CN107748540A - A kind of estimation of multiple axes system profile errors and iteration control method based on Newton method - Google Patents

Abstract

A multi-axis system contour error estimation and iterative control method based on Newton's method belongs to the field of multi-axis system motion control. The method uses Newton's method to calculate the exact value of the contour error, and reduces the contour error through iterative learning to achieve good multi-axis coordinated control performance. The method includes two parts: contour error estimation and contour error control: the former uses Newton's method to calculate the contour error point (the expected point closest to the current position) by means of extremum search; the latter uses the contour error point and the current The position deviation is used as iterative information, and the trajectory feedforward compensation is generated and optimized in an iterative manner, so as to improve the performance of contour control. The invention utilizes the characteristic of accurate numerical calculation of Newton's method, effectively overcomes the problem of inaccurate tracking in complex contours in traditional contour control methods, and the controller has a simple structure and can achieve excellent contour control effects.

Description

A Contour Error Estimation and Iterative Control Method for Multi-axis System Based on Newton's Method

technical field

The invention relates to a motion control method of a multi-axis system of a numerical control system, in particular to a contour error estimation and iterative control method based on Newton's method.

Background technique

In the CNC system, the machining accuracy of the workpiece depends largely on the multi-axis contour motion accuracy of the machine tool. The index that characterizes the contour motion accuracy is the contour error, that is, the shortest distance from the actual position point to the expected contour during the motion process. In the actual curve (curved surface) machining process, due to the complexity of the expected machining path and the uncertainty of the actual position point, the contour error usually cannot be directly determined by measurement. Therefore, the estimation and control of the contour error in the multi-axis motion system has become an important research content in the numerical control system. The existing practical application methods basically use the independent control of each axis or the cross-coupling control method, which cannot be done by these existing methods. As far as the accurate estimation of contour error is concerned, for some complex or extreme contours (such as high-speed and large-curvature contours), the contour error estimation has a large deviation compared with the real situation; and due to the deterioration of the contour error estimation performance, making The control effect of the contour error cannot be guaranteed, which affects the contour processing effect in the actual application process.

Therefore, there is a need for an estimation and control method of contour error that can be effectively applied to the actual multi-axis motion system, which can realize accurate contour error estimation under arbitrary contour conditions, and at the same time ensure the contour motion control performance according to the estimated contour error. Newton's method is a simple and effective numerical calculation method, which can be used to find the minimum value of the function. By establishing a function representing the distance from the actual position point to the desired contour, and calculating the minimum value of the function, the contour error can be obtained. Point and contour errors. Using the obtained contour error information, iterative learning is carried out to complete the expected trajectory pre-compensation of the contour motion, and the performance of the contour motion can be improved.

Contents of the invention

The purpose of the present invention is to propose a contour error estimation and iterative control method based on Newton's method to solve the problems raised in the above-mentioned background technology, so that it can be applied to any complex contour or extreme contour conditions, and can achieve accurate contour error estimation and good contour error control performance.

To achieve the above object, the present invention provides the following technical solutions:

S1: According to the dynamic characteristics of each independent axis in the multi-axis system, design corresponding feedback controllers respectively;

S2: Establish the vector representation of the contour error vector to be determined with respect to time t in the multi-axis system:

in, is the desired trajectory, is the actual motion position, is the contour error vector;

S3: Establish an index function J(t) that characterizes the contour error:

S4: According to the following iteration formula, iterate the time t:

Among them, t _i represents the time parameter corresponding to the ith iteration, m is the total number of iterations, Denotes the velocity of the desired profile at time t _i of the ith iteration;

S5: Establish the criterion for stopping the iterative calculation: after the i-th iteration is completed, judge Whether it is true, where σ is a very small constant, is the absolute value of the derivative of the index function at the time parameter t _i , if the above judgment condition is established, then execute step S6, otherwise continue to execute S4-S5 until the condition is met;

S6: Calculate optimal time t _m , contour error point vector and contour error

S7: Calculate the low-pass filter Q(s): Wherein s is a differential operator, ζ=0.7, represents the damping ratio of this second-order low-pass filter, f _s represents the cut-off frequency of this filter;

S8: Use the filter Q in step S7 to correct the contour error calculated in step S6 Perform zero-phase low-pass filtering to obtain a smooth contour error signal:

S9: Use the smoothed contour error as a trajectory pre-compensation item to correct the original expected trajectory, and the corrected expected trajectory is:

S10: Experiment with the expected trajectory corrected in step S9, and then repeat steps S2-S9 until the profile performance meets the requirements.

The present invention has the following advantages and prominent technical effects: firstly, the present invention proposes a brand-new idea and method of contour error estimation, which is different from the contour error calculation method based on the geometric characteristics of the expected motion track in the prior art means, and the present invention adopts The method of numerical calculation, off-line calculation and solution to obtain relatively accurate contour error, to achieve accurate error estimation for any complex contour, even under extreme contour conditions such as high speed and large curvature, the accuracy of error estimation can still be guaranteed; then according to the contour error Accurate estimation, a contour error control method that achieves desired trajectory pre-compensation through iterative learning is proposed, which can effectively improve the contour control performance.

Description of drawings

Figure 1 is a block diagram of contour error estimation and iterative control based on Newton's method.

Fig. 2 is a comparison result diagram (unit: m) of the contour error of the Newton method proposed by the present invention and several other methods in the circular contour motion control.

Detailed ways

The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings and the examples of the present invention. Obviously, the described embodiment is a specific implementation of the present invention for the contour motion control of the linear motor two-axis system, and not all the embodiment. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

In Fig. 1, the expected trajectory of each axis is provided by the actual processing requirements. The Newton algorithm and the contour error iteration part are the algorithms to be implemented. The multi-axis system model is determined by the dynamic model of each axis and the designed feedback controller. The actual position is determined by The sensor measurement signal is obtained.

The main idea of designing a two-axis linear motor contour motion control system based on Newton’s method is to establish the vector representation of the contour error vector to be determined in the two-axis system with respect to time t, and find the point where the derivative of the function is zero by Newton’s method, that is, the The minimum value of the function, according to the definition of the contour error, the minimum value is the contour error; the known conditions required by the solution process based on the Newton method are the desired position and the desired speed of the desired trajectory of each axis at any time, which is for many It is easy to implement for the axis motion system. After obtaining the contour error, calculate the size of the contour error components in each axis direction, and then perform zero-phase filtering on each component without phase deviation, and use the filtered signal as a trajectory correction to pre-compensate the original desired trajectory Finally, the contour motion control experiment is carried out, and the above process is repeated to achieve the convergence of the contour error. For the two-axis linear motor motion platform, the driving voltage is obtained by the input signal of the controller (ie, the control function) after the amplification of the servo drive amplifier, and the grating displacement sensor installed on the linear motor motion guide rail can feedback the motor of each axis in real time. Position information, calculate the contour error according to the relative position relationship between the actual position point and the expected contour; according to the estimated contour error, the pre-compensation of the expected trajectory of each axis can be designed to improve the contour control performance. Combined with the block diagram of contour error estimation and iterative control based on Newton's method in Figure 1, the specific steps are described in detail:

Step S1: According to the dynamic characteristics of each independent axis in the multi-axis system, design corresponding feedback controllers respectively. For the X and Y axes in the two-axis system, the corresponding feedback controllers are designed respectively to ensure that each axis can complete independent and stable motion control; there are no strict requirements for the specific controller type, here the adaptive robust controller As an example, both axes can achieve good trajectory tracking control. The closed-loop system formed by the feedback controller and the dynamic models of each axis is the multi-axis system model (P ₁ ... P ₂ ... P _n ) shown in Fig. 1 .

Step S2: Establish the vector representation of the contour error vector to be determined with respect to time t in the multi-axis system:

in, is the desired trajectory, is the actual motion position, is the contour error vector. For a two-axis system, the contour error components along the X and Y axes are:

ε _x (t) = R _dx (t) - X _x (t)

ε _y (t) = R _dy (t) - X _y (t)

Where R _dx (t) and R _dy (t) represent the desired trajectory of the X and Y axes respectively, and X _x (t) and X _y (t) represent the actual positions of the X and Y axes respectively;

Step S3: Establish an index function J(t) that characterizes the contour error:

For the two-axis system, the index function can be specifically expressed as:

Step S4: According to the following iteration formula, time t is iterated:

Where t _i represents the time parameter corresponding to the ith iteration, m is the total number of iterations, Denotes the velocity of the desired profile at time t _i of the ith iteration. For a two-axis system, in and Respectively represent the expected speed of the X and Y axes at the time t _i ;

Step S5: establish the criterion for stopping the iterative calculation: after the i-th iteration is completed, judge Whether it is true, where σ=1×10 ^-9 , if the above judgment conditions are true, execute step S6, otherwise continue to execute S4-S5 until the conditions are met;

Step S6: Calculate the optimal time as t _m and calculate the contour error point vector as Calculate the contour error as The components of the contour error along the X and Y axes are:

Step S7: Design the low-pass filter Q: Among them, s is a differential operator, ζ=0.7, represents the damping ratio of the second-order low-pass filter, f _s represents the cut-off frequency of the filter, according to the actual situation of the frequency characteristics of the two-axis linear motor platform f _s =20Hz;

Step S8: Use the filter Q in S7 to calculate the contour error in S6 Perform zero-phase low-pass filtering to obtain a smooth contour error signal:

The smoothed contour errors for the X-axis and Y-axis are:

In the actual operation process, zero-phase filtering is essentially to filter the contour error The forward and reverse of the time domain sequence pass through the digital filter respectively, and the smoothed contour error is summed with the previous storage result as a new smoothed contour error, and stored. The specific operation process is shown in Figure 1;

Step S9: Use the smoothed contour error as a trajectory pre-compensation item to correct the original expected trajectory, and the corrected expected trajectory is obtained as:

For a two-axis system, the expected trajectories of the X-axis and Y-axis are respectively modified as:

Step S10: Use the trajectory corrected in S9 to conduct an experiment again, and then repeat steps S2-S9 until the contour performance meets the requirements. The contour error can be reduced by using the trajectory and compensation that meet the contour motion accuracy requirements and applying it to the actual machining process of the corresponding contour.

According to Figure 2, in the circular contour motion control, compared with the independent control of each axis of ARC, CCC, and CCILC, the proposed Newton method can achieve the best contour error control effect.

Claims (1)

1. A multi-axis system contour error estimation and iteration control method based on Newton's method is characterized by comprising the following steps:

s1: and respectively designing corresponding feedback controllers aiming at the dynamic characteristics of each independent shaft in the multi-shaft system.

S2: establishing a vector representation of a contour error vector to be determined in a multiaxial system with respect to time t:

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wherein,in order to obtain the desired motion profile,in order to be able to actually move the position,is a contour error vector;

s3: establishing an index function J (t) for representing the contour error:

<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>|</mo> <mo>|</mo> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>t</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow>

s4: the time t is iterated according to the following iteration formula:

<mrow> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>X</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <mo>|</mo> <msub> <mover> <mi>R</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mover> <mi>R</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow>

wherein, t_iRepresents the time parameter corresponding to the ith iteration, m is the total iteration number,representing the time t of the desired profile at the i-th iteration_iThe speed of the pump;

S5: establishing a criterion for stopping iterative computation: after the ith iteration is finished, judgingIf it is true, where σ is an extremely small normal number,As a derivative of the index function at a time parameter t_iIf the above-mentioned judgment condition is true, executing step S6, otherwise, continuing executing S4-S5 until the condition is satisfied;

s6: calculating an optimal time t_mContour error point vectorAnd contour error

S7: calculating the low-pass filter q(s):where s is a differential operator, ζ is 0.7, which represents the damping ratio of the second-order low-pass filter, and f_sRepresenting the cut-off frequency of the filter;

s8: the contour error calculated in step S6 is corrected using the filter Q in step S7Performing zero-phase low-pass filtering to obtain a smooth contour error signal:

<mrow> <mover> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>Q</mi> <mi>T</mi> </msup> <msup> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>Q</mi> </mrow>

s9: correcting the original expected motion track by taking the smoothed contour error as a track precompensation term to obtain a corrected expected track which is as follows:

<mrow> <msub> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mover> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>

s10: the experiment was performed using the desired trajectory corrected in step S9, and then steps S2-S9 were repeated until the profile performance satisfied the requirements.