TWI719544B - The method of system identification and servo tuning - Google Patents

Abstract

The present invention provides a method of system identification and servo tuning, which excites responses of a drive systems for machine tools by the output of sweep signal to obtain the frequency responses of a velocity loop and a position loop. Through transfer function of the velocity loop and transfer function of the position loop, it calculates and identifies Rotary Inertia—J _M, damping coefficient of the rotary motion—B _M, table mass—M _t, damping coefficient of the lead-screw—C _tand stiffness coefficient of the lead-screw—K of a drive systems for machine tools by algorithm, and further identifies frictional force and value of backlash through variant velocity of the drive systems for machine tools and reciprocating operation, so as to analyze the influence which parameters of servo controller impact on the drive systems for machine tools. Through system bandwidth, it limits the resonant peak, gain margin and phase margin to find out the optimum servo controller parameters K _p, K _vpand K _vi, which are adjusted and inputted in the said servo controller. There by, it can achieve the goal of optimizing tuning and to reduce the vibration circumstance of drive system for machine tools, which guarantee its function and precision requirements.

Description

System identification and servo tuning method

The present invention provides a system identification and servo adjustment method, especially a method that can identify the tool drive system and find the most suitable servo controller parameters for the current condition of the tool drive system through intelligent algorithms, so as to improve the performance of the tool drive system. Performance and work accuracy.

According to the fact that the manufacturing industry’s requirements for the accuracy of finished products are increasing day by day, in addition to requiring certain processing quality, shortening the processing cycle is also an important goal; therefore, how to make computer numerical control (CNC) machine tools work in different processing environments It is an important issue to maintain high speed and high precision under other conditions; there are already many documents discussing the mechanical structure, motion control, feed drive system, spindle, CNC servo controller and interpolator in CNC machine tools. Propose different methods to improve processing performance; in the traditional design process, engineers need to spend a lot of time and cost to manufacture and test physical prototypes to detect areas that need improvement to optimize their design; and in the current design process, the machine is Compared with the traditional design method, the simulation prototype technology is adopted through the computer, which reduces a lot of time and cost. However, the adjustment of the machine still has to rely on experience or trial and error. This method is inefficient and cannot determine whether the servo parameters have been optimized. .

Since the performance of the machine tool system will directly affect the processing quality, the study of the five-axis feed drive model is of great significance for the development of virtual systems. At present, many documents have discussed the topic of virtual drive system, and proposed a virtual feed model, including motor structure, friction and backlash and other nonlinear characteristics and noise detection, but it assumes that the lead screw is a rigid body, and ignores the work Due to the characteristics of the table structure, the performance of the virtual feed drive system model is still reduced.

In view of this, our inventors have devoted themselves to further research on the identification and adjustment of machine tool systems, and proceeded to develop and improve them, hoping to have a better invention to solve the above problems, and after continuous testing and modification, we have the potential The invention is born.

The purpose of the present invention is to solve the aforementioned problems. In order to achieve the above objectives, our inventors provide a system identification method, the steps of which include: outputting a sweep signal in a tool drive system for sweeping, thereby stimulating the tool The drive system responds and obtains the frequency response of a speed loop and a position loop; wherein the tool drive system has at least one servo controller that controls at least one motor, at least one guide rod that is driven to rotate by the motors, and At least one driving platform respectively driven by the guide rod; establishing a speed loop transfer function, and calculating it to identify the moment of inertia J _M of the motor and the damping coefficient B _{M of the} rotary motion in the tool driving system; and establishing A position loop transfer function, and the rotational inertia and the damping coefficient of the rotational motion are substituted into the position loop transfer function, and the mass M _{t of} a driving platform, the damping coefficient Ct of the guide rod and the rigidity K of the guide rod are identified by calculation.

為

；其中，K _p、K _vp、K _vi為伺服控制器之參數，K _t為馬達轉矩常數；且其係經演算法計算以鑑別該轉動慣量J _M及阻尼係數B _M。 According to the system identification method described above, the speed loop transfer function

for

; Among them, K _p , K _vp , K _vi are the parameters of the servo controller, and K _t is the motor torque constant; and it is calculated by an algorithm to identify the moment of inertia J _M and the damping coefficient B _M.

；並限制

；其中，

及

為速度迴路之頻率響應，N _v為速度迴路之頻率響應數據之長度、

及

分別為速度迴路之頻率響應的大小及相位權重值。 According to the system identification method described above, the algorithm is a PSO (Particle Swarm Optimization) algorithm, and the optimization problem is defined as

; And limit

;among them,

and

Is the frequency response of the speed loop, N _v is the length of the frequency response data of the speed loop,

and

They are the magnitude and phase weight of the frequency response of the speed loop.

為

；其中，

According to the system identification method described above, wherein the motor, the guide rod and the driving platform of the tool driving system are arranged in a linear axis, and the position loop transfer function of the linear axis

for

;among them,

；且其係經演算法計算以鑑別該驅動平台質量M _t、導桿之阻尼係數C _t及導桿之剛性K。

; And it is calculated by an algorithm to identify the drive platform mass M _t , the damping coefficient C _t of the guide rod and the rigidity K of the guide rod.

為 According to the system identification method described above, wherein the guide rod of the tool driving system is connected to one end of the driving platform, so that the driving platform rotates around the guide rod, thereby forming the rocking table The setting of the rotation axis A, and the position loop transfer function of the rotation axis A

for

；且其係經演算法計算以鑑別該驅動平台質量M _t。

; And it is calculated by an algorithm to identify the quality of the driving platform M _t .

為 According to the system identification method described above, wherein the guide rod of the tool driving system is connected to the center of the driving platform, so that the driving platform rotates with the guide rod as the rotation axis C, and The position loop transfer function of the rotation axis C

for

；且其係經演算法計算以鑑別該轉動慣量J _M及阻尼係數B _M。

; And it is calculated by an algorithm to identify the moment of inertia J _M and the damping coefficient B _M.

According to the system identification method described above, the algorithm is a PSO (Particle Swarm Optimization) algorithm, and the optimization problem is defined as

；以及 limit

;as well as

； limit

；

及

為位置迴路之頻率響應，N _p為位置迴路之頻率響應數據長度、 w _p1及 w _p2分別為位置迴路的頻率響應之大小及相位權重值。 among them,

and

Is the frequency response of the position loop, N _p is the frequency response data length of the position loop, w _p1 and w _p2 are the magnitude and phase weight value of the frequency response of the position loop respectively.

、負轉時之黏滯摩擦係數

、黏滯摩擦之初始係數

及靜摩擦係數

。 According to the system identification method described above, the steps further include: setting a path for the tool drive system to perform variant speed operation; capturing the current data generated by the servo controller to the motor and the corresponding speed data; Establish a steady-state friction force function, and use an algorithm to identify the viscous friction coefficient during forward rotation

, Viscous friction coefficient during negative rotation

, The initial coefficient of viscous friction

And static friction coefficient

.

為

；其中，dv為受靜摩擦影響之低速範圍；透過演算法計算以鑑別該正轉時之黏滯摩擦係數

、負轉時之黏滯摩擦係數

、黏滯摩擦之初始係數

及靜摩擦係數

。 According to the system identification method described above, the steady-state friction force function

for

; Among them, dv is the low-speed range affected by static friction; calculated by algorithm to identify the viscous friction coefficient during forward rotation

, Viscous friction coefficient during negative rotation

, The initial coefficient of viscous friction

And static friction coefficient

.

According to the system identification method described above, the algorithm is a PSO (Particle Swarm Optimization) algorithm, and the objective function E _{new that} defines the optimization problem is

；

；

；

；

為誤差權重。 among them,

Is the error weight.

According to the system authentication method described above, the steps further include:

Capture the drive platform position data and motor speed data when the tool drive system moves back and forth; and when the motor reaches the same position, subtract the position between the drive platform and the guide rod, and identify a backlash through the least square method value.

The present invention also provides a servo tuning method, which is applied to the system identification method described above. The tuning steps of the speed loop include: defining the system bandwidth Bw _vel of the speed loop that maximizes the closed loop; restriction; A resonance peak dependent on the frequency response of the speed loop; defining a gain margin and phase margin dependent on the frequency response of the speed loop; defining the proportional gain value K _vp and the integral gain value K _vi among the parameters of the servo controller And obtain the proportional gain value K _vp and the integral gain value K _vi , and adjust the input to the servo controller.

為速度迴路頻率響應之最大值，且界定

。 According to the above-mentioned servo tuning method, the resonance peak

Is the maximum value of the frequency response of the speed loop, and defines

.

；其中，

為所述工具驅動系統速度迴路之開迴路轉移函數，

為相位交叉頻率；並限制增益邊限G _M>10 dB。 According to the above-mentioned servo tuning method, the gain margin G _M is

;among them,

Is the open-loop transfer function of the speed loop of the tool drive system,

Is the phase cross frequency; and limit the gain margin G _M >10 dB.

；其中，

為所述工具驅動系統速度迴路之開迴路轉移函數，

為增益交叉頻率；並限制相位邊限P _M> 45˚。 According to the above-mentioned servo tuning method, the phase margin P _M is

;among them,

Is the open-loop transfer function of the speed loop of the tool drive system,

Is the gain crossover frequency; and limits the phase margin P _M > 45˚.

為

。 According to the above-mentioned servo tuning method, _{the ratio between the proportional gain value K vp} and the integral gain value Kvi

for

.

；求得伺服控制器之參數K _p，並調整輸入於該伺服控制器。 According to the above-mentioned servo tuning method, it further includes the steps of a position loop: define the system bandwidth Bw _pos of the position loop that maximizes the closed loop; limit it to the parameter K _p of the servo controller; limit a dependent on this The resonance peak of the frequency response of the position loop; define a gain margin and phase margin that depend on the frequency response of the position loop; limit the system bandwidth of the position loop that maximizes the closed loop

; Obtain the parameter K _{p of} the servo controller, and adjust the input to the servo controller.

，且相依於該位置迴路頻率響應之共振峰值M _pp之限制為

，其中，共振峰值M _pp為位置迴路頻率響應之最大值。 According to the above-mentioned servo tuning method, the parameter K _{p of the} servo controller is limited to

, And the limit of _{the resonance peak M pp} that depends on the frequency response of the loop at that position is

, Where the resonance peak M _pp is the maximum value of the frequency response of the position loop.

According to the above-mentioned servo tuning method, the gain margin G _{M is} limited to >15dB, and the phase margin P _{M is} limited to 45˚.

According to the above-mentioned servo tuning method, the steps further include: setting a feedforward control unit on the servo controller, and defining a constant coefficient AF that the feedforward control unit is dependent on and controls the speed and acceleration; making the position loop The frequency response of is close to the level, and the minimum value of the function E that defines the optimization problem is

；擷取函數E為最小值時之常數係數AF，並對應輸入於該前饋控制單元。

; Capture the constant coefficient AF when the function E is the minimum value, and correspondingly input it to the feedforward control unit.

Based on the above description and settings, it is obvious that the present invention mainly has the following advantages and effects, which are described in detail as follows:

1. The present invention stimulates the response of the tool drive system by outputting a frequency sweep signal to obtain the frequency response of a speed loop and a position loop; and uses the transfer function of the speed loop and the transfer function of the position loop to calculate and identify the tool through an algorithm The motor moment of inertia J _{M of the} driving system, the damping coefficient B _{M of the} rotational motion, the mass of the driving platform M _t , the damping coefficient C _t of the guide rod and the rigidity K of the guide rod, and can further be driven by the tool driving system’s variant speed and The reciprocating operation is used to identify the friction and backlash values, so as to analyze the influence of the servo controller parameters on the tool drive system, and then achieve the purpose and effect of identifying the tool drive system.

_{2. The present invention can also find the best servo controller parameters K p} , K _vp , K _{vi based on the} aforementioned identification results, through the system bandwidth, and to limit the resonance peak, gain margin and phase margin , And adjust the input to the servo controller to achieve the purpose of optimizing the adjustment, thereby reducing the vibration phenomenon of the tool driving system, and improving the performance and working accuracy of the tool driving system.

Regarding the technical means of our inventors, several preferred embodiments are described in detail below in conjunction with the drawings, in order to provide a thorough understanding and approval of the present invention.

The present invention provides a system identification and servo adjustment method. In a specific embodiment, it is mainly used to identify a tool drive system 1. As far as the tool drive system 1 is concerned, it can be a five-axis CNC machine tool. It contains three linear axes (X-axis, Y-axis, and Z-axis) and two rotary axes (A-axis and C-axis). As shown in Figure 1, it mainly includes a host computer 11, a servo controller 12, and A mechanical structure 13; among them, as far as the host computer 11 is concerned, it is mainly created by the operator through a numerical control (NC) program or using a CAD/CAM application program to generate discrete numerical position commands for each servo controller 12; servo control The controller 12 can be divided into a PID (Proportional Integral Derivative) controller 121 and a feedforward control unit 122; in one embodiment, the servo controller 12 is based on three loop control, including current loop control, speed loop control and Position loop control, so high-performance motion control can be provided by adjusting the parameters of the servo controller 12; the mechanical structure 13 can be divided into a motor 131, a guide rod 132 and a drive platform 133. The servo controller 12 is coupled and sends commands to The motor 131 generates torque to rotate the driving guide rod 132 and then drive it to the driving platform 133. The guide rod 132 may be a screw rod;

The linear axis model system of the tool drive system 1 is shown in Figure 2, where T is the torque of the motor 131 [Nm], J _m is the moment of inertia of the motor 131 [kgm ² ], and B _m is the damping coefficient of the rotary motion [ Ns / m], M _t is the mass of the drive platform 133 [kg], C _t is the damping coefficient of the guide rod 132 [Ns / m], K is the rigidity of the guide rod 132 [N / m], R is the rotation from the motor 131 The conversion ratio of the angle to the position of the drive platform 133 [mm / rev], θ _m is the rotation angle of the motor 131 [rad], and x _act is the position of the drive platform 133 [m];

As far as the rotating shaft model is concerned, the mechanical structure 13 of the A-axis is a shaker structure. As shown in Figure 3, the guide rod 132 is connected to one end of the driving platform 133, so that the driving platform 133 can be moved around. The guide rod 132 rotates, thereby forming the setting of the rotating shaft A of the rocking table structure. The mechanical structure 13 of the C axis is the rotating platform of the direct drive mechanism. As shown in Figure 4, the guide rod 132 is connected to The center of the driving platform 133 allows the driving platform 133 to rotate with the guide rod 132 as the rotation axis C.

是角度指令，

是驅動平台133角度，

是角速度指令，

是表角速度；該工具驅動系統1包含前饋控制單元122，其係可用於改善伺服系統性能，前饋控制單元122包括速度及加速度前饋控制，其中 VF是前饋控制系統的開關； VF的值為1或0，如果 VF= 1，則表示打開前饋控制系統；反之，如果 VF= 0，則意味著關閉前饋控制系統； AF是加速度前饋控制系統的常數係數。 In one embodiment, a complete five-axis CNC tool drive system 1 is shown in Figure 5, where K _p is a position controller, in this embodiment a proportional ( P ) controller is used, and K _v is a speed control , a system using the present embodiment, proportional-integral (PI) controller, K _i is a current controller according to the present embodiment based PI controller is used, L _a is the armature inductance, R _a is the armature resistance, K _t is Torque constant, K _e is the electromagnetic interference and electric field (EMF) constant, ω _cmd is the angular velocity command, x _cmd is the position command,

Is the angle command,

Is the 133 angle of the drive platform,

Is the angular velocity command,

Is the surface angular velocity; the tool driving system 1 includes a feedforward control unit 122, which can be used to improve the performance of the servo system, the feedforward control unit 122 includes speed and acceleration feedforward control, where VF is the switch of the feedforward control system; VF The value is 1 or 0. If VF = 1, it means that the feedforward control system is turned on; on the contrary, if VF = 0, it means that the feedforward control system is turned off; AF is the constant coefficient of the acceleration feedforward control system.

In one implementation, the tool drive system 1 of the present invention is a Microcut-MCU-5X five-axis machine tool, which is equipped with a HEIDENHAIN controller and TNC640, and by using HEIDENHAIN software such as TNCOPT, TNCSCOPE, TNCREMO, etc., the computer can be directly connected The controller obtains operating data such as the spindle speed of the motor 131, the position of the driving platform 133, the speed and acceleration of each axis, and so on.

[Identification of speed loop and position loop]

Therefore, the present invention uses a sinusoidal frequency sweep signal for system identification, and obtains the corresponding frequency response through the servo-oriented software TNCOPT, and the sinusoidal frequency sweep function does not include a feedforward controller; the implementation steps are as follows:

S001: Output a frequency sweep signal in a tool driving system 1 to perform frequency scanning, so as to stimulate the tool driving system 1 to respond, and obtain the frequency response of a speed loop and a position loop of each axis; as shown in Figures 6a to 6e.

為

；其中，K _p、K _vp、K _vi為伺服控制器12之參數，K _t為馬達131轉矩常數；且其係經演算法計算以鑑別該轉動慣量J _M及阻尼係數B _M； S002: Establish a speed loop transfer function, and perform calculations to identify the moment of inertia J _M of the motor 131 and the damping coefficient B _{M of the} rotary motion in the tool drive system 1; in one embodiment, the speed loop transfer function

for

; Among them, K _p , K _vp , K _vi are the parameters of the servo controller 12, and K _t is the torque constant of the motor 131; and it is calculated by an algorithm to identify the moment of inertia J _M and the damping coefficient B _M ;

The present invention is mainly calculated through the PSO (Particle Swarm Optimization) algorithm. Since the PSO algorithm is easy to implement and has fewer selection parameters to provide calculation efficiency, it is mainly based on the definition of optimization problems and particle update standards. Among them, The particle update is mainly composed of three parts; the first part is the current speed affecting the effect of inertial motion; the second part is the cognitive part, based on the particle's own judgment; the third part is the social part, searching for solutions based on the best solution of the group Space; the present invention uses the linear adjustment of the learning factor of the PSO algorithm, and the linear adjustment of the learning factor is expressed as:

為正常數；

及

。

是允許的最大迭代數， g是粒子的當前迭代次數。 among them,

Is a normal number;

and

.

Is the maximum number of iterations allowed, and g is the current number of iterations of the particle.

）；並且將每顆粒子的當前解作為其局部最優解（

）；在初始群體粒子中，找到適應值的極值作為群體最優適應值（

）；並將具有群體最優適應值的粒子的位置作為群體最優解（

）；在每次迭代後，更新粒子參數時，重新計算粒子適應值；比較適應值的變化並更新最佳適應值和解決方案。 Take the current fitness value of each particle as the local optimal fitness value of each particle (

); and take the current solution of each particle as its local optimal solution (

); In the initial population particles, find the extreme value of the fitness value as the optimal fitness value of the group (

); and take the position of the particle with the optimal fitness value of the group as the optimal solution of the group (

); After each iteration, when the particle parameters are updated, the particle fitness value is recalculated; the changes in the fitness value are compared and the best fitness value and solution are updated.

Therefore, regarding the speed loop transfer function, the optimization problem can be expressed as

；

；

； And limit

；

及

為TNCOPT測量速度迴路之頻率響應，N _v為速度迴路之頻率響應數據之長度、

及

分別為速度迴路之頻率響應的大小及相位權重值；藉此，即可鑑別速度迴路中之轉動慣量J _M及阻尼係數B _M。 among them,

and

For TNCOPT to measure the frequency response _{of the speed loop, N v} is the length of the frequency response data of the speed loop,

and

They are the magnitude of the frequency response of the speed loop and the phase weight value; by this, the moment of inertia J _M and the damping coefficient B _M in the speed loop can be identified.

For the speed loop, the system uses a frequency response of 1-300 [rad / s], because this frequency response range is mainly used for processing.

為

；其中，

S003: Establish a position loop transfer function, and substitute the rotational inertia and the damping coefficient of the rotational motion into the position loop transfer function, and the mass M _{t of} a driving platform 133, the damping coefficient Ct of the guide rod 132, and the guide rod 132 are identified by calculation The rigidity K; in one embodiment, according to the linear axis model, the position loop transfer function

for

;among them,

；且其係經演算法計算以鑑別該驅動平台133質量M _t、導桿132之阻尼係數C _t及導桿132之剛性K。

; And it is calculated by an algorithm to identify the mass M _{t of} the drive platform 133, the damping coefficient C _t of the guide rod 132 and the rigidity K of the guide rod 132.

為 The structure of the rotary axis (A axis and C axis) is different from that of the linear axis; the mechanical structure 13 of the A axis is a shaker structure; and the position loop transfer function of the rotary axis A

for

。

.

為 The mechanical structure 13 of the C-axis is a direct drive mechanism, and the power from the motor 131 is not reduced, so it can only identify the moment of inertia J _M and the damping coefficient B _M , the position loop transfer function of the rotating shaft C

for

。

.

By using the PSO algorithm, the parameters of the position loop can be identified; in addition, the corresponding optimization problems for the linear axis and the rotary axis are

；以及 limit

;as well as

； limit

；

及

為位置迴路之頻率響應，N _p為位置迴路之頻率響應數據長度、 w _p1及 w _p2分別為位置迴路的頻率響應之大小及相位權重值；藉此，即可鑑別驅動平台133質量M _t、導桿132之阻尼係數Ct及導桿132之剛性K。 among them,

and

Is the frequency response of the position loop, N _p is the frequency response data length of the position loop, w _p1 and w _p2 are the size and phase weight value of the frequency response of the position loop, respectively; by this, the quality of the driving platform 133 M _t , The damping coefficient Ct of the guide rod 132 and the rigidity K of the guide rod 132.

The goal of identification is to ensure that the overall frequency response, bandwidth and resonance frequency are correct. To speed up identification, use the moment of inertia J _M and the damping coefficient B _{M of the} speed loop identification result as known knowledge to identify the position loop parameters.

Among them, the parameter settings of the PSO algorithm used in the present invention are shown in Table 1 below:

【Table 1】 parameter Speed loop Position loop Number of particles 35 30 Number of iterations 1000 1500 Inertial weighing ( w ) 0.9 1 Learning parameters c _{1 b} 1.5 1.5 c _{1 s} 0.5 0.5 c _{2 b} 1.5 1.5 c _{2 s} 0.5 0.5 Wrong weighing w _{v 1} =1 w _{p 1} = 1 w _{v 2} = 0.3 w _{p 2} = 0.2

The identification result parameters of each axis are shown in Table 2 below:

0.038085 0.055463 0.030151 0.030324 1.8874 Bm (Ns/m) 5.1249 8.8442 3.4242 3.8205 0.5 M _t / m(kg) 241.0744 655.6798 123.8739 311.5166 X C _t (Ns/m) 3.4295

9.7142

4.1544

X X K(N/m) 1.4571

1.0069

1.0237

X X 【Table 2】 parameter X axis Y axis Z axis A axis C axis

0.038085 0.055463 0.030151 0.030324 1.8874 Bm (Ns/m) 5.1249 8.8442 3.4242 3.8205 0.5 M _t / m (kg) 241.0744 655.6798 123.8739 311.5166 X C _t (Ns/m) 3.4295

9.7142

4.1544

X X K (N/m) 1.4571

1.0069

1.0237

X X

[Identification of Friction]

、負轉時之黏滯摩擦係數

、黏滯摩擦之初始係數

及靜摩擦係數

。 Since the nonlinear phenomenon affects the performance of the tool drive system 1, in the feed drive system, the friction and backlash of the nonlinear phenomenon cannot be ignored; in one embodiment of the present invention, the variable speed data obtained by the circular test is used to To identify friction, it is not necessary to obtain a large amount of speed data and current data at each different speed as known, but only one path is set for the tool drive system 1 to perform variable speed operation; capture the servo controller 12 Generate current data and corresponding speed data commanded to the motor 131; establish a steady-state friction force function, and use an algorithm to identify the viscous friction coefficient during forward rotation

, Viscous friction coefficient during negative rotation

, The initial coefficient of viscous friction

And static friction coefficient

.

表示為 In a specific embodiment, the present invention uses a simplified friction force model, as shown in Figure 7, and the simplified steady-state friction force function

Expressed as

；其中，dv為受靜摩擦影響之低速範圍；此外，摩擦力在運動轉向時具有更明顯的影響，因此，本發明係於不同速度使用不同的學習權重予以鑑別之，即對於較低速度使用較大的權重並且對較高速度使用較小的權重。因此，選擇優化的目標函數E _new為

; Among them, dv is the low-speed range affected by static friction; in addition, friction has a more obvious impact on the movement and steering. Therefore, the present invention uses different learning weights to identify different speeds, that is, the use of higher speeds for lower speeds Large weights and use smaller weights for higher speeds. Therefore, the optimized objective function E _new is selected as

；

；

；

；

是誤差權重。 among them,

Is the error weight.

The PSO algorithm parameter settings for friction identification are shown in Table 3 below:

【table 3】 parameter Simplified model Number of particles 20 Number of iterations 300 Inertial weighing ( w ) 0.9 Learning parameters c _{1 b} 1.5 c _{1 s} 0.5 c _{2 b} 1.5 c _{2 s} 0.5

The friction identification results of the present invention are shown in Table 4 below:

0.0003399 0.0002776 0.0003542 0.0007542 0.0001880

0.0003399 0.0002474 0.0003542 0.0011542 0.0001880

0.9421 0.9971 0.8479 1.1479 0.6255

1.5685 1.4357 1.5416 1.5816 0.7209

10 10 10 10 5 【Table 4】 parameter X axis Y axis Z axis A axis C axis

0.0003399 0.0002776 0.0003542 0.0007542 0.0001880

0.0003399 0.0002474 0.0003542 0.0011542 0.0001880

0.9421 0.9971 0.8479 1.1479 0.6255

1.5685 1.4357 1.5416 1.5816 0.7209

10 10 10 10 5

[Identification of Backlash]

Through the single-axis back and forth movement of the tool driving system 1, the position signal of the driving platform 133 and the speed signal of the motor 131 can be obtained by the linear scale and the rotary encoder. Therefore, by calculating the speed of the motor 131 to obtain the position signal of the guide rod 132, the relationship between the position signal of the guide rod 132 and the position signal of the driving platform 133 can be obtained; as shown in Figure 8, the relationship between the guide rod 132 and the driving platform 133 The backlash indicates that x _act is the position of the driving platform 133, x _l is the position of the guide rod 132, and D _b is the backlash value; it can also indicate the driving platform 133 and the guide rod 132 when moving forward or backward The theoretical error value is half of the backlash value. In order to ensure that the error between the guide rod 132 and the platform remains at half of the backlash value, the moving speed needs to be very slow. During the back and forth movement, the position data of the drive platform 133 is captured. And motor 131 speed data. When the motor 131 reaches the same position, compare the position error of the front and rear platforms, subtract the position between the driving platform 133 and the guide rod 132, and identify a backlash value through the least square method. Expressed as:

為驅動平台133及導桿132之間之位置差值，L 是路徑數據的長度。 among them,

Is the position difference between the driving platform 133 and the guide rod 132, and L is the length of the path data.

[Servo Tuning Method-Speed Loop]

Since the response of the tool drive system 1 is too fast, it will often cause structural vibration, so by adjusting its parameters, its stability, performance and working accuracy can be improved.

As shown in Figure 9, the present invention also provides a servo tuning method, which is applied to the system identification method described above, and in one embodiment is actually applied to MCU-5X with a HEIDENHAIN controller. The frequency response of the speed loop is used to adjust the parameters of the speed controller, and its purpose is to maximize the system bandwidth of the closed loop speed loop, so as to obtain better response performance and improve the steady-state error; the adjustment steps of the speed loop include:

_{Define the system bandwidth Bw vel} of the speed loop that maximizes the closed loop;

為速度迴路頻率響應之最大值，且界定

，限制共振峰值之目的在於避免更大的過衝及振動情形； Limit a resonance peak that depends on the frequency response of the speed loop; in one embodiment, the resonance peak

Is the maximum value of the frequency response of the speed loop, and defines

, The purpose of limiting the resonance peak is to avoid greater overshoot and vibration;

；其中，

為所述工具驅動系統1速度迴路之開迴路轉移函數，

為相位交叉頻率；並限制增益邊限G _M>10 Db；該相位邊限P _M為

；其中，

為所述工具驅動系統1速度迴路之開迴路轉移函數，

為增益交叉頻率；並限制相位邊限P _M> 45˚。 Define a gain margin and phase margin that depend on the frequency response of the speed loop. The gain margin and phase margin are used to confirm the stability and robustness of the overall system; in one embodiment, the gain margin G _M is

;among them,

Is the open-loop transfer function of the speed loop of the tool drive system 1,

Is the phase cross frequency; and limit the gain margin G _M >10 Db; the phase margin P _M is

;among them,

Is the open-loop transfer function of the speed loop of the tool drive system 1,

Is the gain crossover frequency; and limits the phase margin P _M > 45˚.

為

。 _{Defines the ratio between the proportional gain value K vp} and the integral gain value K _{vi in} the parameters of the servo controller 12; in one embodiment, the ratio between the proportional gain value K _vp and the integral gain value Kvi

for

.

Under the condition that the above constraint conditions are met, the proportional gain value K _vp and the integral gain value K _{vi are obtained} , and the adjustment input is input to the servo controller 12 to achieve the goal of optimizing the speed loop of the tool drive system 1.

[Servo Tuning Method-Position Loop]

The servo tuning method of the present invention further includes a step of a position loop. The frequency response data of the position loop is used to adjust the parameters of the position controller. The steps include:

Defining the optimization problem is to maximize the system bandwidth Bw _pos of the position loop of the closed loop;

，

增加的目標為提高響應速度；惟，

過大會導致位置迴路的共振峰變大甚至使系統變得不穩定，故須予限定； It is limited to the parameter K _p of the servo controller 12; in one embodiment, the parameter K _{p of the} servo controller 12 is limited to

,

The goal of the increase is to improve the response speed; however,

Too big will cause the resonance peak of the position loop to become larger and even make the system unstable, so it must be limited;

，其中，共振峰值M _pp為位置迴路頻率響應之最大值；其中，限制共振峰值係可避免更大的過衝和振動情形；由於位置迴路將直接影響產品的軌跡和質量，故過衝的限制比速度迴路更嚴謹。 Limit a resonance peak dependent on the frequency response of the position loop; in one embodiment, the limit of _{the resonance peak M pp dependent on the frequency response of the position loop is}

, Where the resonance peak M _pp is the maximum value of the frequency response of the position loop; among them, limiting the resonance peak can avoid greater overshoot and vibration; because the position loop will directly affect the trajectory and quality of the product, the overshoot is limited More rigorous than the speed loop.

Define a gain margin and phase margin that depend on the frequency response of the position loop; in one embodiment, limit the gain margin G _M > 15dB and limit the phase margin P _M >45˚; the gain margin of the position loop The limit and phase limit are used to confirm the stability and robustness of the system. During processing, the external load will directly affect the gain limit and phase limit of the position loop. Therefore, the gain limit and phase limit are more limited than the speed loop. tolerant.

；在符合上述約束條件的情況下，求得伺服控制器12之參數K _p，並調整輸入於該伺服控制器12，藉以優化工具驅動系統1之位置迴路。 Limit the system bandwidth of the position loop that maximizes the closed loop

; Under the condition that the above-mentioned constraint conditions are met, the parameter K _{p of} the servo controller 12 is obtained and adjusted and input to the servo controller 12 to optimize the position loop of the tool drive system 1.

[Servo Tuning Method-Position Loop with Feedforward Control Unit 122]

The aforementioned servo tuning method is to adjust the parameters of the speed controller and the position controller without the feedforward control unit 122. Here, consider the influence of the feedforward control unit 122 on the frequency response of the position loop, and adjust the feedforward control. Therefore, the optimization problem of the parameters of the unit 122 is to make the frequency response close to the level. By appropriately setting the feedforward parameters, the response distortion can be avoided and the servo lag can be eliminated. The steps further include: defining the feedforward control unit 122 dependent and controlling the speed and acceleration A constant coefficient AF; make the frequency response of the position loop close to the level, and define the minimum value of the function E of the optimization problem as

；擷取函數E為最小值時之常數係數AF，並對應輸入於該前饋控制單元122；前饋控制單元122之功能可以改善伺服落後和響應衰減，故加工頻率在位置迴路的頻寬內，藉可避免響應失真。

; Capture the constant coefficient AF when the function E is the minimum value, and correspondingly input it to the feedforward control unit 122; the function of the feedforward control unit 122 can improve the servo lag and response attenuation, so the processing frequency is within the bandwidth of the position loop , Which can avoid response distortion.

The parameter settings of the PSO algorithm used in the servo tuning method of the present invention are shown in Table 5 below:

【table 5】 parameter Speed loop Position loop Position loop with feedforward control unit 122 Number of particles 10 10 20 Number of iterations 300 300 300 Inertial weighing (w) 0.9 1 0.9 Learning factory c _{1 b} 1.5 1.2 1.5 c _{1 s} 0.5 0.2 0.5 c _{2 b} 1.5 1.2 1.5 c _{2 s} 0.5 0.2 0.5

The preset parameters of each axis before adjustment are shown in Table 6 below:

【Table 6】 parameter X axis Y axis Z axis A axis C axis K _p 48 32 60 16 32 K _vp 10 10 8 12 200 K _vi 1000 1000 800 1400 20000 VF 1 1 1 1 1 AF 0.0282 0.0458 0.0251 0.02 1.2333

The bandwidth values of each axis before tuning are shown in Table 7 below:

【Table 7】 Bandwidth value (Hz) X axis Y axis Z axis A axis C axis Bw _{Vel .} 42.866 22.18 47.881 73.623 41.109 Bw _{Pos .} 8.52 6.41 12.026 1.302 5.562 Bw _{Cri .} 61.817 38.756 61.388 x 23.97

The servo controller 12 parameters of each axis after adjustment are shown in Table 8 below:

【Table 8】 parameter X axis Y axis Z axis A axis C axis K _p 69 46 100 36 61 K _vp 18 20 15 twenty four 496 K _vi 1890 1941 1575 2546 49825 VF 1 1 1 1 1 AF 0.0364 0.0776 0.0349 0.008 1.1799

The bandwidth values of each axis after tuning are shown in Table 9 below:

【Table 9】 Bandwidth value (Hz) X axis Y axis Z axis A axis C axis Bw _{Vel .} 84.375 55.449 93.209 147.238 82.218 Bw _{Pos .} 12.838 8.935 20.391 3.67 11.121 Bw _{Cri .} 51.552 32.294 51.807 x 122.774

Please also refer to the figures 10a.1 to 10e.3. It can be observed that the bandwidth of the speed loop and position loop has been improved, and the frequency response of the final servo tuning result is better than before the tuning.

In order to verify that the optimization of the servo adjustment method can be effectively applied to the tool drive system 1, the time domain experiment is used to prove the result of the servo adjustment, and the circular test is used here, and the feed rate is 1200 [mm / min] and the radius 1 is set. [mm] Perform verification, as shown in the contour error of the circular trajectory experiment in Figures 11a to 11c and Table 10 below:

【Table 10】 path Contour error Tracking error round Root mean square error (mm) Maximum (mm) Root mean square error (mm) Maximum (mm) XY circle before 0.0102 0.0215 0.5089 0.5228 Rear 0.0046 0.0118 0.5060 0.5133 improve 54.9% 45.1% 0.57% 1.82% XZ circle before 0.0066 0.0142 0.5087 0.5140 Rear 0.0029 0.0068 0.5064 0.5085 improve 56.1% 52.1% 0.45 1.07% YZ circle before 0.0101 0.0190 0.5092 0.5218 Rear 0.0049 0.0116 0.5067 0.5133 improve 51.5% 38.9% 0.49% 1.63%

From the foregoing, it can be observed that the contour error is significantly improved, and the tracking error is slightly improved. After comparing the contour error and the degree of improvement of the tracking, it is obvious that the servo tuning result of the present invention is reliable.

[Machine aging diagnosis method]

When the machine is aging, the machine is usually more prone to vibration, bandwidth changes, and system response changes. Therefore, the change of the parameters in the aforementioned identification method can be used to diagnose whether the machine is aging. The steps are as follows :

S004: Define a variation value and a threshold value. The variation value is selected from at least one of the bandwidth BW, the first resonance frequency F _r , the moment of inertia J _m , the damping coefficient B _m , the damping coefficient C _t and the rigidity The group formed by K;

S005: Repeatedly record the variation value at each time point in the aforementioned identification method, and diagnose that the tool driving system 1 is aging when the variation value of the variation value is greater than the threshold value.

In a specific embodiment, as shown in Figures 12a to 12c, they are _{the system response of the variation of the damping coefficient B m} of the motor 131, the variation of the damping coefficient C _{t of the} guide rod 132, and the variation of the stiffness K of the guide rod 132, which can be observed When the variation of the damping coefficient B _{m of the} motor 131 corresponds to the deterioration of the system response; when the _{variation of the damping coefficient C t of the} guide rod 132 corresponds to the increase of the system resonance peak; when the variation of the stiffness K of the guide rod 132 corresponds to the decrease of the system resonance frequency and the resonance peak It becomes larger, so the aging of the machine can be judged by identifying the variation of the parameters.

In addition, the changes in bandwidth, resonance frequency, and resonance peak can be observed from the frequency domain signal. In addition, the profile error and tracking error deterioration can be observed from the time domain signal; therefore, in a specific embodiment, the change is The value includes stiffness K, bandwidth BW and first resonance frequency F _r , and the threshold is set to -20%; when stiffness K, bandwidth BW, and first resonance frequency F _r decrease at the same time by 20%, it is judged It has been aging, it is recommended to adjust or maintain the machine.

In another embodiment, the tool driving system 1 can also be operated by defining a path, such as a circular test; and recording and comparing the running trajectory of the tool driving system 1; and by setting an error value; and It is diagnosed that the tool driving system 1 is aging when the error of the trajectory compared to the path is greater than the error value.

In another embodiment, it is also possible to identify the steady-state friction force as described above, and diagnose that the tool driving system 1 is aging when it is greater than the threshold.

When it is diagnosed as aging, the aforementioned servo tuning method or related maintenance can be performed to improve the performance and accuracy after aging.

In summary, the technical means disclosed in the present invention can effectively solve the conventional problems and achieve the expected purpose and effect. It has not been seen in the publications, has not been used publicly, and has long-term progress before the application. The patent law claims that the invention is correct. Yan filed an application in accordance with the law and prayed that Jun Shanghui would give a detailed examination and grant a patent for invention.

However, the above are only a few preferred embodiments of the present invention, and should not be used to limit the scope of implementation of the present invention, that is, all equivalent changes and modifications made in accordance with the scope of the patent application of the present invention and the content of the invention specification are It should still fall within the scope of the invention patent.

1 Tool drive system 11 Main computer 12 Servo controller 121 PID controller 122 Feedforward control unit 13 Mechanical structure 131 Motor 132 guide rod 133 Drive Platform

Figure 1 is a schematic diagram of the basic structure of the tool drive system of the present invention. Figure 2 is a schematic diagram of the structure of the linear axis model of the present invention. Figure 3 is a schematic diagram of the structure of the A-axis rotating shaft model of the present invention. Figure 4 is a schematic diagram of the structure of the C-axis rotating shaft model of the present invention. Figure 5 is a schematic diagram of the structure of the tool drive system of the present invention. Figure 6a is the signal diagram of the input signal and output signal of the position loop and the speed loop of the X axis. Figure 6b is the signal diagram of the input signal and output signal of the Y-axis in the position loop and the speed loop. Figure 6c is the signal diagram of the input signal and output signal of the Z axis in the position loop and the speed loop. Figure 6d is the signal diagram of the input signal and output signal of the A axis in the position loop and the speed loop. Figure 6e is the signal diagram of the input signal and output signal of the C axis in the position loop and the speed loop. Figure 7 is a schematic diagram of the simplified friction model of the present invention. Figure 8 is a schematic diagram of the backlash between the guide rod and the driving platform of the present invention. Figure 9 is a simplified flow chart of the servo tuning method of the present invention. Figure 10a.1 is a comparison diagram of signals before and after adjustment of the X axis in the speed loop of the present invention. Figure 10a.2 is a comparison diagram of the signals before and after adjustment of the X axis in the position loop of the present invention. Figure 10a.3 is a comparison diagram of signals before and after tuning of the X-axis in the feedforward position loop of the present invention. Figure 10b.1 is a comparison diagram of the signals before and after adjustment of the Y-axis in the speed loop of the present invention. Figure 10b.2 is a comparison diagram of signals before and after adjustment of the Y-axis in the position loop of the present invention. Figure 10b.3 is a comparison diagram of signals before and after adjustment of the Y-axis in the feedforward position loop of the present invention. Figure 10c.1 is a comparison diagram of signals before and after adjustment of the Z axis in the speed loop of the present invention. Figure 10c.2 is a comparison diagram of signals before and after adjustment of the Z axis in the position loop of the present invention. Figure 10c.3 is a comparison diagram of signals before and after adjustment of the Z axis in the feedforward position loop of the present invention. Figure 10d.1 is a comparison diagram of the signals before and after adjustment of the A-axis in the speed loop of the present invention. Figure 10d.2 is a comparison diagram of the signals before and after adjustment of the A-axis in the position loop of the present invention. Figure 10d.3 is a comparison diagram of signals before and after adjustment of the A-axis in the feedforward position loop of the present invention. Figure 10e.1 is a comparison diagram of the signals before and after adjustment of the C axis in the speed loop of the present invention. Figure 10e.2 is a comparison diagram of signals before and after adjustment of the C axis in the position loop of the present invention. Figure 10e.3 is a comparison diagram of signals before and after adjustment of the C-axis in the feedforward position loop of the present invention. Figure 11a is a comparison diagram of the contour error of the trajectory of the present invention in the XY plane before and after the adjustment of the machine. Figure 11b is a comparison diagram of the contour error of the trajectory before and after adjusting the machine in the XZ plane of the present invention. Figure 11c is a comparison diagram of the contour error of the trajectory of the present invention in the YZ plane before and after the adjustment of the machine. Figure 12a is a signal comparison diagram of the attenuation of the damping coefficient of the motor of the present invention. Figure 12b is a signal comparison diagram of the attenuation of the damping coefficient of the guide rod of the present invention. Figure 12c is a signal comparison diagram of the attenuation of the rigidity of the guide rod of the present invention.

Claims (18)

A system identification method, the steps include: outputting a frequency sweep signal in a tool driving system to perform frequency scanning, thereby stimulating the response of the tool driving system, and obtaining the frequency response of a speed loop and a position loop; wherein, the tool driving system has At least one servo controller, which controls at least one motor, at least one guide rod driven and rotated by the motor, and at least one driving platform respectively driven by the guide rod; establishes a speed loop transfer function, and calculates it To identify the moment of inertia J _M of the motor and the damping coefficient B _{M of the} rotary motion in the tool drive system; the speed loop transfer function

(s) is

; Among them, K _p , K _vp , K _vi are the parameters of the servo controller, and K _t is the motor torque constant; and it is calculated by an algorithm to identify the moment of inertia J _M and the damping coefficient B _M ; the algorithm is PSO (Particle Swarm Optimization) algorithm, and define the optimization problem as

; And limit

,

>0; where G _v ( jω _i )| _{dB and} ∠ G _v ( jω _i )| _{dB are} the frequency response _{of the speed loop, N v} is the length of the frequency response data of the speed loop, w _{v 1} and w _{v 2} respectively Is the magnitude and phase weight value of the frequency response of the speed loop; and establishes a position loop transfer function, and substitutes the rotational inertia and the damping coefficient of the rotational motion into the position loop transfer function, and the mass of a driving platform M _t , The damping coefficient C _t of the guide rod and the rigidity K of the guide rod. The system identification method according to claim 1, wherein the motor, the guide rod and the driving platform of the tool driving system are arranged in a linear axis, and the position loop transfer function of the linear axis

(s) is

; among them,

,

,

,

And it is calculated by an algorithm to identify the mass M _{t of} the driving platform, the damping coefficient C _t of the guide rod and the rigidity K of the guide rod. The system identification method according to claim 1, wherein the guide rod of the tool driving system is connected to one end of the driving platform, so that the driving platform rotates around the guide rod, thereby forming a rocker The setting of the rotary axis A of the bed, and the position loop transfer function of the rotary axis A

(s) is

And it is calculated by an algorithm to identify the quality of the driving platform M _t . The system identification method according to claim 1, wherein the guide rod of the tool driving system is connected to the center of the driving platform, so that the driving platform rotates with the guide rod as the rotation axis C , And the position loop transfer function of the rotation axis C

(s) is

And it is calculated by an algorithm to identify the moment of inertia J _M and the damping coefficient B _M. The system identification method according to any one of claim 1 to claim 4, wherein the algorithm is a PSO (particle swarm optimization) algorithm, and the optimization problem is defined as

limit

,

,

>0; and

limit

,

,

>0; where G _p ( jω _i )| _dB and ∠ G _p ( jω _i ) are the frequency response _{of the position loop, N p} is the frequency response data length of the position loop, w _p1 and w _p2 are the frequency of the position loop respectively The magnitude and phase weight of the response. The system identification method according to claim 1, wherein the steps further include: setting a path for the tool drive system to perform variable speed operation; capturing the current data and the corresponding speed generated by the servo controller to the motor Data; establish a steady-state friction function, and use an algorithm to identify the viscous friction coefficient f _a during forward rotation, the viscous friction coefficient during negative rotation f _b , the initial coefficient of viscous friction f _d and the static friction coefficient f _d . The system identification method according to claim 6, wherein the steady-state friction function F _ss,new is

; Among them, dv is the low-speed range affected by static friction; the viscous friction coefficient f _a during forward rotation, the viscous friction coefficient f _b during negative rotation, the initial viscous friction coefficient f _d and The coefficient of static friction f _d . The system identification method according to claim 7, wherein the algorithm is a PSO (particle swarm optimization) algorithm, and the objective function E _{new that} defines the optimization problem is

subject to

,

,

,

,and dv >0

-

>0; Among them, w ₁ and w ₂ are error weights. The system identification method according to claim 1, wherein the steps further include: acquiring the driving platform position data and motor speed data when the tool driving system moves back and forth; and when the motor reaches the same position, driving the platform and the guide rod Subtract the positions between the two, and identify a backlash value through the least square method. A servo tuning method, which is applied to the system identification method described in any one of claim 1 to claim 9, and the tuning steps of the speed loop include: defining the system that maximizes the closed loop speed loop Bandwidth Bw _vel ; limit a resonance peak dependent on the frequency response of the speed loop; define a gain margin and phase margin dependent on the frequency response of the speed loop; define the proportional gain value K _{vp in} the parameters of the servo controller and The ratio between the integral gain value K _vi ; and the proportional gain value K _vp and the integral gain value K _{vi are obtained} , and the adjustment input is input to the servo controller. The servo tuning method according to claim 10, wherein the resonance peak value M _vp is the maximum value of the frequency response of the speed loop, and M _{vp is defined}

1.5. The servo tuning method according to claim 10, wherein the gain margin G _M is

Among them, GH _v ( jω ) is the open-loop transfer function of the speed loop of the tool driving system, and ω _c is the phase cross frequency; and the gain margin G _{M is} limited to >10dB. The servo tuning method according to claim 10, wherein the phase margin P _M is P _M =180 ° +∠[ GH _v ( jω _g )]; wherein, GH _v ( jω ) is the tool drive system The open-loop transfer function of the speed loop, ω _g is the gain crossover frequency; and the phase margin P _{M is} restricted to >45°. The servo tuning method according to claim 10, wherein the ratio R _pi between the proportional gain value Kvp and the integral gain value Kvi is R _pi = K _vi / K _vp = 100±5%. The servo tuning method described in any one of claim 10 to claim 14, further includes a position loop step: define the system bandwidth Bw _pos of the position loop that maximizes the closed loop; limit it to the servo controller The parameter K _p ; limit a resonance peak that depends on the frequency response of the position loop; define a gain margin and phase margin that depend on the frequency response of the position loop; limit the system bandwidth Bw _{pos of the position loop that maximizes the closed loop .} <

; Obtain the parameter K _{p of} the servo controller, and adjust the input to the servo controller. The servo tuning method according to claim 15, wherein the parameter K _{p of the} servo controller is limited to K _p

_{100, and the resonant peak value M pp} of the frequency response of the loop depends on the position and the limit is M _pp

1. Among them, the resonance peak Mpp is the maximum value of the frequency response of the position loop. The servo tuning method according to claim 15, wherein the gain margin G _M is restricted to >15 dB, and the phase margin P _{M is} restricted to 45°. According to the servo tuning method of claim 15, the steps further include: arranging a feedforward control unit in the servo controller, and defining a constant coefficient AF that the feedforward control unit is dependent on and controls the speed and acceleration; The frequency response of the position loop is close to the level, and the minimum value of the function E that defines the optimization problem is

The constant coefficient AF when the function E is the minimum value is captured and input into the feedforward control unit correspondingly.

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