KR20000027185A - Method for controlling transmission velocity using neural network - Google Patents

Abstract

PURPOSE: A method for controlling transmission velocity using neural network is provided to improve an accuracy by computing an accurate error using a contour error model and an inter combination controller and adding the computed error to a control input. CONSTITUTION: A multi-layer neural network(31) simulates a relation of a transmission velocity(F(k)) and a contour error. A repetition learning control unit(32) computes an optimum transmission velocity. The relation of the transmission velocity for determining a reference input of a CNC X-Y servo axis and the contour error by the reference input indicate a nonlinear characteristics. A moving characteristics of two servo axes is simulated in real time using the multi-layer neural network(31). Information of a system is obtained through a neural network inversion method and a suitable transmission velocity is obtained using a repetition learning control method.

Description

Feed speed control method using neural network

The present invention relates to a feed rate control method for improving the machining precision and the machining speed of a CNC machine tool.

Computer Numerical Control (CNC) Machine tools continue to advance toward higher speed, higher precision, and higher intelligence in order to improve machining accuracy and increase production efficiency. The CNC controller simultaneously controls the movement of several servo axes, and the movement of the tool in two- or three-dimensional space is achieved by the movement of these servo axes.

However, a contour error is inevitably generated due to a mechanical defect or the like due to a difference in dynamic characteristics or disturbance between several axes. Since the contour error increases as the machining speed increases, it is necessary to study a control method that can reduce the contour error while increasing the machining speed in order to achieve the high-speed, high-precision machining objective.

Increasing the machining speed in a CNC machine tool increases the amount of time delay of the servo drive system, resulting in an error in the machining shape, and there is a concern that a high frequency resonance phenomenon of the servo system may occur due to an increase in the machining speed. On the other hand, if the machining speed is lowered, high precision can be realized, but there is a problem that productivity is lowered due to longer machining time.

As a conventional method for solving such a problem, Imamura et al. Attempted to control the feed rate by dividing the feed velocity into the contour of the ellipse within the allowable range by using a nonlinear program method (F. Imamura and H. Kaufman, "Feedrate optimization for machine tool control subject to contour error constraints", Proc. 1988 American Control Conference, pp. 81-86, 1989), Chuang et al. In this paper, we tried to control the feed rate through a linear relational equation (HYChuang and CHLiu, "Techniques in cross-coupled digital adaptive feedrate control for multiaxis machine tools", Control and Dynamic Systems, vol. 72, pp. 265-301, september 1996). However, since the relationship between the feed rate and the contour error is very non-linear, the relation such as chau is difficult to cope with actual machining.

In addition, Yang et al. Tried to improve performance by analytically delineating the machining path using optimal control (CDYang, "Optimal feedrate control strategy for high-speed high-accuracy corner motions", Proc. 32-nd IEEE Conference on Decision and Control.pp.2517-2522, 1993.), which is difficult to apply when the model is non-linear or uncertain, Tsai et al. (MCTsai et al., "DSP-based motion control by H ^∞ axis-controller and fuzzy adaptive feedrate", Control Eng. Practice, vol. 3, No. 11, pp. 1587-1597, 1995). The disadvantage is that you need to know the rules of expert knowledge.

SUMMARY OF THE INVENTION The present invention is directed to solving the problems of the prior art as described above, and an object of the present invention is to include a nominal tolerance in an objective function to achieve an optimum feed rate in real time within a nominal tolerance of a contour error given during machining of a CNC. The present invention provides a feed rate control method that can shorten the overall machining time and increase productivity.

Another object of the present invention is to use an iterative learning control method in order to obtain an optimum feed rate, by using a neural network to simulate the information of the dynamic characteristics of the CNC system, that is, the relationship between the feed rate and the contour error. In addition, even when uncertainty exists in the system, the present invention provides a method of controlling a transfer song with improved control performance.

1 is a diagram for explaining contour error;

2 is a diagram illustrating a relationship between two points of a reference trajectory and contour error;

3 is a configuration diagram of a neural network control device implementing the neural network feed speed control method proposed in the present invention for a CNC X-Y servo axis;

4 is a structural diagram of a 4-5-1 multilayer neural network used in the present invention;

5 is a view showing the contour error which is a result of processing using a neural network feed speed control method according to the present invention at the time of circular machining;

FIG. 6 is a diagram showing a feed speed in the case of FIG. 5; FIG.

FIG. 7 is a view showing the contour error result and the internal and external tolerance of the error in FIG.

8 illustrates contour error values for an involute path;

9 is a diagram showing a feed speed in the case of FIG. 8;

Fig. 10 is a diagram showing the result of contour error for corner machining;

FIG. 11 is a diagram showing a feed speed in the case of FIG. 10; FIG.

Fig. 12 is a view in which the contour error resulting from the machining result and the inner and outer boundary values of the corner machining are all enlarged by 800 times and expressed in the X-Y plane.

Explanation of symbols on the main parts of the drawings

31: multilayer neural network 32: iterative learning control unit

In order to achieve the above object, the feed speed control method using the neural network according to the present invention is a method for controlling the feed speed of the servo shaft of a computer numerical control machine tool, the dynamic characteristics of the servo shaft using a multi-layer neural network Simulating in real time; And obtaining a feed rate by an iterative learning control method for learning with a maximum gradient method according to a given objective function.

Hereinafter, a neural network feed speed control method for high precision high speed machining according to the present invention will be described in detail with reference to the accompanying drawings.

First, the contour error modeling of a CNC machine tool is demonstrated.

The CNC machine tool generates a knot point for each axis at every sampling time by interpolating the given curve for the given feed rate for any curve machining and tracking the difference between the reference path and the actual machining path. Used as input to the controller. The points between the points of the reference path are regarded as straight lines to generate the reference trajectories as shown in FIG. 1 is a diagram for explaining contour error.

In Fig. 1, if the reference position at any t sampling time is P ^* (t) and the position where the actual machining position is delayed by the amount of time delay is P (t), E is the tracking error and the closest reference in the actual machining path. The vector to the point on the path is defined as the contour error. Therefore, if the closest note point from the current position is P ^* ₁ and P ^* ₂ , the contour error vector E _c is P (t) and P ^* _c (t) is an arbitrary point between the two points P ^* ₁ and P ^* ₂ . It is a vector of and. This contour error directly determines the machining precision.

The distance from all points on the reference trajectory is calculated to find the two points closest to the current position, which may take a long time. Therefore, if you define a variable window of appropriate size and store the past value of the reference trajectory in memory and find the distance between the reference trajectory within the window and the position of the actual trajectory at the present moment, the two points closest to the past reference trajectory can be found. It also reduces computation time. The size of the variable window is determined from the position of P ₁ ^* at the t sampling time to the position where the distance decreases and then grows again.

As described above, the contour error may be calculated by finding two points having the shortest distance from the current position and obtaining a distance between a straight line and one point as shown in FIG. 2. 2 is a diagram for explaining the relationship between two points of the reference trajectory and the contour error.

In FIG. 2, the slope of a straight line connecting two points P ₁ * and P ₂ * is expressed by Equation 1 below.

When the error vectors of P ₂ ^* and P are set to the x-axis component e _x 'and y-axis component e _y ', the contour error vector E _c can be expressed as Equation 2 below, and the magnitude of the contour error ε is It can be expressed as Equation 3.

Hereinafter will be described a feed rate control method using a neural network according to the present invention.

Since the relationship between the feed rate for determining the reference input of the CNC XY servo axis and the contour error due to the reference input shows a very strong nonlinear characteristic, the present invention simulates the dynamic characteristics of the two servo axes in real time using a multilayer neural network. The neural network inversion method is used to obtain the information of the system and to obtain the proper feed rate using the iterative learning control method.

3 is a view for explaining the configuration of the neural network control device implementing the neural network feed speed control method proposed in the present invention for the CNC X-Y servo axis. The neural network controller shown in FIG. 3 includes a multi-layer neural network 31 for simulating the relationship between the feed rate F (k) and the contour error ε (k) and an iterative learning controller 32 for obtaining an optimum feed rate. ).

In FIG. 3, the multilayer neural network 31 uses 4-5-1 multilayer neural network because it aims to simulate the nonlinear dynamic characteristics of the CNC system.

4 is a view for explaining the structure of the 4-5-1 multilayer neural network used in the present invention.

In FIG. 4, W _ji is a weight of the input layer and the hidden layer, and W _oj is a weight of the hidden layer and the output layer. These weights are adjusted by the error backpropagation method according to the objective function of Equation 4 below.

When n _o and n _j are the inputs of the neural network output layer and the hidden layer, respectively, and f (·) is the hyperbolic tangent activation function of each node of the neural network, the output equation of the neural network learned as described above is expressed by Equation 5 below. Same as

If you learn enough at this time, the output and contour error of the neural network are approximated.

Using the dynamic characteristics information of the system obtained by the inversion method of the neural network, the proper feedrate is obtained by the iterative learning method.

In addition to the nonlinear relationship between the feed rate and the contour error, the contour error determines the machining precision and the feed rate relates to the productivity, which are inversely related to each other. Therefore, the nominal tolerance of the user's desired contour error is put into the objective function in order to maintain the precision to some extent, i.e. the contour error falls within the allowable value, and to increase the processing speed as much as possible. In addition, since the objective function becomes complicated when the positive and negative tolerances of the contour error are different, the absolute value of the contour error can be taken as one objective function. Therefore, the objective function to be used for the iterative learning is shown in Equation 6 below.

In Equation 6, ε _b (> 0) is a boundary value determined by the user so that the contour error does not exceed the limit of the tolerance (| ε | _max ). The iterative learning rule using the maximum slope method according to the objective function is expressed by Equation 7 below.

In Equation 7, t is the number of repetitions, η is the repetition learning rate, α is a moment value for increasing the convergence of repetitive learning.

In the iterative learning rule of Equation 7, ∂E / ∂F may be expressed as a chain law as shown in Equation 8 below.

Since ∂ | ε | / ∂F in Equation 8 is information on the dynamic characteristics of the system, the equation 5 and the chain law are applied to obtain this information from the simulated neural network. Can be.

In Equation 9, the first partial derivative of the right side is set to '1' on the assumption that the multilayer neural network has been sufficiently learned.

In this way, the non-linear dynamic characteristics of the system are obtained from the neural network, and it is repeated several times to obtain the optimum feed rate by learning according to the objective function.

In the following, the simulation is performed on the model of the X-Y servo axis of the TNV-40 vertical machining center in order to examine the feasibility of the neural network feed speed control method according to the present invention.

The plant model of each axis includes nonlinear elements such as saturator, disturbance, friction, etc. Each axis includes a PI type speed controller for speed control and a PD type tracking controller for position control. In order to obtain a high-precision response, a PI-type cross-link controller was used.

The parameter values of the X-Y axis used in the experiment are summarized in Table 1 below.

inertia Viscous friction Coulomb Friction Disturbance J (㎏㎡) B (Nms) F _i (Nm) D _i X-axis 0.0103 0.0336 0.2 0.1 Y-axis 0.012 0.0308 0.3 0.1

The values of the parameters used in the tracking controller (C _ti , i = x, y), the mutual coupling controller (C _cc ), and the speed controller (C _vi , i = x, y) for controlling the speed of the motor are shown in Table 2 below. Summarized in

C _ti = k _p + k _ds s C _vi = k _sp + k _si / s C _cc = K _p + K _i / s k _p k _d k _sp k _si K _p K _i X-axis 5.5 0.02 1.3 2.35 5 0.8 Y-axis 4.95 0.02 1.3 2.35

The number of repetitions in the repetitive learning method was performed 5 times by the trial and error method, and the moment value was 0.1. And the boundary value which does not exceed the nominal tolerance of contour error shall be 0.003 mm.

In this experiment, the learning rate was set to 0 and 60. If the learning rate is 0, the velocity is of a constant magnitude, that is, through the acceleration section to prevent the increase of the contour error due to the sudden speed change without controlling the feed rate. It means the constant speed processing of 50 mm / min. And the learning rate 60 is the numerical value determined by the trial and error method.

First, experiments were performed on circles, such as the following Equation 10, which is a general nonlinear path.

In Equation 10, R was 10 mm as the radius of the circle.

Fig. 5 shows the contour error which is the result of processing using the neural network feed speed control method according to the present invention at the time of circular machining, and Fig. 6 shows the feed speed in this case.

As shown in Figures 5 and 6, while processing within the tolerance can be seen that the feed rate is properly adjusted and the processing speed is faster. In addition, the measurements showed that the maximum contour error was about the same, but the machining time was reduced by 12.4% in one cycle. In addition, Fig. 7 shows the contour error result in Fig. 5 and the internal and external tolerance values of the error 200 times, and is shown in the actual X-Y plane. As shown in Fig. 7, it can be seen that the actual contour is machined within the tolerance.

Next, the experiment was performed on the involute path represented by Equation 11 as another nonlinear path.

Fig. 8 shows the contour error values for the involute path, and Fig. 9 shows the feed speed at that time. As shown in Fig. 8 and Fig. 9, the machining time could be reduced by about 8% by appropriately calculating the feed rate for the involute path by the control method according to the present invention. However, even in this case, both the constant speed machining and the feed rate control slightly exceeded the tolerances of the contour error.

Next, we performed an experiment on corner machining with both linear and nonlinear paths. Fig. 10 shows the result of the contour error for the corner machining, and Fig. 11 shows the feed speed at this time. Fig. 12 is an 800-fold enlargement of both the inner and outer boundary values of the corner machining and the contour error resulting from the machining, and is expressed in the X-Y plane.

As shown in Figs. 10, 11, and 12, when the contour error exists inside the boundary, the feed rate is increased by the controller to increase the processing speed, and when approaching the boundary again, the feed speed is gradually decreased. You can see it shrink. As a result, even in the case of corner machining, the contour error is almost the same in the case of controlling the feed rate, but the machining time for the 10 mm straight line after the corner was reduced by 12.3%.

Table 3 below summarizes the machining results for circle, involute and corner contours.

won Involute corner Learning rate 0 60 0 60 0 60 | Ε _c | peak (mm) 0.0034 0.0033 0.0090 0.0090 0.0028 0.0029 Frequency in seconds 1.291 1.131 1.277 1.178 0.749 0.657

As described above, the present invention provides a feed rate neural network control method having an objective function for increasing the machining speed at the highest feed rate while maintaining machining accuracy for two X-Y servo axes of a CNC machining center. In addition, by using a state-of-the-art contour error model rather than a conventional error modeling method and using a mutual coupling controller, accuracy can be improved by calculating a more accurate error even in a general nonlinear contour and adding a control input. The proposed feedrate neural network control method based on the contour error modeling can improve the machining performance by changing the feedrate to the iterative learning control method according to the contour error, compared to the conventional method of maintaining a constant feedrate.

Claims (1)

In the method of controlling the feed rate of the servo axis of a computer numerical control machine tool, When W _ji is the weight of the input layer and the hidden layer of the multilayer neural network, and W _oj is the weight of the hidden layer and the output layer, these weights are adjusted by the error back propagation method according to the following objective function: When n _o and n _j are the inputs of the neural network's output layer and the hidden layer, respectively, and f (·) is the hyperbolic tangent activation function of each node of the neural network, the neural network's output equation as described above is expressed as Characterized in that, Simulating the dynamic characteristics of the servo axis in real time using a multilayer neural network ; And Obtaining a feed rate by an iterative learning control method for learning with the maximum gradient method according to the objective function of the equation In the above equation, ε _b (> 0) is a boundary value determined by the user so that the contour error does not exceed the limit value | ε | _max of the tolerance. Feed rate control method using a neural network comprising a.