通过电机的三环参数整定以及观测器的观测结果进行驱动系统的控制，驱动系统包括由两根滚珠丝杠驱动的龙门横梁，其两端的位置信号可以由光栅尺以及编码器测得，并将位置信号反馈给伺服控制系统，以此构建反馈补偿闭合回路。
在本实施例中：请参阅图3，步骤1包括：
步骤11：采用广义三自由度坐标系(Z,θ,Y)或位置坐标系(Z1,Z2,Y)建立横梁组合体的三自由度运动学模型；
步骤12：获取龙门横梁机构的横梁移动过程中的微分方程；
步骤13：对横梁移动过程中的微分方程进行化简。
作为本发明再进一步的方案：步骤11中：采用位置坐标系(Z1,Z2,Y)或广义三自由度坐标系(Z,θ,Y)建立横梁组合体的运动学模型：
两个模型可互相转换，其中：θ为横梁的偏转角度、L为横梁跨度、z为横梁平动位移量、y为移动部件距离横梁重心的位移量、z1和z2为两轴平动位移量、M为横梁质量、m为移动部件质量。
龙门横梁同步驱动结构一般由两个相同的伺服电机分别驱动Z1和Z2轴的滚珠丝杠带动横梁上下移动，同时横梁上的滑枕与刀架(下文统称为移动部件)在Y轴上移动，同时将其看作集中质量块，而横梁两侧运动不同步导致的最终结果为横梁会有小角度的扭转。
在本实施例中：请参阅图3，步骤12中：龙门横梁转动惯量J可以表示为：
根据拉格朗日方程建立横梁移动过程中的微分方程需要提前定义与其动态性相关的能量表达式，包括动能T、弹性势能V、瑞利耗散函数D、横梁质量M；移动部件质量m，表达式如下：

瑞利耗散函数D中：k1、k2分别为横梁两侧与滑座之间的摩擦系数、kbh为横梁与移动部件之间的摩擦系数；
由于龙门横梁为刚体结构，可认为势能不变，即：
V＝0；(4)
对于广义三自由度坐标系(Z,θ,Y)，其对应的广义力为：
其中，Fi和fi(i＝1,2,3)是伺服电机驱动力和摩擦力(i＝1,2,3分别代表沿Z,θ,Y方向)。
联合(2)～(5)，代入到带耗散的拉格朗日方程(6)中：
其中：广义坐标qj＝(Z,θ,Y)；广义力Fj＝(Fz,Fθ,Fy)；L＝T-V。；
龙门横梁机构的横梁移动过程中的微分方程可以表示为：
其中，M、C、K分别为质量矩阵、阻尼系数矩阵、刚度系数矩阵；H为科里奥利向心矩阵；广义坐标向量：q＝(Z,θ,Y)T；广义力向量：F＝(Fz,Fθ,Fy)T。
在本实施例中：请参阅图3，步骤13中：龙门横梁在实际运动过程中，扭转角度θ很小(θ<0.0001rad),故可化简为cosθ≈1；sinθ≈0，则(7)中质量矩阵M中元素可近似为：
同理，科里奥利向心矩阵中所有元素可以忽略不计，即H≈0；取系统动力学方程中 关于z和θ两式进行分析，可以将(7)化简为：
Ms、Cs、Ks分别为化简后的质量矩阵、阻尼系数矩阵、刚度系数矩阵；化简后的广义坐标向量：qs＝(Z,θ,Y)T；化简后的广义力向量：Fs＝(Fz,Fθ,Fy)T。
(9)式中各矩阵形式如下：
对于y轴，其独立的运动学微分方程为：
在本实施例中：步骤2包括：
步骤21：构建伺服电机的控制模型；
步骤22：构建伺服系统三环建模；
步骤23：完成伺服系统三环参数整定。
在本实施例中：请参阅图4，步骤21中：根据永磁电机在d-q坐标系下的数学模型，并选用id＝0的控制方法实现d、q两轴解耦，得到在id＝0控制方式下的永磁同步电机控制模型。
图4中：KE＝npψf，称为电机反电动势系数。KT＝1.5npψf，称为电机转矩常量(np为磁极对数；ψf为永磁体磁链)。
在本实施例中：请参阅图5，步骤22中：基于永磁同步电机控制模型，对伺服控制系统进行设计，电流环、速度环以及位置环是三个相互关联且基于PID控制器的闭环负反馈调节系统，伺服控制系统对电流环、速度环、位置环三环进行控制，达到控制电机的输出转矩、运行速度、输出位置的目的。
在图5中电流环和速度环使用PI控制器，位置环使用P控制器，Kp、Kv、Ki分别为位置环、速度环、电流环的反馈系数。故电流环和速度环需要整定比例系数和积分时间常数，位置环只需整定比例系数。
在本实施例中：请参阅图6，步骤23中：龙门机床横梁双驱动两侧选用相同的电机，通过伺服系统三环建模先进行单侧的伺服系统的三环参数整定，然后用具有相同控制参数的两伺服系统共同驱动龙门机床横梁，实现同步控制。
利用MATLAB/Simulink中的PID Tuner工具进行各参数的整定结果如图6所示。
在本实施例中：请参阅图7，步骤3中：龙门机床横梁同步驱动交叉耦合同步控制结构示意图如图7所示。伺服控制系统主要包括电机以及所需设计的观测器，通过电机的三环参数整定以及观测器的观测结果进行驱动系统的控制。驱动系统主要包括由两根滚珠丝杠驱动的龙门横梁，其两端的位置信号可以由光栅尺以及编码器测得，并将位置信号反馈给伺服控制系统。
在本实施例中：请参阅图8，步骤4中：DOB(干扰观测器)包括对象的传递函数P(s)、对象的名义模型Pn -1(s)、干扰观测值控制输入r、测量噪声ζ、低通滤波器Q(s)，等效干扰d(外界干扰、名义模型的建模误差折合)；
低通滤波器Q(s)的设计影响DOB的实际性能，故DOB的设计问题转化为低通滤波器Q(s)的设计问题，Q(s)的模型描述为：
其中，τ是时间常数(截止频率的倒数)；N是分母阶数；M是分子阶数；N-M是相对阶；
Q(s)的阶次会影响系统的稳定性，分母阶次越大，系统越稳定，高阶次的Q(s)出现相位滞后现象，削弱对干扰的补偿作用；分子阶次增大会抵消相位滞后现象，提高系统抗干扰能力，但会破坏系统稳定性；
龙门横梁的同步控制系统的名义模型Pn(s)可以通过基于最小二乘法的参数辨识原理获得，采集驱动力矩信号作为输入信号和横梁端的位移信号作为输出信号来对控制对象进行参数辨识。得到的名义模型Pn(s)如(13)所示：
以模型(13)作为两轴的名义模型，考虑控制精度、系统鲁棒性和稳定性，在满足(12)的所有式子中，模型(14)的性能是最好的，其相对阶次为2，可以获得较好的抗干扰性能和噪音抑制性能。
模型(14)为Q31(s)型低通滤波器，时间常数选为τ＝0.005s，可得：
在具体实施例中：请参阅图9、图10、图11，本控制算法经验证测试结果显示，使用DOB观测器可以对横梁质心变化产生的同步误差有很好的调节能力(图9)，最大同步误差为0.33mm，相比于使用传统PID控制器的最大同步误差0.48mm有很好的补偿效果。当受到阶跃干扰时(图10、图11)，采用DOB观测器的同步误差调节时间0.8s，虽大于PID控制器的0.5s；但同步误差最大值仅为0.24mm远小于PID控制器的0.4mm。上述结果表明：横梁同步控制的干扰抑制性能和系统稳定性在加入DOB观测器后得到了显著提高。
对于本领域技术人员而言，显然本发明不限于上述示范性实施例的细节，而且在 不背离本发明的精神或基本特征的情况下，能够以其他的具体形式实现本发明。因此，无论从哪一点来看，均应将实施例看作是示范性的，而且是非限制性的，本发明的范围由所附权利要求而不是上述说明限定，因此旨在将落在权利要求的等同要件的含义和范围内的所有变化囊括在本发明内。不应将权利要求中的任何附图标记视为限制所涉及的权利要求。
此外，应当理解，虽然本说明书按照实施方式加以描述，但并非每个实施方式仅包含一个独立的技术方案，说明书的这种叙述方式仅仅是为清楚起见，本领域技术人员应当将说明书作为一个整体，各实施例中的技术方案也可以经适当组合，形成本领域技术人员可以理解的其他实施方式。

Claims (10)

  1. 一种龙门机床动梁交叉耦合控制方法，其特征在于：
    该龙门机床动梁交叉耦合控制方法包括：
    步骤1：建立考虑横梁上滑枕的横梁动力学模型，同时将该模型进行化简用于观测器的设计；
    步骤2：按照单边伺服控制系统参数整定的方法进行，实现两端电机PID控制参数整定；使用相同控制参数的伺服系统共同驱动横梁上下移动，实现同步控制；
    步骤3：采用交叉耦合同步控制来反馈两轴之间的相互影响，并设计干扰观测器将输出补偿到相应的轴，构成另外一个闭环回路；
    步骤4：设计干扰观测器，并对干扰进行补偿，提高系统的鲁棒性的同时减小同步误差。
  2. 根据权利要求1所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤1包括：
    步骤11：采用广义三自由度坐标系或位置坐标系建立横梁组合体的三自由度运动学模型；
    步骤12：获取龙门横梁机构的横梁移动过程中的微分方程；
    步骤13：对横梁移动过程中的微分方程进行化简。
  3. 根据权利要求2所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤11中：采用位置坐标系或广义三自由度坐标系建立横梁组合体的运动学模型：
    两个模型能够互相转换，其中：θ为横梁的偏转角度、L为横梁跨度、z为横梁平动位移量、y为移动部件距离横梁重心的位移量、z1和z2为两轴平动位移量。
  4. 根据权利要求2所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤12中：龙门横梁转动惯量J表示为：
    根据拉格朗日方程建立横梁移动过程中的微分方程需要提前定义与其动态性相关的能量表达式，包括动能T、弹性势能V、瑞利耗散函数D、横梁质量M；移动部件质量m，表达式如下：

    瑞利耗散函数D中：k1、k2分别为横梁两侧与滑座之间的摩擦系数、kbh为横梁与移动部件之间的摩擦系数；
    由于龙门横梁为刚体结构，势能不变，即：
    V＝0；
    (4)
    对于广义三自由度坐标系，其对应的广义力为：
    其中，Fi和fi是伺服电机驱动力和摩擦力；
    联合(2)～(5)，代入到带耗散的拉格朗日方程(6)中：
    其中：广义坐标qj＝(Z,θ,Y)；广义力Fj＝(Fz,Fθ,Fy)；L＝T-V。；
    龙门横梁机构的横梁移动过程中的微分方程表示为：
    其中，M、C、K分别为质量矩阵、阻尼系数矩阵、刚度系数矩阵；H为科里奥利向心矩阵；广义坐标向量：q＝(Z,θ,Y)T；广义力向量：F＝(Fz,Fθ,Fy)T。
  5. 根据权利要求2所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤13中：龙门横梁在实际运动过程中，cosθ≈1；sinθ≈0，则(7)中质量矩阵M中元素为：
    科里奥利向心矩阵中H≈0；取系统动力学方程中关于z和θ两式进行分析，可以将(7)化简为：
    Ms、Cs、Ks分别为化简后的质量矩阵、阻尼系数矩阵、刚度系数矩阵；化简后的广义坐标向量：qs＝(Z,θ,Y)T；化简后的广义力向量：Fs＝(Fz,Fθ,Fy)T。
    (9)式中各矩阵形式如下：
    对于y轴，其独立的运动学微分方程为：
  6. 根据权利要求1所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤2包括：
    步骤21：构建伺服电机的控制模型；
    步骤22：构建伺服系统三环建模；
    步骤23：完成伺服系统三环参数整定。
  7. 根据权利要求6所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤21中：根据永磁电机在d-q坐标系下的数学模型，并选用id＝0的控制方法实现d、q两轴解耦，得到在id＝0控制方式下的永磁同步电机控制模型。
  8. 根据权利要求6所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤22中：基于永磁同步电机控制模型，对伺服控制系统进行设计，电流环、速度环以及位置环是三个相互关联且基于PID控制器的闭环负反馈调节系统，伺服控制系统对电流环、速度环、位置环三环进行控制，达到控制电机的输出转矩、运行速度、输出位置的目的。
  9. 根据权利要求6所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤23中：龙门机床横梁双驱动两侧选用相同的电机，通过伺服系统三环建模先进行单侧的伺服系统的三环参数整定，然后用具有相同控制参数的两伺服系统共同驱动龙门机床横梁，实现同步控制。
  10. 根据权利要求1所述的龙门机床动梁交叉耦合控制方法，其特征在于，步骤4中：DOB包括对象的传递函数P(s)、对象的名义模型Pn -1(s)、干扰观测值控制输入r、测量噪声ζ、低通滤波器Q(s)，等效干扰d；
    低通滤波器Q(s)的设计影响DOB的实际性能，故DOB的设计问题转化为低通滤波器Q(s)的设计问题，Q(s)的模型描述为：
    其中，τ是时间常数；N是分母阶数；M是分子阶数；N-M是相对阶；
    Q(s)的阶次会影响系统的稳定性，分母阶次越大，系统越稳定，高阶次的Q(s)出现相位滞后现象，削弱对干扰的补偿作用；分子阶次增大会抵消相位滞后现象，提高系统抗干扰能力，但会破坏系统稳定性；
    龙门横梁的同步控制系统的名义模型Pn(s)通过基于最小二乘法的参数辨识原理获得，采集驱动力矩信号作为输入信号和横梁端的位移信号作为输出信号来对控制对象进行参数辨识。得到的名义模型Pn(s)如(13)所示：
    以模型(13)作为两轴的名义模型，考虑控制精度、系统鲁棒性和稳定性，在满足(12)的所有式子中，模型(14)的相对阶次为2；
    模型(14)为Q31(s)型低通滤波器，时间常数为τ＝0.005s，可得：
PCT/CN2023/111894 2022-08-16 2023-08-09 一种龙门机床动梁交叉耦合控制方法 WO2024037394A1 (zh)

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