WO2009109673A1

WO2009109673A1 - Fuzzy logic-based control methods for drilling processes

Info

Publication number: WO2009109673A1
Application number: PCT/ES2008/070039
Authority: WO
Inventors: Rodolfo Haber Guerra; Fernando MARTÍNEZ PUENTE; Raúl Mario DEL TORO; Bruno Caballero Retamosa
Original assignee: Consejo Superior De Investigaciones Científicas
Priority date: 2008-03-03
Filing date: 2008-03-03
Publication date: 2009-09-11

Abstract

The invention relates to a control method for drilling processes performed by a CNC machine (2, 3) controlled using a control means (4), in which the CNC machine (2, 3) and the control means (4) are connected by a network means (5), L_max representing the maximum total delay involved in the drilling process. According to the invention, the control diagram is a simple closed loop diagram, the inner line of which comprises a block that represents the machining process, a fuzzy controller and scaling factors K_e, K_ce and GC.

Description

PROCEDURE OF CONTROL BASED ON BLURRY LOGIC FOR DRILLING PROCESSES

D E S C R I P C I O N

OBJECT OF THE INVENTION

The main object of the present invention is to provide control procedures (single-loop blur, internal neuro-fuzzy model and linear PID) to efficiently control drilling processes, so as to minimize the wear of the drill bit and maximize it Ia rate of material removal.

BACKGROUND OF THE INVENTION

The drilling processes have a significant impact on the production in many industries, such as the aerospace industry, the automotive industry, etc. In spite of this, generally the conditions of the drilling process are generally chosen from a data manual for drilling, and the experience and skill of the operator are necessary. It must adjust the speed of advance if the process is too slow or unstable, if an overload occurs or if vibrations appear.

As the depth of the drilling increases, it is more difficult to obtain the extraction of the chips from the hole, and there is an increase in the friction between the bit and the piece. Forces and major pairs also have negative effects, such as faster wear of the drill, appearance of vibrations and risk of breakage. Approximately from a depth greater than three times the diameter of the bit, the control strategy based on the operator's skill is not sufficient, and another type of force control in real time is required. In addition, a drilling that is not

SUBSTITUTE SHEET (RULE 26) controls properly unnecessarily wears Ia bit, reducing its useful life. This implies the need to change the drill more frequently, which causes the consequent loss of production time.

So far, the effort has been directed mainly towards the development of adaptive controllers. Adaptive controllers, however, are often too slow, since the parameters are estimated in real time and the controller's gains are adjusted accordingly. Furthermore, if they are not adjusted carefully, complex and undesirable behaviors may occur.

Therefore, there is a need in the technique to develop control strategies to optimize the conditions of the drilling processes, and particularly to maximize the useful life of the drills and the material removal rate.

DESCRIPTION OF THE INVENTION

In the present document, the term "machining" refers jointly to milling, drilling, grinding, turning, and in general any process whose objective is to modify the shape of a solid piece by extracting part of the material by cutting it .

On the other hand, the term "drilling" refers here to any process whose objective is to make a circular hole in a solid piece. Therefore, not only industrial drilling processes are included, but also, for example, drilling processes carried out in the field of medicine, such as bones or teeth.

The rotating tool that physically makes the hole is called "bit", while the object that is drilled is called "piece". As mentioned above, a piece can be a metal plate, the tooth of a patient, or others. In addition, the term "piece program" is defined as the set of actions that a drill is desired to perform on the piece to be drilled. For example, a part program could be to make a hole of diameter D and depth H at a forward speed V.

The term "internal sensor" refers to a sensor included as standard in a CNC machine, as opposed to the term "external sensor", which refers to an additional sensor installed in the CNC machine for a specific purpose.

According to this, typical drilling installation comprises:

a) A CNC-machine: In the present document, it will be understood that the CNC-machine comprises a machine tool and a CNC, both provided by the manufacturer.

The machine tool is the apparatus that physically performs the drilling process, and comprises a base to which a drill is attached which, thanks to electric motors, advances and rotates at the same time, so that the material of a piece is pierced. which is located under the drill. The two variables that define the drilling process are, therefore, the longitudinal speed of advance and the speed of rotation of the drill. In addition, normally the manufacturer of the drill specifies a maximum drilling depth that is not advisable to overcome.

In order to know the force that the bit applies to the piece, the machine tool usually includes a set of internal sensors that measure process variables directly or indirectly. In the present document, the term "force" or "resultant force" refers to the sum of the three components of the force that the drill performs on the piece. It is common, for example, that the machine tools have internal sensors that measure the intensity of current supplied to each of the motors, which intensity is in turn proportional to the torque applied by said motors. Other available variables (internally) are the power consumed and the cutting torque. The machine also has position and speed sensors for the axes (to place the drill bit in the position where it must drill) and encoders for the speed of rotation. The CNC uses these sensors to keep constant the speeds of advance and rotation by means of the internal control loops to the CNC, as well as the position of the drill bit. Other internal sensors that usually include temperature sensors, etc.

On the other hand, depending on the architecture of the CNC, used by its manufacturer, usually exists at the low level a PLC or PLC. Currently, the CNC is basically a computer with closed architecture (access restricted to some variables and internal parameters) or open (access to all variables and parameters) that controls the operation of the machine tool so that it can carry out a program of drilling another desired piece program. The CNC is connected to the machine tool so that it processes the program for the manufacture of the piece (part program). From this program the CNC algorithms (interpolation, position control, speed, trajectory) require the signals from the sensors installed in the machine tool and execute the sending of the necessary commands for its operation, such as the intensities of the engines, etc. The CNC is provided by the machine tool manufacturer, in such a way that the term "CNC machine", in this document, refers jointly to the machine tool and the CNC.

b) A means of control: It is usually a computer connected to the CNC that sends the part program to be executed. In addition, the control means receives information from the internal sensors of the CNC-machine, through a network medium, or, additionally, from external sensors installed in the machine tool. Furthermore, parameters and variables of internal CNC operation related to the execution of the part program such as the speed of advance and the speed of rotation can be monitored (and in some cases modified) from the control means.

c) A network medium: The control means is connected to the CNC through a network medium, which can be a field bus, belonging to the PROFIBUS family or others. Other system configurations that allow the use of network media such as Ethernet or Internet are possible. In any case, the network medium is characterized by the maximum delay it introduces in the transmission of monitoring and control signals between the CNC and the control means, which will be called L gave _{me the} network- The overall delay of the drilling process L _max , therefore, the sum of the delay introduced by the network means L gave _me network and the delay due to the dead time of the drilling process L drilled, ie L _max = L drilled + L network

The present document describes control procedures for high performance drilling processes based on fuzzy, neuro-fuzzy and PID controllers, whose objective is to maximize the material start-up and the life of the bit, and for this they try to keep the force constant. resulting from the bit on the piece.

The fuzzy logic is used for the resolution of a variety of problems, mainly those related to the control of complex industrial processes and decision systems in general, the resolution Ia compression of data. These systems are generally robust and tolerant of inaccuracies and noise in the input data. Fuzzy logic is based on fuzzy sets, whose elements are associated with a membership function that indicates to what extent the element is part of that fuzzy set. The forms of the most typical membership functions are trapezoidal, triangular and Gaussian. That is, the fuzzy logic is based on heuristic rules of the form Sl (antecedent)

THEN (consequential), where the antecedent and consequent are also fuzzy sets, either pure or the result of operating with them.

The rules that determine the belonging of the elements to the fuzzy sets is based, in the case of drilling processes, on the operator's experience.

Blurry control

Thus, according to a first aspect of the present invention, a closed-loop control method, based on a fuzzy controller, is described for drilling processes performed by a CNC-machine controlled from a control means, where the machine-

CNC and the control medium are connected by a network medium, and where the maximum overall delay of the drilling process is L _max . The network medium can be an MPI, Profibus, Ethernet, Internet, or other network, and its global maximum delay L _max , according to preferred embodiments of the invention, is greater respectively 0.2 and 0.4 seconds.

The internal line of the loop of the control scheme corresponding to the first aspect of the invention comprises, fundamentally, blocks corresponding to scale factors for the inputs and outputs of the drilling process, also known as gains or parameters of the controller, a block corresponding to the fuzzy controller and a block representing the drilling process.

The drilling process is represented by a function G _t (s) that models the dynamics of the drilling process. This function includes a maximum delay L _max that includes the dead time of the drilling process (intrinsic delay of the process, delayed) and the delay due to the network medium (Lmedio red) - The function Gt (s) can be obtained using methods known in the art from the performance of tests and the taking of data, either by internal sensors belonging to the CNC-machine, or by external sensors installed ad hoc.

The fuzzy controller is based on rules that emulate the actions of the operator during the control of a drilling process, with the advantage that the fuzzy controller is much more robust (less sensitive to the disturbances that occur such as variations in the hardness of the material, wear of the tool, etc) in industrial environments than other regulators. It is also fast and precise in its application. The fuzzy controller includes three stages: smudging, inference and desemborronado.

In the smearing or blurring, the entries of physical or dimensionless units are converted into membership values. In the inference the inputs are processed and with known mechanism (Sup-Min, Sup-Prod, etc ...) the output is obtained. Finally, the output is converted to physical units (percents, increases in speeds, displacements, etc.) in the unbundling or de-busting stage.

The rules are obtained from the operator and then in controllers of two inputs and one output are extended to bases of 9, 25 or 49 rules. A procedure for designing these rule bases is to use known templates of these rule bases on which certain rules are modified, added and eliminated depending on the application and technical knowledge about the drilling process.

The implementation usually goes from a search table with numerical elements (faster and less precise since the table has a fixed size with a number of predefined elements) until a computational procedure that calculates in real time the output (less fast and more precise). It is equivalent to a computer program that receives two inputs and offers an output being deterministic (the same outputs always occur at the same inputs), invariant in time (does not change) and non-linear (non-linear relationship between inputs and exit).

As for the scale factors, considering two inputs and one output, they are usually one for each input and the output. These three scale factors constitute the controller's gains and decisively influence the desired (optimal) operation of the control procedure. The three values are usually adjusted by different procedures, although the adjustment of the two scaling factors of the inputs is sufficient to obtain the desired operation of the controller.

Thus, to adjust the control loop it is only necessary to calculate the optimal values of the scale factors, which are obtained from:

- the knowledge of the function G _t (s) that models the drilling process,

- the knowledge of the maximum delay L _max , which is the sum of the delay Medium network caused by the network means and the delay due to the dead time of the drilling process Unedited- According to a preferred embodiment of the invention, the maximum challenge of The network is greater than 0.2 seconds, and greater than 0.4 seconds according to a more preferred embodiment of the invention.

- The use of a merit index (also known as a cost function) that one wishes to minimize, such as the integral of the absolute value of the error (IAE), the integral of absolute value of the error by time (ITAE), the integral of quadratic error (ISE) and the integral of the squared error by time (ITSE), just to mention some indices. The minimization of these indices allows the optimization of the process, such as maximizing the starting rate, maximizing the useful life of the bit, minimizing vibrations, etc.

First, an initial adjustment is made in which a value of 1 is assigned to all the scale factors, although other initial values can be assigned from the technical knowledge of the process. Subsequently, the values of the scale factors that minimize one of the aforementioned criteria are obtained. In this way, the controller is adjusted or tuned to the optimal values of these scale factors for the corresponding merit index (behavior index or cost function). Known methods are used, such as the Nelder-Mead method, simulated temple, crossed entropy, genetic algorithms, or others.

In addition, according to a preferred embodiment of the invention, the anticipatory control is combined with the fuzzy controller, by adding a block that relates the reference or prescribed value (reference or reference value that is desired to remain constant during the process) with the scale factor (gain) of the output. In this way, the scale factor of the output is the result of multiplying the reference value by a constant (for drilling, k = 0.0005). In this way, whenever the reference or the prescribed prescribed value changes, the scale factor of the output will change

Neuro-Blurry Control

On the other hand, a second aspect of the present invention describes a control method by internal model (IMC) based on neuro-fuzzy controllers for drilling processes performed by a CNC machine controlled from a control means, where the CNC machine and the control means are connected by a network means, and where the maximum overall delay of the drilling process is L _max . According to preferred embodiments of the invention, the parameters that define the neuro-fuzzy controllers are determined in such a way that a merit index is minimized, such as, for example, the IAE, ITAE, ISE and ITSE. In addition, the network medium can be an MPI network, PROFIBUS, Ethernet, Internet, and in general any network medium used in the industry. The connecting means is characterized by its global maximum delay L _max , which in preferred embodiments of the invention is greater than 0.2 seconds, and in another even more preferred embodiment of the invention, L _max is greater than 0.4 seconds.

The BMI is a well-established contribution in the literature to design controllers so that the process model is used explicitly (direct synthesis) in the design procedure of a controller. However, when the mathematical model of the Gt (s) process is not available or it is very sophisticated, the IMC can use an explicit model obtained by experimental identification (known as "black box" contribution).

On the other hand, neural networks (have shown an excellent ability to represent any non-linear function with the desired degree of precision.) Because of this feature, neural networks are suitable for the identification and control of non-linear systems. a block anticipative to the control system by internal model, which relates the difference between the reference and the output with the control input to the drilling process itself.

Two particular embodiments are described below in relation to this second aspect of the invention that combine networks neurons with fuzzy logic in control schemes by internal model.

ANFIS

An embodiment of the present invention combines the control by internal model (IMC) with a neuro-fuzzy scheme called ANFIS to control the cutting force of a drilling process so that the rate of material removal is maximized, at the same time that the useful life of the bit is also maximized. The ANFIS system is one of the first known neuro-fuzzy systems. As a reference, we present the document by Dash, et al "Fuzzy and neural controllers for dynamic systems", of the Proceedings of the International Conference on Power Electronics and Power Systems, IEEE, in Singapore. The principle of the ANFIS scheme is based on the extraction of fuzzy rules in each level of a neural network. Once the rules are obtained, they must provide the necessary information of the overall behavior of the process.

TWNFI

In another embodiment of the present invention, the control by internal model (IMC) is combined with the neural networks, the fuzzy logic and the transductive techniques.

From the perspective of psychology and medicine (pediatrics), transductive reasoning uses a particular element or detail of an event to judge or anticipate a second element or event. This process can lead to creative or divergent perceptions of the environment, and in some cases can lead to excessive generalization. From the point of view of the Theory of Systems and modeling of systems, the transductive methods generate a model in a single point of the workspace. For each new data that has to be processed, the closest examples among the known data are looked for, with the aim of creating a new local model that dynamically approaches the process in the new state as faithfully as possible. It is, therefore, to give more importance to the specific information related to the data to be processed than to the general information provided by the entire training set.

The transductive methods have some advantages over the inductive ones since, on occasion, creating a valid model for the entire space or region of operation is a difficult task and in some cases the result is insufficient. The dynamic generation of personalized local models allows the extension of knowledge (represented as the set of known data) in a simple way, allowing incremental learning online. In addition, these strategies have the ability to function properly with a reduced training set.

Among the various transductive techniques available, the present invention employs the TWNFI (Transductive Weighed Neuro-Fuzzy Inference system), used by Song and Kasabov for obtaining local models of the process in "TWNF I-a system of neuro-fuzzy transductive inference with normalization of data for personalized modeling ", published in Neural Networks, 19, 1591 - 1596, document cited as reference. This control scheme provides the characteristic advantages of the three techniques that form it:

Neuronal: excellent ability to model any non-linear function with a high degree of precision, in addition to having a high learning capacity. Blurry: semantic transparency, ability to represent human thought and excellent behavior in situations of uncertainty and imprecision.

Transductive: estimation of the model in a single input-output set of the space, using only information related to said set.

PID control + filtering

Finally, according to a third aspect of the invention, a control procedure is provided for drilling processes performed by a CNC-machine controlled from a control means, where the CNC-machine and the control means are connected by a means of a network, where L _{max is} the maximum overall delay of the drilling process, and where the control scheme is a closed-loop PID control scheme whose internal line comprises a PID block characterized by three factors called K _p , k, and k _d , and a block that represents the drilling process.

Furthermore, according to preferred embodiments of the invention, the network medium can be MPI, Profibus, Ethernet, Internet, etc. being in a preferred embodiment of the invention overall maximum delay L _max of the drilling process of 0.2 seconds, and in a still more preferred embodiment of the invention, L _max is greater than 0.4 seconds.

The initial calculation of the factors K _p , k, and k _d is carried out, in a preferred embodiment, using the Ziegler-Nichols method, based on the knowledge of the transfer function in the Laplace transform domain of the drilling process high performance and delay global maximum L _max, which comprises the delay due to dead times and the delay caused by the network medium. Subsequently, the choice of parameters can be optimized by means of methods such as Nelder-Mead, simulated tempering, and others known in the art, following minimization criteria based on merit indexes, such as, for example, the integral of the absolute value of the error (IAE), the integral of absolute value of the error by time (ITAE), the integral of quadratic error (ISE) and the integral of the squared error by time (ITSE), just to mention some indices.

In addition, the method comprises pre-filtering the input signal. The reference or prescribed value is not entered directly into the control system, but is filtered with a filter:

where Gf (z) is the transfer function in the Z domain, Fr 'is the filtered reference value, Fres the reference value and τis the filter coefficient.

DESCRIPTION OF THE DRAWINGS

To complement the description that is being made and in order to help a better understanding of the characteristics of the invention, according to a preferred example of practical realization of the same, a set of drawings is included as an integral part of said description. where, with illustrative and non-limiting character, the following has been represented:

Figure 1 shows a diagram of the drilling system according to the invention. Figure 2.- Shows a scheme of the fuzzy control system in simple loop.

Figure 3.- It shows a scheme of the fuzzy partitions and the membership functions for ΔF, Δ ² F and Δf.

Figure A - Shows a graph representing the response of the drilling force to an input in a drilling process where the control signals are transmitted through a network medium.

Figure 5.- Represents a diagram of the devices that make up the system in a preferred embodiment of the invention.

Figure 6.- Represents a graph of the ITAE index that results from the optimization.

Figure 7.- Represents the corresponding input factors for the fuzzy controller.

Figure 8 .- Represents the response to the step of the cutting force.

Figure 9.- Represents the behavior of the cutting force in an embodiment of the present invention.

Figure 10.- Represents the variations in the speed of advance for the minimum, medium and maximum delays.

Figure 11.- Represents the behavior of the ITAE (dashed line) and the ITSE (solid line) when delays occur.

Figure 12.- Graph representing the overshoot in the presence of delays

Figure 13.- Graph showing the behavior of the cutting force in relation to the drilling depth.

Figure 14.- Graph showing the cutting force in uncontrolled drilling processes and controlled by a fuzzy regulator.

Figure 15.- Graph showing the variations in the speed of advance in uncontrolled drilling processes and controlled by a fuzzy regulator.

Figure 16.- Scheme that represents the architecture of the ANFIS system.

Figure 17.- Control scheme by internal model (IMC).

Figure 18.- Graph that represents the functions of belonging, rules and outputs of the direct ANFIS model.

Figure 19.- Graph that represents the functions of belonging, rules and outputs of the ANFIS inverse model.

Figure 20.- Graph that represents the response of the direct model in an ANFIS system.

Figure 21.- Graph that represents the response of the inverse model in an ANFIS system.

Figure 22.- Architecture of the ANFIS-IMC system in an embodiment of

Ia invention. Figure 23.- Graph that represents the response of the real system in an ANFIS system.

Figure 24.- Graph that represents the control action in a system

ANFIS.

Figure 25.- Example of the evolutionary grouping algorithm for two inputs.

Figure 26.- Membership function generated from the results of the ECM algorithm of Figure 26.

Figure 27.- Membership function generated from the results of the ECM algorithm of Figure 26.

Figure 28.- Represents a block diagram of the TWNFI algorithm.

Figure 29.- Represents the direct model of the drilling process obtained by TWNFI.

Figure 30.- Represents the inverse model of the drilling process obtained by TWNFI.

Figure 31.- Represents the control scheme by internal model in

Ia network.

Figure 32.- Represents the statistical distribution of the induced delays in the network obtained with a set of 10,000 samples.

Figure 33.- Represents the cumulative distribution of the delays induced by the network obtained with a set of 10,000 samples.

Figure 34.- Represents the architecture of the TWNFI-CMI control in a preferred embodiment of the invention.

Figure 35.- Shows a graph of the response of the real system.

Figure 36.- Shows a graph showing the control action in the control action when the material is drilled 17-4PH.

Figure 37.- Shows a PID control scheme with a previous filter.

PREFERRED EMBODIMENT OF THE INVENTION

Example 1: Fuzzy controller in simple closed loop

An example of a preferred embodiment of the invention is described below where a fuzzy control scheme by simple loop is used, whose general scheme is represented in figure 2, to control a drilling process carried out by means of a system (1) such as which is shown in Figure 1, in which an accelerometer (9) arranged on the drill bit (6) of a machine tool (2) is observed. The part to be drilled (6) is located on a dynamometer platform (8). Finally, the CNC (3) controlling the operation of the machine tool (2) is connected to a PCI (4) by means of a connection means, which in this case is an MPI network (5). In Figure 2, the reference number 10 represents the fuzzy controller. The usual steps have been followed to define the input and output membership functions and to construct fuzzy control rules in the design of a control procedure blur of two inputs and one output. The fuzzy control performs actions in real time to modify the advance speed / of the bit (6). The manipulated or output variable is the increment of the feed rate (Af, as a percentage of the initial value programmed in the CNC machine). The error and output vectors are:

where ΔF is the error in the resultant force (in newtons), A ² F is the change in the error in the resulting force (in newtons) and K _e , K _ce and GC are scale factors for the inputs (error and change in the error) and output (change in the speed of advance) respectively.

The torque values applied by the motors that move the bit (6) are acquired from an open architecture CNC (3). The reference value of the force (F _r ) is obtained from the combination bit (6) / material of the piece (7). For each sampling period k, the error in the resulting force and the change in the error in the resulting force are calculated as:

where AF is the error in the resulting force (in newtons) and A ² F is the change in the error in the force resulting in the instant k.

The blurred partition of speech universes is based on prior knowledge and experimental results. The universe of Speech input variables consist of three membership functions of triangular shape in the range of [-150, 150]. The universe of discourse of the output variables consists of five trapezoidal belonging functions, equally spaced, and established according to the maximum modification of the nominal advance speed under nominal cutting conditions (around 10% for the speed of nominal advance). Figure 3 shows the resulting fuzzy partition. Three fuzzy sets of three and five are used for the inputs and output. They are, NB, big negative; NM, negative medium; ZE, zero; PM, positive medium; and PB, large positive.

The process of selecting the belongings is the result of combining the process of trial and error with several empirical design guidelines obtained mostly from the knowledge of the process and from simulation studies. The membership functions are essential to achieve adequate control. When membership functions are used, the resulting system is the sum of a non-linear global controller (static part) and a non-linear local PLC controller (which changes dynamically with respect to the input space). Therefore, this type of membership function is relevant to deal with processes of non-linear behavior, such as the drilling process. The selection of the type of fuzzy input and output sets is a key step in the design of a fuzzy controller.

A series of rules are considered, which consist of linguistic statements that link each antecedent with its respective consequence, with the following syntax:

IF ΔF is PB AND Δ ² F is PB THEN Δf is PB

These fuzzy rules provide important principles and relevant information about the drilling process. Under normal drilling conditions, the constant feed speed is set conservatively, according to data manuals about drilling, bits and materials. However, the feed rate values are adjusted manually in real time depending on the cutting parameters, to optimize the drilling process. In order to maintain a constant resultant force, the advance speed must be reduced when the force increases (that is, due to an increase in the depth of the drilling). On the other hand, when the force decreases, the advance speed should be increased to maximize the speed of material extraction. A total of 9 control rules are developed, which extend to 49 rules, which are shown in the following tables:

The sub-product composition operator is selected for the interference compositional rule. Using the algebraic product operation and developing the fuzzy implications and applying the maximum binding operation, one obtains, considering the particular case of the "Sup-Product" inference method and applying the T2 (product) standard:

Developing the implication and applying the co-norm Si (MAX the maximum value, but it can be another: there are more than 30 valid for the control, this one is the most used), where ω represents the rotation speed of the bit (6) :

where my is 9, 25 or 49 rules.

Similarly, it can be done considering Ti (minimum) or T2 (product) as the norm. They are the two most used in control. The center of gravity was selected as the deborrosification method:

where Af (DW) is the crisp value Δf¡ (Δw¡) to a clear input given (ΔF¡, Δ ² Fj), and μ _R (Δf¡) (μ _R (Δw¡)) is the function of belonging to the union. The control scheme considering only as an action variable Δf.

There are basically three traditional unbundling methods: maximum, mean of maximums (MOM) and center of area (COA). It has been known for some time that the COA produces a least squares error smaller than the MOM. In all cases, the maximum produces worse results than the other methods, despite its simplicity and less computing time. From the point of view of the dynamics of the control loop, the MOM produces a better transient response, while the COA behaves better in the steady state. Additionally, the MOM behaves like a multi-level relay, and the COA behaves like an integral proportional controller (Pl). Recently they have been developed other disembedding strategies under the same point of view, that is, the formal treatment of the uncertainty regarding the validity of the probabilistic distribution of the output generated by the decision-making process of fuzzy systems (that is, the conversion of The probabilistic distribution of the fuzzy output set in a probabilistic distribution function The strategy of the COA method for desembornado is selected due to its adequate behavior in steady state and its use in experimental and industrial fuzzy controllers.

The control action generated for each sampling instant defines the final actions that are applied. The strategy used to compute / and ω determines what type of fuzzy regulator is used. The output scale factor (GC) multiplied by the control action generated at each sampling time provides the final actions that will be applied to the cutting parameters of the CNC machine (2, 3).

Furthermore, the present invention admits the possibility that the control is carried out through network means with relatively large delays, either a field bus or other possibilities, such as Internet, Ethernet, etc. In this example, the network medium is the field bus MPI (5), very similar to PROFIBUS, which operates according to a master-slave scheme between devices connected to a network. Each slave is assigned a set of slaves that polls periodically. The access to the network, in this case an MPI network (5), is regulated by a witness that moves between the masters. This type of distributed control systems are affected by instabilities due to the retransmission of data by slaves and the asynchronous activities carried out by teachers. The multipoint interface (MPI) or MPI network (5) is a programming interface for the SIMATIC S7 series from Siemens that resembles the PROFIBUS protocol. The interface of the MPI network (5) is identical to that of the standard PROFIBUS RS485. The transmission speed can be increased up to 12 MB / sec with the use of an MPI network (5). The architecture of the control system for a CNC machine (2, 3) based on an MPI network is shown in Figure 1.

When the control signal (forward speed order) is transmitted through the MPI network (5), the introduction of a delay is inevitable. Figure 4 shows the response to the step of the resultant force to

Ia order of speed of advance in a process of drilling of high performance. The maximum global delay (L _max ) is around 0.4 seconds, including both the dead time process (delayed) and the delay introduced by the network (L _mechanical network) -

The fuzzy control procedure described in the present example works even with the delays introduced by the MPI network (5). The data acquisition system consists of a dynamometer, a load amplifier and the hardware and software modules described in figure 5. The cutting forces are measured with a piezoelectric dynamometer Kistler 9257B mounted between the piece and the drill table. The electrical load is then transmitted to the four-channel Kistler 5070A amplifier through a network cable. The interface hardware module consists of a network block and a 16-channel AT-MIO-16E-1 A / D acquisition card with a maximum sampling frequency of 500 kHz. The A / D device transforms the analog signal into a digital signal, so that the Simulink program can read the data and the force components for the three axes can be obtained, processed and displayed. Real-Time Windows Target (RTWT) allows real-time execution of Simulink models. The output of the fuzzy controller is connected to the process through an MPI network (5) with a default transmission speed of 187.5 Kbits / s. A CP5611 card connects the PC that implements the fuzzy control procedure. The interface of the MPI network (5) is a master client (active station) and manages exchanges with Siemens S7 PLCs. The system has two masters, the man-machine control (MMC 103) and a numerical control unit (NCU 573.3)

To check the efficiency of the closed-loop control procedure, the fuzzy control is tested by simulation using the Simulink software. In optimization, the adjustment of the fuzzy controller is based on an optimization criterion of a merit index. The objective is to obtain the optimal parameters for the input scale factors

where the merit index or ITAE cost function is minimal.

The integral of time due to absolute error (ITAE) or index of merit describes the quality of the response of the system to an external disturbance. In this study, a step in the reference of force as a disturbance is considered, and the objective is to assess the precision with which the system follows reference changes using the ITAE criterion. The optimization is done here using a simplex search algorithm for unrestricted optimization. The cost function is evaluated by simulation, so a process model is necessary. The adjustment is carried out using the Matlab / Simulink software and the optimization tools. The minimum ITAE = 463.07 is reached in iteration 64, corresponding to [K _e , Kce] opt = [0.0559, 0.1156]. The ITSE criterion is 3.0432 x 10 ⁵ , and the maximum overshoot or overshoot is 0.30%. The results of the simulation are shown in figures 6 and 7. The response to step of the system is shown in figure 8. It is observed in it how the resulting force is optimally regulated with respect to the reference value.

The delay L of the MPI network (5) is simulated assuming a random delay between 0 and 0.6 seconds, and 100 simulation tests are carried out for each set of simulation parameters. The maximum, minimum and average value of the ITAE index are then calculated. For the minimum randomly generated delay of 0.0077 seconds, the maximum overshoot or overshoot was -0.86% and the ITAE index was 289.87. For the average delay of 0.2783 seconds, the maximum overshoot or overshoot was -0.2131% and the ITAE was 389.30. The worst case occurs for the maximum random delay, 0.5966 seconds, where the maximum overshoot or overshoot is 1.38% and the ITAE is 697.30. Figures 9 and 10 show the simulation results corresponding to the response of the system to the step for the three delays. Figure 9 represents the behavior of the resultant force, while Figure 10 represents the variations of the forward speed in each case. It is deduced from the simulation results that the optimum adjustment achieved in the simulation guarantees a transient response without maximum overshoot or overshoot, with a rise time of around 0.7 seconds.

The influence of the delay on the deterioration of the ITAE and ITSE indices is shown in Figure 11. The increase in the ITAE and ITSE indices with the increase in the delay is not too pronounced, which demonstrates the robustness of the fuzzy controller in the presence of a dead time plus a delay introduced by the MPI interface. The ITAE (solid line) and the ITSE (dashed line) increase with the delay in a non-linear way.

The influence of the delay in the transitory response is also analyzed considering a random delay. The random delay is distributed evenly between 0 and 0.6 seconds. A simulation analysis is performed using 1000 delay samples. Figure 12 shows the behavior of the maximum overshoot or overshoot in the presence of delays of up to 0.6 seconds. It is evident from this graph that a transient response can be achieved without maximum overshoot or overshoot, despite the delays.

The execution example is completed with a test using a machine tool (2) Kondia HS1000 equipped with a CNC (3) Sinumerik 840D. The drill bit (6) used is a 10 mm Sandvik. diameter. The material of the piece (7) to be drilled is GGG40 with a hardness number of 233 HB. The nominal feed speed and nominal speed are f ₀ = 100 mm./min and w _o = 87O rpm, with a maximum cutting depth of 10 mm. (equal to the diameter of the hole).

Figure 13 shows the experimental results that correspond to the drilling of the piece (7) GGG40 with the drill (6) of 10 mm. diameter. Figures 14 and 15 represent the behavior of the controlled and uncontrolled force and the variations in the speed of advance for both cases analyzed. In order to suppress the increase in the resultant force, the advance speed is gradually decreased when the depth increases, and the resulting force is suitably regulated in the given reference. The good behavior of the transitory response is verified by the ITAE (17.72), ITSE (9.23) and IAE (16.46) indices. However, the drilling time increases by 5.75% when controlling the drilling force.

Example 2: ANFIS neuro-fuzzy control

ANFIS implements the Takagi-Sugeno model for the structure of the If-Then rules of the fuzzy system. The architecture of ANFIS, which is represented in Figure 16, has five layers. The nodes represented with squares are nodes whose parameters are adjustable, while the nodes represented by circles are fixed nodes.

Next, ANFIS is presented for the particular case of a system of one input and one output.

1 ^a Layer: In the first layer smearing occurs. The output of each node is represented by Ol, i, where i is the i-th node of layer I:

where f is the forward speed entering the node and A i is the fuzzy set associated with the node. If we use a Gaussian function as a fuzzy belonging function we would obtain the following expression, where a, b, and d, are the adjustable antecedent parameters:

2 ^a layer: In the second layer multiply the input signals and

The output is the result of applying the maximum rule.

3 ^a layer: The third layer normalizes the importance of each rule:

4 ^a layer: The fourth layer calculates the consequent, or what is the same, the function of Takagi-Sugeno for each fuzzy rule, where m and c are the consequent parameters.

5 ^a

layer: Finally, the fifth layer performs the undocking by computing the general output as the sum of the input signals:

ANFIS uses as a learning strategy the retro-propagation or backward propagation of errors to determine the antecedent of the rules. The consequent of the rule is estimated by means of the method of least squares. In the first step or "step forward", the input models are propagated and the optimal consequents are estimated by an iterative procedure of least squares, while the antecedents remain fixed. In the second step or "backward step", the error backpropagation procedure is used to modify the background while the consequents remain constant. This procedure is repeated until the stop condition is reached (error criterion).

When the values of the antecedents are fixed, the general output of the system can be expressed as a linear combination of the following:

On the other hand, the antecedents are updated by a criterion of

"gradient-descending", where η is the learning rate for ay. If f is an invertible matrix:

On the other hand, from the classical point of view, the control by internal model uses a closed-loop control scheme in which both a direct model (G _M ) of the process to be controlled (G _t ) located in parallel with it, intervene. as well as an inverse model (G _M '). The delay is represented by L and the disturbances by d (figure 17).

The use of control by internal model (IMC) theoretically guarantees robustness and stability of the control system in the presence of external disturbances. In addition, it is possible to add a preemptive block arranged in parallel with the blocks G _F and G _M 'of figure 17.

The filter Gf is included in the control system in order to reduce the high frequency gain and improve the robustness of the system. It also serves to smooth the rapid and abrupt changes in the signals, improving the response of the controller:

where ki and l <2 are design parameters and usually k ₁ = k ₂ . An IMC scheme can be implemented using an ANFIS neuroborpore system. First, the ANFIS system is trained to learn the dynamics of the process through input-output data. In this way the so-called direct model is obtained. Another ANFIS system is trained to learn the inverse dynamics of the process and to function as a non-linear controller. In this way the so-called inverse model is obtained. We describe both procedures below.

In this embodiment, the forward speed has been considered as the input variable and the average cutting force as the output variable for the direct model.

In order to make a better fit of the model, an initial model is created by introducing a set of training data (178 data) to the neuroborbary system to subsequently adjust the parameters of the model initially created by introducing a set of test data into the neuroborbary system. (209 data) different from the previous ones.

Drills are made, using a system analogous to that of Example 1, on specimens of nodular cast iron GGG40, material widely used in the aerospace industry. The nominal operating conditions were rotational speed of 870 rpm, initial speed of 100 mm / min, and depth of cut of 15 mm.

In the phase of obtaining the models, certain parameters are modifiable such as the number of membership functions in the smudging, the class or type of said functions, as well as the order of the Takagi-Sugeno rules of unbundling. Likewise, the accuracy of the model can be improved by changing the parameters of the learning process (hybrid learning or error backpropagation, number of iterations, step size, etc.). The choice of the correct variables and the optimal parameters has been made based on obtaining a balance between the error criterion of the square root of the mean square error (RMSE) and the dynamic response of the model.

Several tests have been carried out with Takagi-Sugeno systems of zero order and of first order, with Gaussian, sigmoidal, triangular and trapezoidal membership functions, as well as with different numbers of membership functions, ranging from two to nine. From the study carried out, it was obtained that the direct and inverse models that best adjust the response of the system are those that use two belonging functions in the smudging phase, these functions being of the Gauss bell type, and with Takagi-Sugeno rules of order zero or constants (figures 18 and 19).

Takagi-Sugeno output functions:

Medium Strength (low) = 173.8 N Medium Strength (high) = 931, 5 N

Rule 1: If Advance Speed is "low" then Medium Strength is

"low"

Rule 2: If Advance Speed is "high" then Medium Strength is "high"

The increase in the number of membership functions and the order of the T-S systems does not produce significant improvements in the accuracy.

As mentioned previously, obtaining the inverse model has not been done by inverting the model. Another training has been carried out with the average force as input and the speed of advance as output. Takagi-Sugeno output functions:

Speed Advance (low) = 12.42 mm / min Speed. Advance (high) = 127.4 mm / min

Rule 1: If Medium Strength is "low" then Advance Speed is

"low"

Rule 2: If Medium Strength is "high" then Advance Speed is "high"

The training parameters were 100 iterations of the algorithm (a greater number of iterations causes an overtraining and, as a result of this, unwanted peaks in the system output), hybrid training mode (only with backpropagation of the error the value of desired output) and step size of 0.01 (the increase of this value does not produce a significant improvement of the output and a greater computation of operations).

For reasons of speed and simplicity, the models were obtained by means of a tool provided by the well-known Matlab software. The training time in the models is around 0.14 seconds for both the direct model and the inverse model.

These times are obtained in a computer with Intel Core2 processor

CPU 6400 - 2.13 GHz with Windows XP Professional operating system. The training is done offline.

Although we have chosen models that, a priori, have a mean square error percentage greater than other models, the choice has been based on their dynamic behavior is better (responses without oscillations) and are very simple. A fundamental requirement of the direct model is that the transient response is good because of the negative influence of the overshoot in the useful life of the bit (6).

The responses of the direct and inverse models are represented in figures 20 and 21. The mean square error (RMSE) for both cases is summarized in the following table:

Certainly the errors are high. However, in the application that concerns us, simple and computationally efficient models are required in real time. In addition, these models represent the dynamics of the drilling process in an approximate way but with fewer errors than other more complex models.

Tests are carried out in a drilling system (2) comprising a machine tool (2) Kondia HS1000 equipped with a

CNC (3) open Sinumerik 840D. In the experiments, a drill bit (6) with a diameter of 10 mm was used. Sandvik R840-1000-30-AOA made of solid carbide with TiN / TiAIN coating.

The control has been carried out through a PC (4) that is connected to the CNC (3) through an MPI network (5), as shown in Figure 22. The models and the control scheme are implemented in Simulink Real-Time Windows Target software.

For reading and writing data through the MPI network (5) it has been developed an application in C language. In case of failure or loss of information from the MPI network (5), the control system has programmed a safety mechanism in the CNC (3) that keeps the speed of advance constant on the process.

In order to check the effectiveness of the control system developed, several tests have been carried out with the nominal conditions of forward speed f = 100 mm / min, speed of rotation n = 870 rpm and 14 mm. in the depth of cut recommended for the GGG40. The force is measured through a dynamometer platform (8) Kistler 9257B. The values of speed of rotation, speed of advance and other parameters contributed by the CNC (3) are transmitted through the MPI network (5).

The results of the experimental tests are shown in figures 23 and 24. It can be observed that despite the demanding initial condition and the delay, the neuroborbic system IMC is able to meet the design requirements with a rapid response (time of establishment of 2 seconds) and without overshoot. With the control system it is possible to increase the material removal rate. In addition, the quality in the transient response and the non-existence of overshoot and oscillations in the response contribute from the industrial point of view to a better use of the useful life of the drill (6).

The following table shows a comparison between the merit indices obtained by different control procedures:

Example 3: Neuro-fuzzy control TWINFI

TWNFI is the acronym that collects the literature for a neuro-fuzzy transductive and dynamic inference system, originally proposed by Song and Kasabov, which implies the creation of particular local models for each sub-space of the problem, using a modification of the Euclidean distance .

The entries to this system can be expressed in different units of measurement. However, normalization is recommended. In this work, each of the input data is normalized

according:

where μj is the average and σj is the standard deviation of the known data set or training set.

Once the normalization (Xj) has been carried out, the customized local model is created from the data of the training set closest to each new input data. For the selection of this subset of data, the weighted Euclidean distance is used:

where P is the number of elements of the vector or input data, ^x is the vector of input data, is each of the vectors or data of the

training set.

The size of this subset (N _q ) is a parameter of the algorithm.

The weights (W _j ) of each component of the input vector (whose values are between 0 and 1) are obtained in a subsequent process of adjustment of the model and reflect the importance of each variable. Initially, all have the unit value.

When the examples have already been selected, the custom model is created. The neuro-fuzzy inference system used by

TWNFI employs a Mamdani inference engine whose fuzzy membership functions are Gaussian, both in the background and in the consequential if-then rules. The fact that these functions are derivable, allows the subsequent use of a backward propagation algorithm (back-propagation, in English), based on least squares and descent by gradient, to optimize its parameters.

The algorithm of evolutionary grouping (ECM) defined by Song and is used to create membership functions and fuzzy rules.

Kasabov in "DENFIS: Dynamic evolutionary neural-fuzzy inference system and its application for the prediction of time series", IEEE,

Transactions in fuzzy systems, 10, 144-154, which is incorporated herein by reference. It is an iteration algorithm for the online dynamic grouping of a data set.

Start with an initial set for the first data. For the following data the algorithm, starting from the Euclidean distances and the grouping threshold value (D _t hr), adds it to an existing set (updating the center and the radius thereof) or creates a new set. The resulting groups or clusters are circular and are used to create the Gaussian membership functions. For this, the center of the set is taken as center of the Gaussian function, and the radius as width (figures 25, 26 and 27).

If we consider that the system has P inputs, an output and M fuzzy rules defined initially through the grouping algorithm, the lth rule has the form:

Ri: If Xi is Fn and X ₂ is F | ₂ y ... xp is F _IP , so y is Gi. (Cluster l)

where

Here myn are the centers of the Gaussian functions for the inputs and outputs, a and δ are the widths, i = 1, 2, ..., N _q is the index that represents the number of nearest neighbors, j = 1, 2 , ..., P represents the number of input variables, and I = 1, 2, ..., M represents the number of fuzzy rules.

The m and n centers as well as the widths a and δ are obtained as a result of the ECM grouping algorithm, while the parameter αy is chosen by design (initially with a unit value) and represents the weight each of the functions of belonging to the input . All these parameters and other important factors are adjusted later with the algorithm of backward propagation of the errors as described by Song and Kasabov.

Using the center method of the modified area as the undoing method, the output value of the system for an input vector

It is calculated as follows:

Once the model is obtained, and using the input-output pairs of the closest training data, the system deals with

minimize the following objective function:

being

as vector of distances calculated in the first step.

In Figure 28 can be seen in more detail all the different steps that follows TWNFI for the creation of the model.

Although a different grouping algorithm could be used ECM, as well as another learning algorithm for the optimization of parameters other than the backwards propagation of errors, this work is based on ECM and retro-propagation by the speed and simplicity of both methods.

On the other hand, internal model control (IMC) is a well-used and well-established technique in the design of intelligent controllers. This closed-loop control scheme explicitly uses a model (G _M ) of the dynamics of the drilling process to be controlled located in parallel with it (G _t ). On the other hand, it also contains another model of the inverse of the plant dynamics (G _M ') located in series with the process and acting as controller.

One of the advantages of this type of control is that its stability and robustness properties can be analyzed and manipulated in a clear and simple way, even for non-linear systems. However, the inversion of non-linear models is not an easy task, and analytical solutions may not exist. In certain cases, the solution may be impossible to implement despite the existence of a solution. Another associated problem is that the inversion of the process model can lead to unstable controllers when the system is of a non-minimum phase.

In this patent the TWNFI algorithm is used to create the models (direct and reverse) online. Before each new entry to the control scheme, both models are calculated. By means of this neuro-fuzzy inference technique, the creation of the inverse model is simpler and always offers a solution.

The direct model must be trained to learn the dynamics of the process. To achieve this, a TWNFI system is used with a set of training composed of input-output data, in which the inputs correspond to forward speed values, while the cutting force is used as the output variable (figure 29).

For the calculation of the inverse model, instead of proceeding to invert the direct model obtained in an analytical mode, another TWNFI system is used in which your training set contains data with values of shear force as input and velocity values of advance as an exit. In this way, the control system manages to learn the inverse dynamics of the high-performance drilling process (figure 30).

The training data of both the direct model and the inverse model have been obtained from real drilling operations with specimens of material GGG40 under the conditions that appear in the table that is shown a few pages below in this document. This set of data does not have to be very extensive since representative values of each operating region are sufficient.

The inverse models G _M 'and direct G _M are auto-regressive and moving average (ARMA) since they use previous states of the input and output variables to get a better approximation in the force-advance relationships of the training set of the TWNFI algorithms:

where

is the shear force estimated by the direct model and f (k) the forward speed calculated by the inverse model.

The degree of accuracy of the models will be determined by Ia choice of certain parameters of the TWNFI algorithm such as number of nearest neighbors, number of iterations and learning rates of the error propagation algorithm, threshold value of the grouping of sets (parameter of the grouping algorithm used), etc. When choosing an optimal value of these parameters, the aim is to find a balance between the error of the local models with respect to the linear theoretical model and the dynamic response of them.

Once the models have been obtained, it is decided to also include a low-pass filter (G _F ) in the control scheme.

where ki and l <2 are design parameters and usually ki = k ₂ .

The filter is incorporated into the control system in order to reduce the high frequency gain and improve the robustness of the control system. It also serves to smooth the rapid and abrupt changes in the signals, improving the response of the controller.

Figure 31 shows the control scheme by internal network model. In it, the layout of the direct and inverse models GM and GM ', respectively, can be observed. In addition, the GF filter and the drilling process represented by G _{t are shown} . The delay (including the one introduced by the different levels of the network and the intrinsic to the drilling process) is included in block L. The issues related to the delay L and the architecture of the control system through a network media will be explained below.

The development of information technologies and Communications has allowed the widespread use of network control and supervision systems for distributed processes, both hierarchically and geographically.

Certainly, the use of network control systems entails important advantages such as reliability, improvement of resource utilization, ease of maintenance and diagnosis of errors, and above all, the possibility of reconfiguration of its various components. However, it is clear that the use of these networks introduces a series of delays in the systems that can cause instabilities in the process. In fact, in the field of process control, the delay introduced by the networks themselves (Profibus, Profinet, etc.) is usually incorporated into the models. As described in the previous section, all the delays (inherent to the process and the network) have been grouped in this case in block L.

Within the different existing network technologies, field buses have been consolidated as the most used industrial communication networks. These technologies have numerous advantages, among which its deterministic behavior stands out, and therefore it is possible to limit the delays and know the maximum delay due to the network. However, among its drawbacks are the high cost of hardware and the difficulty of integration with other products

Recently, Ethernet is being used in the field of industrial automation, due to the low cost, availability and high transmission speeds. The main technical obstacle of Ethernet in industrial environments is its nondeterministic behavior, which makes it in principle inappropriate for applications with real time requirements. Ethernet does not consume time in the bus arbitration, but the collision of packages can cause delays in the sending and even loss of information. For these reasons, a priori, it is impossible to predict the delay in sending information. The main difficulty of network control in general, and through Ethernet in particular, is that, although the control system is robust to the variations contemplated in the design, it may not be entirely tolerant of delays in communications not modeled

However, the use of switched Ethernet (whose network element is the switch) eliminates the possible collisions in the transmission of the information, increasing the efficiency of the network. As collisions do not occur, the network is not unstable due to high traffic loads and the delay is drastically reduced. Therefore, it has become a very promising alternative for network control systems. This embodiment of the invention addresses the control of the high performance drilling process through the switched Ethernet network technology, although the use of the Internet or other networks of similar maximum delays is also valid.

On the other hand, communication with the processes to be controlled can not always be carried out directly via Ethernet. For example, certain manufacturers of Computer Numeric Controllers (CNC) only establish communications through proprietary protocols using the software tools provided.

For this reason, in this example they have been established in the system

(11) Drilling two network levels. The first network level (15) has a computer PC1 (14) connected to the CNC (13) of open process architecture through a Profibus network (15) and using proprietary software. From the technical point of view the existence of proprietary software imposes restrictions on the connectivity to the open architecture CNCs (13). The model of the drilling process was obtained through this Profibus network (15). The maximum delay at this Profibus network level (15) is 0.4 seconds:

where τ _S c is the delay in the communications of the sensor to PC1 (14), T _CA the delay in sending the control action of PC1 (14) to the CNC (13) and Drilling the intrinsic delay to the drilling process itself performed by the machine tool (12).

A second network level is also defined, in this case an Ethernet network (15 '), which connects another personal computer PC2 (14') to PC1 (14). PC2 (14 ') incorporates free software and a real-time intermediary system (RT-CORBA). The TWNFI-CMI control system is finally implemented on this computer. In case of failure in the Ethernet network (15 '), a security mechanism in PC1 (14) keeps the control action constant in the CNC (13).

Taking into account experimental results about delays in manufacturing processes where the machine tools are connected to computers in local networks by means of Ethernet, as well as studies known in the art (Figures 32 and 33), it can be established as the maximum delay of the Ethernet network (15 ') a time of 5x10-3 seconds:

where Ts2 is the delay in sending data to PC2 (14 ') and T _A2 is the delay in sending the control action of PC2 (14 ') to PC1 (14).

It can be verified from all these data that the delay introduced by the Ethernet network (15 ') is negligible compared to that introduced by the Profibus network (15) (0.4 s >> 0.005 s).

Assuming that the maximum delay is known, it is possible to perform control through the Ethernet network (15 '), although it has been proven that it is equally valid to use the Internet as the second network level.

The control system obtained is applied to a drilling process. In order to check the robustness of the control system, different drilling tests have been performed on stainless steel specimens hardened by precipitation 17-4PH (martensilic), which is a material highly used in the naval and aerospace industry. The optimal conditions recommended by the manufacturers of drill bits for the drilling of this material, as well as other data of interest are presented in the following table.

Interestingly, the TWNFI algorithm that generates the direct and inverse personalized models, only has in its training set data from tests performed on nodular casting specimens with GGG40 spherical graphite. It also tries to demonstrate in this work that the control is valid for another series of conditions for which it has not been trained. The characteristics that are operated with GGG40 material are also shown in the previous table in order to compare the differences of both materials.

The actual tests have been carried out using a high-speed drilling system (11) comprising a machine tool (12) Kondia HS1000 equipped with a CNC (13) open Sinumerik 840D. Due to manufacturer restrictions, the communication with the open architecture CNC (13) must be carried out through a proprietary protocol based on the Profibus network (15). PC1 (14) has a Windows 2000 operating system and the application for reading CNC variables (13) is developed in Labview.

The force is measured through a Kistler dynamometer platform

9257B and it is sent to PC1 (14). The values of speed of rotation, speed of advance and other parameters contributed by the CNC (13) are also transmitted through the Profibus network (15). In this first network level, the processing of the measured force signal F _{M takes place} .

The control has been carried out from the PC2 (14 ') that is connected to the PC1 (14) previously commented through an Ethernet network (15'). In the PC1 (14 ') l is the TWNFI-CMI control system developed in C ++, performing the control over a platform in RT-Corba and under the RT-Linux operating system. The TWNFI-CMI control system calculates the control action (f) based on the measurement of the received force and sends it to PC1 (14), which will later write the variable in the open architecture CNC (13).

The algorithm parameters chosen have been the same for the direct model and for the inverse model (with the exception of the training sets that represent different dynamics although they contain the same data). With respect to the TWNFI algorithm itself, a closer number of neighbors (N _q ) of 5 has been chosen, a number of iterations of the error back propagation algorithm of 20 with a learning rate of 0.001. With respect to the ECM algorithm, it has been chosen as a threshold value for the generation of sets

In the experiments, a 10 mm diameter drill Sandvik R840-1000-30-A0A of integral hard metal with TiN / TiAIN coating was used.

In order to make a more complete study of the control system, a comparative study with the neuro-fuzzy ANFIS technique has been carried out in a control scheme by internal model. To compare both systems, the error criterion of the absolute integral of the error over time (ITAE), the absolute integral of the error (IAE) and the integral of the square of the error by time (ITSE) are used as indices of merit. The overshoot is also included due to the great importance that it has in the wear of the drill.

The results of the experimental tests are shown in figures 35 and 36, as well as in the following table.

The control action is wider in range (because it takes extreme values in the training set) but less changeable in time, which favors the performance of the team.

From the practical point of view the existence of an initial condition in the advance speeds adds to the requirements to be met in the transitory response and in the establishment time a greater difficulty.

Example 4: Control by closed loop PID

Finally, Figure 37 shows a control scheme corresponding to the PID closed loop control, which also includes a previous filter located before the control loop.

Claims

1. Control procedure for drilling processes carried out by a CNC machine (2, 3) controlled from a control means (4), where the CNC machine (2, 3) and the control means (4) are connected by network means (5), and L _max being the maximum overall delay of the drilling process, where the control scheme is a simple closed loop scheme whose internal line comprises a block representing the machining process, a fuzzy controller and scale factors K _e , K _ce and GC.

2. Control procedure for drilling processes according to claim 1, wherein the adjustment of the scale factors K _e , Kce and GC and the fuzzy controller is carried out in such a way that an index of merit is minimized.

3. Control procedure for drilling processes according to claim 2, wherein the index of merit is chosen from the following list: IAE, ITAE, ISE and ITSE.

4. Control procedure for drilling processes according to claim 1, wherein the control scheme further comprises a forward block that relates the input value to the scale factor GC.

5. Control procedure for drilling processes according to claim 1, wherein the maximum overall delay L _max of the drilling process is greater than 0.2 seconds.

6. Control procedure for drilling processes according to claim 1, wherein the maximum overall delay L _max of the drilling process is greater than 0.4 seconds.

7. Control procedure for drilling processes according to claim 1, wherein the network means (5) is chosen from the following list: MPI, Profibus, Ethernet and Internet.

8. Control procedure for drilling processes carried out by a CNC machine (2, 3) controlled from a control means (4), where the CNC machine (2, 3) and the control means (4) are connected by network means (5), and L _max being the maximum overall delay of the drilling process, where the control scheme is a control scheme by internal model that combines fuzzy controllers and neural controllers.

9. Control procedure according to claim 8, wherein the neuro-fuzzy controller is adjusted so that an index of merit is minimized.

10. Control procedure according to claim 9, wherein the index of merit is chosen from the following list: IAE, ITAE, ISE and ITSE.

11. Control procedure for drilling processes according to claim 8, wherein the maximum overall delay L _max of the drilling process is greater than 0.2 seconds.

12. Control procedure for drilling processes according to claim 8, wherein the maximum overall delay L _max of the drilling process is greater than 0.4 seconds.

13. Control procedure for drilling processes according to claim 8, wherein the network medium (5) is chosen from the following list: MPI, Profibus, Ethernet and Internet.

14. Control procedure for drilling processes according to claim 8, wherein the control scheme by internal model is an ANFIS control scheme.

15. Control procedure for drilling processes according to claim 8, wherein the control scheme by internal model is a TWNFI control scheme.

16. Control procedure for drilling processes carried out by a CNC machine (2, 3) controlled from a control means (4), where the CNC machine (2, 3) and the control means (4) are connected by network means (5), and L _max being the maximum overall delay of the drilling process, where the control scheme is a simple closed loop control scheme whose internal line comprises a block representing the drilling process and a PID controller, and further comprising a filter arranged before the control loop.

17. Control procedure according to claim 16, wherein the adjustment of the parameters of the block corresponding to the PID controller is carried out by means of the Ziegler-Nichols method.

18. Control procedure according to claim 16, wherein the PID controller and the filter are adjusted so that an index of merit is minimized.

19. Control procedure according to claim 18, wherein the index of merit is chosen from the following list: IAE, ITAE, ISE and ITSE.

20. Control procedure according to claim 16, wherein the maximum overall delay L _max of the drilling process is greater than 0.2 seconds.

21. Control procedure according to claim 16, wherein the maximum overall delay L _max of the drilling process is greater than 0.4 seconds.

22. Control procedure for drilling processes according to claim 16, wherein the network medium (5) is chosen from the following list: MPI, Profibus, Ethernet and Internet.