CNC milling machine is an important equipment for machining profiled contour parts in the mechanical industry. The main function of the controller is to issue motion instructions according to the parts' NC machining program to track the given track. The current trend of numerical control machining has been toward high speed and high precision. Development, in order to achieve high production efficiency and processing accuracy. Trajectory controllers with feedback control based on conventional control algorithms have not been able to meet this requirement. Such controllers can achieve certain control accuracy at lower trajectory vector speeds. As the rate of change of the control speed vector increases, the delay phenomenon increases significantly and the trajectory error increases. The purpose of adding a trajectory feedforward error compensator on the basis of the feedback controller is to eliminate the delay and make the control system The closed-loop transfer function remains constant. Even if the control system maintains the same gain at different frequency bands, it can achieve higher trajectory tracking performance [1~4]. One of the characteristics of the CNC milling machine is that the trajectory tracked is known in advance. Therefore, foresee controllers can be added to the feed forward controller to further improve performance. The effect depends on the acquisition of the transfer function of the entire control system (including the controlled object). When the dynamic characteristics of the controlled object are not determined, the compensation term used to correct the error is missing in the feedforward compensator. Therefore, even if predictive control is adopted It can not improve the control performance of the trajectory controller [4]. This paper uses the pseudo-random M sequence signal to identify the dynamic characteristics of a CNC milling machine's servo system. Based on the closed-loop transfer function of the CNC milling machine, the zero-pole is Distribution, design and calculation of the feedforward fore-ahead compensator form and parameters, the effectiveness of this feed forward predictive compensator was verified through experiments.
1 CNC milling machine servo system and experimental device
The object of the study was a three-coordinate milling machine of the DYNAPATH Delta20 CNC system, which was produced in 1993 by the United States' famous AUTOCON company. The CNC system of the milling machine, the servo system and the additional signal generation for the identification experiment, The acquisition device is shown in Figure 1. To simplify the drawing, only the X-axis servo portion is drawn.
Figure 1 Milling CNC system, servo system and signal generation and acquisition device
Fig.1 Structure on servo system of NC mill and identification device
During the identification process, the computer sends a M-sequence binary pseudo-random signal, which is sent to the speed control end of the CNC system via the D/A port of the PCL812 board at an appropriate level, superimposed on the signal of the normal working of the system, at the speed The response signal generated by the output of the motor is stored in the microcomputer data file together with the M signal after A/D conversion.
2 M sequence signal and correlation analysis method identification
2.1 The M-sequence signal and power spectrum identification process uses the maximum-length bi-level pseudo-random M-sequence signal [5]. The M-sequence signal has good statistical properties and the method of generation is simple. In this study, a period of M sequence was previously generated by the microcomputer. The signal is then cyclically output. After preliminary calculations and experiments, it is determined that the cycle length of the M sequence signal is Np=27-1=127, and the basic level time (clock period) is more than 4ms. The power spectrum of the M-sequence signal and the output power spectrum of the CNC milling machine under the excitation of the signal are output when the clock period is 11ms. This M-sequence signal is similar to the white noise, and it can excite the dynamic behavior of the milling machine within the working passband.
Fig. 2 M-sequence signal power spectrum and output power spectrum of CNC milling machine
Fig.2 Power spectrum of M serial signal and output power spectrum of NC mill
2.2 Correlation Analysis - Least Squares Identification System Model The theoretical basis for the correlation analysis method identification is the Wiener_Hopt equation [5]:
(1)
In the formula, Ruu(λ-τ) is the autocorrelation function of the input quantity; Ruy(λ) is the cross-correlation function of the input/output quantity; 
The best estimate for system impulse response.
Having a SISO linear discrete-time system can be expressed as:
y(t)=-a1y(t-1)-a2y(t-2)-...-any(tn)+b1u(t-1)+b2u(t-2)+...+bnu(tn)+e( t)=φTtθ+e(t) (2)
Where: {u(t)} and {y(t)} are the actual measured input and output sequences, respectively, and e(t) is the error term.
φTt=[-y(t-1),...,-y(tn), u(t-1),...,u(tn)
θT=[a1,...an, b1,...,bn]
The vector matrix is ​​in the form of
Y=φTθ+E
The residual is:
The application of least squares identification is to determine the estimated value of the system parameter vector θ 
, to minimize the sum of squared residuals.
Combining the correlation analysis method with the least squares method can identify nonparametric models and parameter models at the same time.
Fig. 3 is the correlation function curve of input and output quantity when X axis is identified (acquired with R9211B instrument) . From the picture can see: Autocorrelation of M series input signal, self-correlation of servo movement output speed and input, output The cross-correlation is significant. This shows that the input and output signals used for identification have high credibility.
Fig. 3 X-axis correlation function curve
Fig.3 Correlation functions on X axis
3 Identification of trajectory control model of CNC milling machine
When the mechanical properties of the CNC milling machine are better, the nonlinear factors can be omitted. Therefore, the sampling sequence u(t) and y(t) between the reference position input quantity and the actual position output quantity can be expressed as a constant coefficient linear difference equation:
y(t)+a1y(t-1)+...+any(tn)=b0u(td)+
B1u(t-1-d)+...+bmu(tmd) (3)
Where d is the delay amount.
Perform Z conversion on (3) to get:
(4)
In equation (4) 
This is the transfer function of the system.
The I/O signal waveforms of the system in the identification experiment are shown in Figure 4 (the clock period of the M sequence signal is 50 ms and the sampling period is 7.81 ms). Using the ARX model structure, the first half of the sampled signal is identified and calculated, and the X axis is obtained. The transfer function, in which the number of delay steps is 4, the dominant pole is 7, and the number of zeros is equal to 6, see Table 1, and the coefficients of the difference equation (3) are calculated in Table 2.
Figure 4 Sample data waveform
Fig.4 Waves of signal measured
Table 1 X-axis dominant zero-pole data
Table 1 Major zero-pole on X axis
The simulated curve is drawn with the identified model and compared with the sampled signal in the latter part of the simulation. The fitting is ideal, as shown in Figure 5.
Figure 5 Sampling Data Curve and Model Simulation Curve
Fig.5 Measured curve and simulated curve
Table 2 Model coefficients
Table 2 Coefficient of model
4 Feed forward foresee compensator design
4.1 Structure of feedforward fore-ahead compensator In a digital-controlled milling machine feedback controller without feed-forward compensation, the position command yd(t) issued by the NC program is the reference position input quantity u(t), so when t>0, The actual dynamic position of the servo system y(t) is not equal to the given position yd(t) (in the servo system, A(Z-1) is not equal to B(Z-1)), and the purpose of adopting the feedforward compensator is to make The actual position tracks the given position yd(t) as closely as possible. For this purpose, the feed forward compensator is designed according to different situations. The relation between the feed forward compensator and the closed-loop feedback system is shown in FIG. 6.
A notable feature of the trajectory control of the CNC milling machine is that the future trajectory points can be known in advance. Therefore, the future value is also considered in the design of the feedforward compensator. That is, the predictive control method is adopted to further reduce the trajectory control error.
In the CNC machine tool system, the zero point outside the unit circle (called the non-minimum phase system) is extremely common [4]. From the identification results, it can be known that the CNC milling machine used in this study is also a non-minimum phase system.
Decompose the zero polynomial B(Z-1) in Figure 6 into:
B(Z-1)=Bin(Z-1).Bout(Z-1).B1(Z-1) (5)
Fig. 6 Positional relationship between feedforward compensator and closed loop feedback system
Fig.6 Location about feedforward preview compensator
And closed-feedback system
Where Bin(Z-1) is the zero point in the unit circle, B1(Z-1) is the zero point on the unit circle, and Bout(Z-1) is the zero point outside the unit circle.
In this way, the transfer function of the milling machine closed-loop system can be expressed as:
(6)
Therefore, the corresponding parts of the feedforward compensator are compensated separately:
{F(Z-1), F(Z)}=F1(Z).F2(Z-1).F3(Z) (7)
Among them, F1(Z)=Zd, which is used to eliminate the influence of the phase difference caused by the system delay d steps; F2(Z-1)=A(Z-1)/Bin(Z-1), used to delete the units that fall in the The pole-zero point in circles and circles; F3(Z) is used to eliminate the influence of the zero outside the unit circle in the system; for F3(Z), if it takes its inverse system 1/Bout(Z-1), it will lead to the system The unstable pole is generated, so it is compensated using its equivalent complex form [2].
Let the system have a total of zero units outside the zero unit circle. 
When the exponential form of its complex number expands to a power series:
(8)
Since the target value of the future s-step in the numerical control trajectory control can be calculated in advance, the equivalent of the inverse system of Bout(Z-1) is implemented after substituting (8). Since these zeros are outside the unit circle, the progression Convergence, therefore taking the first finite term of (8) to obtain an approximate result. Taking into account the gain change caused by taking a finite term, divide equation (8) by the coefficient {1-(rleiθl)-nsZns} to obtain Bout(Z) The approximate inverse system of -1) is:
(9)
4.2 Calculation of the parameters of the feed forward predictive compensator For the transfer function of the X-axis servo system identified by the identified numerically controlled milling machine, the parameters of the feed forward compensator are:
and so
(10)
In formula (10), r1=r2=1.0442, θ1=−θ2=2.04726 rad, h1=h2=0.5
A pair of feedforward anticipatory compensators for a conjugate complex complex zero outside the unit circle is: Fout(Z)=Fout(Z)1+Fout(Z)2
among them:
After determining the number of predictive steps ns, each imaginary item in Fout(Z)1 and Fout(Z)2 can be eliminated one by one, and Fout(Z) becomes a simple real coefficient compensator.
5 Experimental results and analysis
According to the above-identified CNC milling machine model, plus the feedforward fore-ahead compensator (foresee step number 3), a new CNC servo controller is constructed to perform experiments. The Bode plots of the X-axis before and after compensation are shown in Figure 7. .
Figure 7 Bode plots of the X axis before and after compensation
Fig.7 Bode diagrams compensated and un-compensated on X axis
It can be seen from Figure 7 that the amplitude gain and phase-frequency characteristics before compensation significantly decrease with increasing frequency, the gain decreases by approximately 18dB at 4 Hz, the phase lags by approximately 180°, and the gain increases at 10 Hz. About 31dB, the phase lag is about 270°; the gain is about 39dB at 40Hz, and the phase lag is about 700°. After adding the feedforward anticipation compensation, the amplitude gain is basically constant at 25Hz, and the phase frequency characteristic is at the frequency At 100Hz, there is only a phase difference of about 100°.
After comparison, it can be seen that the frequency characteristics of the servo controller of the milling machine after adopting the feed-forward predictive compensator are significantly improved compared with that without the compensator, especially in the low frequency band.
6 Conclusion
The dynamic transfer function of the CNC milling machine was identified by the M-series pseudo-random signal and least-squares method with appropriate parameters. The correlation analysis and the spectrum diagram showed that the I/O signal in the identification process is highly reliable. According to the characteristics of the CNC track, Respectively compensate for the number of delay steps, poles, and zeros in the closed-loop system to form a feedforward predictive compensator. Experimental results show that the frequency characteristics after compensation are greatly improved.
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