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After coordinate transformation, it is sent to each servo axis position controller as a position command, so that each axis moves to the specified position at the same time. The virtual frame is the newly added contour error compensation controller. The design idea is to dynamically correct the interpolation result according to the previous control system operation information, in order to reduce the contour error. The specific process is: collecting the actual arrival position information of each axis in each control cycle, transforming into the workpiece coordinate system via /T1, and subtracting the position command sent from the previous cycle to obtain the following error vector e, and calculating the contour error accordingly. £, and then the compensation vector is calculated by the contour compensation algorithm, and the interpolation result is corrected by the compensation vector, thereby achieving the effect of reducing the contour error. The contour error calculation method has been introduced in the following, and only the contour compensation algorithm is discussed below.

First, the input data of the contour compensation algorithm is the contour error vector, and the output is the correction vector, which is not a single data. The components of the contour error vector are simultaneously processed by the contour compensation algorithm to obtain the corrected vector.

If the contour compensation algorithm takes unity gain, the compensation vector can cancel the contour error caused by the difference of the characteristics of each axis, and the compensation algorithm also reacts quickly. However, since the actual system is affected by the interference, if the contour compensation algorithm is too sensitive, it is possible to amplify the influence of the interference and adversely affect the stability of the system. In addition, in practical applications, when the contour changes continuously, the contour error at different moments also changes continuously. Considering these two factors, the contour compensation algorithm takes the form of a first-order low-pass filter: representing the contour compensation vector. The above equation can be expressed as a difference equation: degenerate into an ordinary multi-axis linkage control system. In addition, the larger the a is, the lower the cutoff frequency of the contour controller is, and the smoother the change of the filter output with time is. Therefore, the conclusion is as follows: If the multi-degree-of-freedom linkage contour control system has the structure shown, the compensation control algorithm is (1) Select, when the gain of the contour controller /3*0+ or ​​a*1-, a stable dynamic contour compensation control system can always be obtained.

This is just a qualitative conclusion about a and / selection. In fact, when /*+, the contour compensation algorithm has lost the effect of compensating the contour error; when a*1-, the filter approximation becomes the integral link. For the process with faster change, the control effect will be greatly improved due to the faster change of the contour error. Attenuated, it is even possible to increase the contour error. Therefore, when selecting the controller parameters, it should be considered in terms of stability and rapidity. Under the premise of system stability, reduce the increase / to achieve the best contour control effect.

4 Experimental verification experiments were carried out on the X and Y axes of a five-axis CNC milling machine. The interpolation calculation and contour compensation algorithm were completed by the industrial computer. The experimental curve was a circle with a radius of 25.464 mm on the X0Y plane, and the feed rate was 600 mm/ Min; there is no rotation coordinate here, so no coordinate transformation is required. The curve interpolation period and the control algorithm of the X and Y axis position controllers are both 4mS, and the contour controller parameter a takes 04 to take 0.5. Under this condition, the experimental results are shown in Fig. 3. The maximum value of the steady-state contour error before contour compensation can be obtained. Up to 37 or more; after the introduction of contour error control, the contour error is reduced by half in the corresponding position of the entire circular contour, and the maximum value is reduced to 19. This result is consistent with the experimentally selected contour control parameters.

It can be seen from U). For a short period of time after the circular over quadrant, there is a large change in the contour error, which is the root cause of a selected as 0 in the experiment. At the same time, since a is 0, the value of Lu is too large, which may affect the stability of the system. Because the experiment is carried out on the machine tool, the safety must be ensured, so the value of P is not large. Nevertheless, it is obvious from the experimental results that the contour error control based on dynamic contour compensation has a good suppression effect on the wheel error, especially the ideal control effect on the slowly varying contour error, and the suppression of the fast-changing contour error. The effect is relatively weak.

Contour control test result

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