Automatic Control of the Weld Bead Geometry

*Guillermo Alvarez Bestard and Sadek Crisostomo Absi Alfaro*

## **Abstract**

Automatic control of the welding process is complex due to its nonlinear and stochastic behavior and the difficulty for measuring the principal magnitudes and closing the control loop. Fusion welds involve melting and subsequent solidification of one or more materials. The geometry of the weld bead is a good indicator of the melting and solidification process, so its control is essential to obtain quality junctions. Different sensing, modeling, estimation, and control techniques are used to overcome this challenge, but most of the studies are using static single-input/singleoutput models of the process and focusing on the flat welding position. However, theory and practice demonstrate that dynamic models are the best representation to obtain satisfactory control performance, and multivariable techniques reduce the effect of interactions between control loops in the process. Also, many industrial applications need to control orbital welding. In this chapter, the above topics are discussed.

**Keywords:** arc welding, feedforward decoupling, multivariable control, weld bead geometry, welding control

## **1. Introduction**

All fusion welds involve the melting and subsequent solidification of the base metal. The geometry of the weld bead is a good indicator of the melting and solidifying process. Generally, weld inspection starts by evaluating this weld bead geometry and is followed by further inspection of the mechanical properties and metallurgical structures [1]. Many resources and time are employed in the final inspection of the weld bead, which is conducted when the part is finished. At that time, the problem usually has no solution or the solution is very expensive. This is one of the reasons why the control of the weld pool geometry is imperative to improve the quality in the weld and to reduce the cost of welded components.

Research and development in this area have increased in the last five decades, starting from simple control methods and analogical devices, as shown in [2], to complex algorithms and digital devices and computers, as shown in [3, 4]. But, in the literature analyses made in [5], it is possible to observe that most of the cases (90%) of the developments work in horizontal position and only 10% work in orbital welding, despite the importance of orbital welding for the industry. It is important to note that this type of welding imposes strong challenges in the use of sensors due to orbital movement (which can be quite irregular) around the piece. The main challenges are in the size and portability of the sensor, flexibility in the

#### **Figure 1.**

*Statistical information of publications about control systems of the weld bead geometry: (a) welding positions; (b) model types; (c) control type.*

communication lines, continuous changes in position and lighting conditions (for optical sensors), and the effects of the force of gravity. These statistical data are shown in **Figure 1a**.

to be controlled. Other factors must also be considered, such as the actual possibility of modifying each of these variables and how these modifications affect other control loops. These correlations are mentioned in the literature, but often they are not totality quantified, indicating that there is still a wide-open field of research in

*Representation of a typical automatic control system: (a) closed-loop control; (b) open-loop control.*

The dead time (transportation lag or time delay) is another important parameter that can be obtained from cross-correlation analysis too [6]. The sampling time for digital control systems must be selected based on the process dynamic, and auto-

An important input to be considered on the control loop is the disturbance. This signal (or signals) can affect the process response and must be compensated by the controller. The open-loop controller cannot compensate for the disturbance action because it does not have a feedback signal. An example of disturbance is small variations in the height of the base metal surface product of heat. These variations change the contact tip to work distance and consequently the arc conditions. If the disturbance is measurable, some techniques can be used to improve the response of

The model or process can be obtained using white or black box techniques. The first modeling technique required great knowledge of the process and its manufacture parameters to be able to create the equations that satisfactorily describe the process, actuator, and sensor. It is important to keep in mind that these parameters may change during the life of the equipment. Then if you use the parameters defined by the manufacturer, you can make the model inaccurate or useless. Because of this aspect and because of the development of powerful methods and

To create a black box model of process for simulation, estimation, prediction, or control purposes, it is necessary that an actuator system and a measurement system modify the state of the process and see its response. With the process input and output values, it is possible to obtain statics or dynamic models of the process, but the actuator and sensor are included in the process model, as shown in **Figure 2a**. This becomes more evident in dynamic models when the dynamic response of the actuator and sensor affects the dynamic of the set. In static models, the use of a different sensor (or actuator), but with the same static gain, does not affect the

Other types of control algorithms are the logic control; those are classified as combinational and sequential. The response of the combinational logic algorithm depends on the inputs on current sampling time only, for example, the torch travel limit was reached, the robot must stop, and the arc must close. On sequential control the response depends on the previous sampling time inputs also, for example, in seam tracking control, it is important to know the last positions reached by

tools for modeling, the black box techniques are more used.

modeling these processes.

**Figure 2.**

correlation techniques can be useful.

*Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

the controller, as shown in [6].

the torch to calculate the next position.

model.

**55**

In addition, most cases apply static models, do not control all parameters of the bead geometry, and do not apply multivariable techniques, as shown in **Figure 1b** and **c**. The dynamic models can be a better representation of the process, producing better prediction results. The research where these models were used represents only 13% of the total, as analyzed in [5]. The black box model approach is widely used. Because of the complex characteristics of the process, a physic model approach is very difficult and needs extensive research and resources.

In this chapter the principal control loops and techniques used for online control of the weld bead geometry are discussed. The more usual variables, control, and techniques to modeling, used in welding power sources and welding robotic systems, are critically discussed. Some examples of singled and multivariable control loops are shown. A decoupling technique for multivariable loops is also explained. The dead time and disturbances that can affect the processes and some techniques to determine them are also explained. A special topic about the embedded systems in the welding process was included.

This chapter aims to create a knowledge base necessary to understand the main control systems in welding processes before addressing more complex control techniques. Its main contributions are the exhaustive literature review that is critically discussed and the solutions provided for the control of each part of the process, especially the control of the weld bead geometry for electric arc welding processes.

### **2. Control loops in welding processes**

A typical automatic closed-loop control is composed of a controller or control system, an actuator system, and a measurement system or sensor, as shown in **Figure 2a**. The controller calculates the control law based on the control error, which is the difference between the set point value and the measurement of the controlled variable. The actuator modifies the process state, based on controller output (manipulate variable), to bring the controlled variable to the desired value. In sequence, to close the loop, the measurement system obtains the value of the controlled variable and sends it to the controller. An open-loop control does not have a measurement system, or the controller does not use its feedback as shown in **Figure 2b**.

The selection of variables to the control loop is a very important task. For this, it is necessary to analyze and quantify the influence of all process variables on the variable to be controlled. A statistical tool to quantify these relationships is the cross-correlation, using experimental data series of these variables and the variable

*Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

**Figure 2.**

communication lines, continuous changes in position and lighting conditions (for optical sensors), and the effects of the force of gravity. These statistical data are

*Statistical information of publications about control systems of the weld bead geometry: (a) welding positions;*

In addition, most cases apply static models, do not control all parameters of the bead geometry, and do not apply multivariable techniques, as shown in

**Figure 1b** and **c**. The dynamic models can be a better representation of the process, producing better prediction results. The research where these models were used represents only 13% of the total, as analyzed in [5]. The black box model approach is widely used. Because of the complex characteristics of the process, a physic model

In this chapter the principal control loops and techniques used for online control of the weld bead geometry are discussed. The more usual variables, control, and techniques to modeling, used in welding power sources and welding robotic systems, are critically discussed. Some examples of singled and multivariable control loops are shown. A decoupling technique for multivariable loops is also explained. The dead time and disturbances that can affect the processes and some techniques to determine them are also explained. A special topic about the embedded systems

This chapter aims to create a knowledge base necessary to understand the main control systems in welding processes before addressing more complex control techniques. Its main contributions are the exhaustive literature review that is critically discussed and the solutions provided for the control of each part of the process, especially the control of the weld bead geometry for electric arc welding processes.

A typical automatic closed-loop control is composed of a controller or control system, an actuator system, and a measurement system or sensor, as shown in **Figure 2a**. The controller calculates the control law based on the control error, which is the difference between the set point value and the measurement of the controlled variable. The actuator modifies the process state, based on controller output (manipulate variable), to bring the controlled variable to the desired value. In sequence, to close the loop, the measurement system obtains the value of the controlled variable and sends it to the controller. An open-loop control does not have a measurement system, or the controller does not use its feedback as shown in

The selection of variables to the control loop is a very important task. For this, it is necessary to analyze and quantify the influence of all process variables on the variable to be controlled. A statistical tool to quantify these relationships is the cross-correlation, using experimental data series of these variables and the variable

approach is very difficult and needs extensive research and resources.

shown in **Figure 1a**.

*(b) model types; (c) control type.*

*Welding - Modern Topics*

**Figure 1.**

in the welding process was included.

**2. Control loops in welding processes**

**Figure 2b**.

**54**

*Representation of a typical automatic control system: (a) closed-loop control; (b) open-loop control.*

to be controlled. Other factors must also be considered, such as the actual possibility of modifying each of these variables and how these modifications affect other control loops. These correlations are mentioned in the literature, but often they are not totality quantified, indicating that there is still a wide-open field of research in modeling these processes.

The dead time (transportation lag or time delay) is another important parameter that can be obtained from cross-correlation analysis too [6]. The sampling time for digital control systems must be selected based on the process dynamic, and autocorrelation techniques can be useful.

An important input to be considered on the control loop is the disturbance. This signal (or signals) can affect the process response and must be compensated by the controller. The open-loop controller cannot compensate for the disturbance action because it does not have a feedback signal. An example of disturbance is small variations in the height of the base metal surface product of heat. These variations change the contact tip to work distance and consequently the arc conditions. If the disturbance is measurable, some techniques can be used to improve the response of the controller, as shown in [6].

The model or process can be obtained using white or black box techniques. The first modeling technique required great knowledge of the process and its manufacture parameters to be able to create the equations that satisfactorily describe the process, actuator, and sensor. It is important to keep in mind that these parameters may change during the life of the equipment. Then if you use the parameters defined by the manufacturer, you can make the model inaccurate or useless. Because of this aspect and because of the development of powerful methods and tools for modeling, the black box techniques are more used.

To create a black box model of process for simulation, estimation, prediction, or control purposes, it is necessary that an actuator system and a measurement system modify the state of the process and see its response. With the process input and output values, it is possible to obtain statics or dynamic models of the process, but the actuator and sensor are included in the process model, as shown in **Figure 2a**. This becomes more evident in dynamic models when the dynamic response of the actuator and sensor affects the dynamic of the set. In static models, the use of a different sensor (or actuator), but with the same static gain, does not affect the model.

Other types of control algorithms are the logic control; those are classified as combinational and sequential. The response of the combinational logic algorithm depends on the inputs on current sampling time only, for example, the torch travel limit was reached, the robot must stop, and the arc must close. On sequential control the response depends on the previous sampling time inputs also, for example, in seam tracking control, it is important to know the last positions reached by the torch to calculate the next position.

In welding processes it is possible to find several control loops with different complexities and purposes. Each control loop has a set point or desired value of the controlled variable (supply by the operator or by a higher-level controller), a controlled variable (obtained from measurement system), a manipulated variable (supplied to the actuator by the control system), and disturbances. For example, on GMAW conventional welding power sources with the constant voltage, you can find an arc controller loop that tries to keep the voltage, the wire feed speed controller, and the gas flow controller (commonly included in the sequential logic controller) constant. The more complex processes have other control loops and sequential controllers to generate the arc signal form.

moves the torch to this *Y* position. These systems do not need feedback because of

To reduce the amount of data in the lookup tables, it is possible to save only the significant changes of welding speed and trajectory and hold the last value in the

To obtain the correct torch trajectory, the weld joint can be scanned before the welding process starts and the center joint can be calculated in all the points of the torch trajectory. With this data, it is possible to define the correct trajectory for the

The seam tracking loop can be transformed on closed-loop, but it is necessary for a profile sensor (e.g., a laser profilometer) to obtain online the joint profile and to make the trajectory analysis. The same control strategy can be used to substitute the lookup table by the algorithm that analyzes the profilometer data. This control strategy is better if the pieces are expected to move or deform during welding, but

The contact tip to work distance (*CTWD*) can be controlled in a closed-loop by a proportional-integral-derivative (PID) controller [6]. The CTWD is measured with a laser profilometer and calculated with the algorithm described in the chapter "On-

(*CTWDsp*). The controller manipulates the step time and the step counter (embedded in the SM3 signal) of the stepper motor associated with the CTWD movement in a robotic flat welding system. The *CTWD*ð Þ 0 is the initial value for the controller

Due to the advanced position of the sensor, the CTWD measurement is in advanced time (*θ*). These future values are saved in a memory element that implements a first input-first output list to supply the correct value to the controller. This loop can use the same profile sensor with that of the seam tracking loop when the

line measurements in welding processes" and compared with the set point

**2.3 Control of width, reinforcement, and penetration of the weld bead**

The principal variables that affect the bead geometry in the conventional arc welding process are the welding voltage, the welding current, the wire feed speed, the contact tip to work distance, and the welding speed. The most common relation found in the scientific literature shows that increasing the electric current by increasing the wire feed speed, for the same welding speed, results in a greater weld bead depth and welding pools with greater volume and production. An increase in electric current, accompanied by a proportional increase of the welding speed (*wire feed speed/welding speed* = *constant*), also results in greater penetration, but the welding pool keeps the same volume. Then, the same welding joint volume can be filled (maintaining production) and ensure its integrity by full penetration (good

stepper motor accuracy in normal working conditions.

torch and move the seam tracking stepper motor accordingly.

output until the new value is found.

*Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

more calculation resources are needed.

**2.2 Control of contact tip to work distance**

algorithm. **Figure 4** shows this closed control loop.

weld joint is scanned before the welding process starts.

quality) at the same time [7].

*Blocks diagram of the contact tip to work distance control loop.*

**Figure 4.**

**57**

In welding robotic systems, you can find several control loops too but related with the torch or piece position and torch or piece travel. The combination of several controllers makes possible the control of the geometry of the weld bead, for example, a loop that changes the set point of voltage input in the welding power source to control the weld bead width based on profile sensor or video camera. Another example is a control loop that changes the wire feed speed in the welding power source and the welding speed in the welding robot to control the weld bead penetration.

These several controllers and actuators, which modify the same process at the same time to reach the manufacture objectives, will also cause interactions between the loops and its strongly coupled variables. A change in a control loop may affect other loops as disturbance and turns the process unstable. In these cases, a multivariable control loop must be considered. In the next sections, examples of control loops used in arc welding processes are shown.

#### **2.1 Control of welding speed and seam tracking**

If the torch trajectory is known, two open-loop controls can be used to govern the torch movement in two axes of the flat welding robotic system that uses stepper motors as actuator elements. In this system, the *X* axis is then governed by the welding speed controller and the *Y* axis by the seam tracking controller. The first loop keeps the welding speed set point, and the second loop applied the torch trajectory correction as shown in **Figure 3**.

The welding speed controller reads a lookup table with the speed set points (*WSsp*) for each torch *X* position and applies the control signals *SM*1 to stepper motor driver to reach the desired welding speed. These control signals are pulses with a time interval that corresponds to the motor speed (step time), and the pulse count is equivalent to distance traveled. The stepper motor driver sends the signal necessary for each coil to the stepper motor, and the stepper motor generates the rotation movement so that the gear transforms it into linear torch movement. The *nT* parameter is the time of the sample, made up of the sample time (*T*) and the sample number (*n*). The *nT T* is the previous sample time.

On the other hand, the seam tracking controller receives the *X* torch position too and finds the correction to the *Y* axis on another lookup table. Then, the controller

**Figure 3.** *Blocks diagram of the welding speed and seam tracking control loops.*

#### *Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

In welding processes it is possible to find several control loops with different complexities and purposes. Each control loop has a set point or desired value of the controlled variable (supply by the operator or by a higher-level controller), a controlled variable (obtained from measurement system), a manipulated variable (supplied to the actuator by the control system), and disturbances. For example, on GMAW conventional welding power sources with the constant voltage, you can find an arc controller loop that tries to keep the voltage, the wire feed speed controller, and the gas flow controller (commonly included in the sequential logic controller) constant. The more complex processes have other control loops and

In welding robotic systems, you can find several control loops too but related with the torch or piece position and torch or piece travel. The combination of several controllers makes possible the control of the geometry of the weld bead, for example, a loop that changes the set point of voltage input in the welding power source to control the weld bead width based on profile sensor or video camera. Another example is a control loop that changes the wire feed speed in the welding power source and the welding speed in the welding robot to control the weld bead

These several controllers and actuators, which modify the same process at the same time to reach the manufacture objectives, will also cause interactions between the loops and its strongly coupled variables. A change in a control loop may affect other loops as disturbance and turns the process unstable. In these cases, a multivariable control loop must be considered. In the next sections, examples of control

If the torch trajectory is known, two open-loop controls can be used to govern the torch movement in two axes of the flat welding robotic system that uses stepper motors as actuator elements. In this system, the *X* axis is then governed by the welding speed controller and the *Y* axis by the seam tracking controller. The first loop keeps the welding speed set point, and the second loop applied the torch

The welding speed controller reads a lookup table with the speed set points (*WSsp*) for each torch *X* position and applies the control signals *SM*1 to stepper motor driver to reach the desired welding speed. These control signals are pulses with a time interval that corresponds to the motor speed (step time), and the pulse count is equivalent to distance traveled. The stepper motor driver sends the signal necessary for each coil to the stepper motor, and the stepper motor generates the rotation movement so that the gear transforms it into linear torch movement. The *nT* parameter is the time of the sample, made up of the sample time (*T*) and the

On the other hand, the seam tracking controller receives the *X* torch position too and finds the correction to the *Y* axis on another lookup table. Then, the controller

sequential controllers to generate the arc signal form.

loops used in arc welding processes are shown.

trajectory correction as shown in **Figure 3**.

sample number (*n*). The *nT T* is the previous sample time.

*Blocks diagram of the welding speed and seam tracking control loops.*

**2.1 Control of welding speed and seam tracking**

penetration.

*Welding - Modern Topics*

**Figure 3.**

**56**

moves the torch to this *Y* position. These systems do not need feedback because of stepper motor accuracy in normal working conditions.

To reduce the amount of data in the lookup tables, it is possible to save only the significant changes of welding speed and trajectory and hold the last value in the output until the new value is found.

To obtain the correct torch trajectory, the weld joint can be scanned before the welding process starts and the center joint can be calculated in all the points of the torch trajectory. With this data, it is possible to define the correct trajectory for the torch and move the seam tracking stepper motor accordingly.

The seam tracking loop can be transformed on closed-loop, but it is necessary for a profile sensor (e.g., a laser profilometer) to obtain online the joint profile and to make the trajectory analysis. The same control strategy can be used to substitute the lookup table by the algorithm that analyzes the profilometer data. This control strategy is better if the pieces are expected to move or deform during welding, but more calculation resources are needed.

### **2.2 Control of contact tip to work distance**

The contact tip to work distance (*CTWD*) can be controlled in a closed-loop by a proportional-integral-derivative (PID) controller [6]. The CTWD is measured with a laser profilometer and calculated with the algorithm described in the chapter "Online measurements in welding processes" and compared with the set point (*CTWDsp*). The controller manipulates the step time and the step counter (embedded in the SM3 signal) of the stepper motor associated with the CTWD movement in a robotic flat welding system. The *CTWD*ð Þ 0 is the initial value for the controller algorithm. **Figure 4** shows this closed control loop.

Due to the advanced position of the sensor, the CTWD measurement is in advanced time (*θ*). These future values are saved in a memory element that implements a first input-first output list to supply the correct value to the controller. This loop can use the same profile sensor with that of the seam tracking loop when the weld joint is scanned before the welding process starts.

#### **2.3 Control of width, reinforcement, and penetration of the weld bead**

The principal variables that affect the bead geometry in the conventional arc welding process are the welding voltage, the welding current, the wire feed speed, the contact tip to work distance, and the welding speed. The most common relation found in the scientific literature shows that increasing the electric current by increasing the wire feed speed, for the same welding speed, results in a greater weld bead depth and welding pools with greater volume and production. An increase in electric current, accompanied by a proportional increase of the welding speed (*wire feed speed/welding speed* = *constant*), also results in greater penetration, but the welding pool keeps the same volume. Then, the same welding joint volume can be filled (maintaining production) and ensure its integrity by full penetration (good quality) at the same time [7].

**Figure 4.** *Blocks diagram of the contact tip to work distance control loop.*

On the other hand, laser welding has an additional set of parameters, such as the laser power and optical adjustments of the laser beam, but it is restricted by the availability of the equipment and difficult to make online adjustment in welding parameters. Shortly, the controllable parameters will become diversified, but right now the focus adjustment can be made by changing the position of focus lens inside the laser head. A review of these topics is shown in [8].

It is important to note that the orbital welding adds more complexity to control, due to the effect of gravity on the transfer of material, the weld pool, and the weld bead formation, in addition to other requirements. So, it is important to consider

Control strategies proposed in [5] are based on a PID controller improved with a decoupling method, a Smith predictor, and a fuzzy self-adaptive algorithm. In the PID control strategy, shown in **Figure 6**, the welding voltage (*U*) and wire feed speed (*WF*) are manipulated by two independent control loops that control the weld bead width (*W*) and the weld bead depth (*D*). The *CTWD* can be considered a disturbance or a manipulated variable, depending on the control strategy. The quantity of material deposited (deposition rate) is indirectly controlled by the relation between *WS* and *WF*, and the weld bead reinforcement depends on the relation between bead width and quantity of material deposited. The values *U*ð Þ 0

The weld bead depth value (*D*) is estimated using the algorithms described in the chapter "On-line measurements in welding processes," and the weld bead width (*W*) can be estimated too or measured using a profile sensor. These values are feedback to the controller and the control errors, which are calculated using the set point of the weld bead depth (*Dsp*) and width (*Wsp*) values. If a laser profilometer is used, the real width and reinforcement of the weld bead are calculated. Note that the measurements have a dead time (*θ*) and these values are zero during the first

While many control algorithms have been proposed, in which approaches are theoretically elegant, most of the industrial processes nowadays are still controlled by proportional-integral-derivative controllers [10–12]. Conventional PID controllers have been widely applied in industrial process control for about half a century because of their simple structure and convenience of implementation [13]. However, a conventional PID controller can have poor control performance for nonlinear and complex systems for which there are no precise mathematical models. Numerous variants of conventional PID controller, such as self-tuning, auto-tuning, and adaptive PID controllers, have been developed to overcome these difficulties. Several online self-tuning or adaptive algorithms are based on fuzzy

The weld bead width measure dead time problem can be solved using a modified Smith predictor as shown in [5]. In the same work, the nonlinear is solved using a fuzzy self-adaptive algorithm for PID tuning. But the control strategy still has a

To improve the controller behavior, the decoupling structures can be incorporated for reducing the interaction between the loops. In this case, the decoupling used is based on feedforward control. These decoupling techniques are useful when the process is affected by strong measurable disturbances. This strategy can help improve the behavior of the controller in the face of this disturbance, but it cannot replace the feedback control [20]. The typical feedforward control is shown in

the orbital angle as a measurable disturbance.

*Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

and *WF*ð Þ 0 are initial values of manipulated variables.

inference systems that were developed in [11, 12, 14–19].

problem, the interdependence between the process variables.

*Typical feedforward control in a single control loop. Adapted from [5].*

sampling times.

**Figure 7**.

**Figure 7.**

**59**

It is important to note that the relations between variables are more complex and multivariable techniques are necessary to describe them. With the multivariable techniques, it is possible to consider the interactions between variables in the process and reduce their effect in the control loop, but the implementation is difficult because of the complexity of the modeling and the control algorithm adjustment. In the literature analysis made in [5], only 9% of the papers use multivariable control loops.

A generic diagram of a multivariable control loop of the weld bead geometry for the GMAW process is shown in **Figure 5**. It used the main variables that affect the process, to control the bead geometry, but it should be noted that due to the interdependence between them, setting the controller parameters and the use of uncoupling become difficult.

The GMAW conventional process can be represented as a multiple-input multiple-output (MIMO) process with three inputs and two outputs, as shown in **Figure 6**. The pairing of controlled and manipulated variables is shown too, and the other variables are considered as disturbances or controlled by other control loops. This selection is based on the bibliographic review and requires the analysis of the relative gains defined in [9].

**Figure 5.**

*Main variables used in the weld bead geometry control in GMAW process.*

#### **Figure 6.**

*Arc welding process represented as a multiple-input multiple-output system, with the depth and width of the weld bead controlled by PID algorithms.*

#### *Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

On the other hand, laser welding has an additional set of parameters, such as the laser power and optical adjustments of the laser beam, but it is restricted by the availability of the equipment and difficult to make online adjustment in welding parameters. Shortly, the controllable parameters will become diversified, but right now the focus adjustment can be made by changing the position of focus lens inside

It is important to note that the relations between variables are more complex and multivariable techniques are necessary to describe them. With the multivariable techniques, it is possible to consider the interactions between variables in the process and reduce their effect in the control loop, but the implementation is difficult because of the complexity of the modeling and the control algorithm adjustment. In the literature analysis made in [5], only 9% of the papers use multi-

A generic diagram of a multivariable control loop of the weld bead geometry for the GMAW process is shown in **Figure 5**. It used the main variables that affect the process, to control the bead geometry, but it should be noted that due to the interdependence between them, setting the controller parameters and the use of

The GMAW conventional process can be represented as a multiple-input multiple-output (MIMO) process with three inputs and two outputs, as shown in **Figure 6**. The pairing of controlled and manipulated variables is shown too, and the other variables are considered as disturbances or controlled by other control loops. This selection is based on the bibliographic review and requires the analysis of the

*Arc welding process represented as a multiple-input multiple-output system, with the depth and width of the*

the laser head. A review of these topics is shown in [8].

*Main variables used in the weld bead geometry control in GMAW process.*

variable control loops.

*Welding - Modern Topics*

uncoupling become difficult.

relative gains defined in [9].

**Figure 5.**

**Figure 6.**

**58**

*weld bead controlled by PID algorithms.*

It is important to note that the orbital welding adds more complexity to control, due to the effect of gravity on the transfer of material, the weld pool, and the weld bead formation, in addition to other requirements. So, it is important to consider the orbital angle as a measurable disturbance.

Control strategies proposed in [5] are based on a PID controller improved with a decoupling method, a Smith predictor, and a fuzzy self-adaptive algorithm. In the PID control strategy, shown in **Figure 6**, the welding voltage (*U*) and wire feed speed (*WF*) are manipulated by two independent control loops that control the weld bead width (*W*) and the weld bead depth (*D*). The *CTWD* can be considered a disturbance or a manipulated variable, depending on the control strategy. The quantity of material deposited (deposition rate) is indirectly controlled by the relation between *WS* and *WF*, and the weld bead reinforcement depends on the relation between bead width and quantity of material deposited. The values *U*ð Þ 0 and *WF*ð Þ 0 are initial values of manipulated variables.

The weld bead depth value (*D*) is estimated using the algorithms described in the chapter "On-line measurements in welding processes," and the weld bead width (*W*) can be estimated too or measured using a profile sensor. These values are feedback to the controller and the control errors, which are calculated using the set point of the weld bead depth (*Dsp*) and width (*Wsp*) values. If a laser profilometer is used, the real width and reinforcement of the weld bead are calculated. Note that the measurements have a dead time (*θ*) and these values are zero during the first sampling times.

While many control algorithms have been proposed, in which approaches are theoretically elegant, most of the industrial processes nowadays are still controlled by proportional-integral-derivative controllers [10–12]. Conventional PID controllers have been widely applied in industrial process control for about half a century because of their simple structure and convenience of implementation [13]. However, a conventional PID controller can have poor control performance for nonlinear and complex systems for which there are no precise mathematical models. Numerous variants of conventional PID controller, such as self-tuning, auto-tuning, and adaptive PID controllers, have been developed to overcome these difficulties. Several online self-tuning or adaptive algorithms are based on fuzzy inference systems that were developed in [11, 12, 14–19].

The weld bead width measure dead time problem can be solved using a modified Smith predictor as shown in [5]. In the same work, the nonlinear is solved using a fuzzy self-adaptive algorithm for PID tuning. But the control strategy still has a problem, the interdependence between the process variables.

To improve the controller behavior, the decoupling structures can be incorporated for reducing the interaction between the loops. In this case, the decoupling used is based on feedforward control. These decoupling techniques are useful when the process is affected by strong measurable disturbances. This strategy can help improve the behavior of the controller in the face of this disturbance, but it cannot replace the feedback control [20]. The typical feedforward control is shown in **Figure 7**.

**Figure 7.** *Typical feedforward control in a single control loop. Adapted from [5].*

#### *Welding - Modern Topics*

The feedforward control tries to anticipate the effect of the disturbance (*d*). The control action is applied directly to the control loop drive element, before the disturbance can affect the controlled variable [6, 20]. Eqs. (1) and (2) usually define the necessary conditions to it, while the feedforward model is obtained in Eq. (3).

$$\frac{\Delta y}{\Delta \nu} = \frac{G\_2(z^{-1})}{1 - CG\_1(z^{-1})} + \frac{FFG\_1(z^{-1})}{1 - CG\_1(z^{-1})} = 0 \tag{1}$$

$$\frac{\Delta \mathbf{y}}{\Delta \nu} = \frac{\mathbf{G}\_2(\mathbf{z}^{-1}) + F\mathbf{F}\mathbf{G}\_1(\mathbf{z}^{-1})}{\mathbf{1} - \mathbf{C}\mathbf{G}\_1(\mathbf{z}^{-1})} = \mathbf{0} \tag{2}$$

$$FF = \frac{G\_2(z^{-1})}{G\_1(z^{-1})} \tag{3}$$

If *<sup>G</sup>*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ and *<sup>G</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ are quite close to first-order transfer function with delay, as it is shown in

$$G\_1(z^{-1}) = \frac{K\_1 z^{p\_1}}{1 - a\_1 z^{-1}} \tag{4}$$

The design and synthesis of PID controllers and fuzzy algorithms in FPGA or microcontroller devices are possible, and the resource consumption is very low, as is shown in [23]. But many other scientific researchers are being developed and tested to solve and improve the control of the welding process. In the next section, some of

**3. Methods or techniques used for modeling and control of the geometry**

The welding process is characterized as multivariable, nonlinear, and timevarying, with stochastic behavior and having a strong coupling among welding parameters. For this reason, it is very difficult to find a reliable mathematical model to design an effective control scheme by conventional modeling and control methods. Due to these characteristics, the use of adaptive techniques has spread in the last decades with favorable results, only overcome by a proportional-integral-derivative controller. The adaptive control has been implemented in some researchers to cope with the problem of the high dependence of process parameters to its operating condition. The main drawback of this method is that it requires online estimation or tuning of the parameters, which is usually a time-consuming operation. The single implementation of PID and low computational resources make it still the most used, as in the rest of industrial applications. A graphic summary is shown in **Figure 9**,

Neural networks, fuzzy methods, and their combinations also stand out. Note that the magnificent behavior of the neural network can be clouded by a slow convergence because of the excessive quantity of neurons or hidden layers. Many research efforts use this approach but neglected the need for the quick response of the control system. Statistical methods, such as the classic autoregressive moving-average and expert systems, are represented too. Other less used techniques include state space, model-free adaptive, first- and second-order model, support vector machine, and finite elements.

**3.1 Some scientific research about the geometry control in arc welding**

Developments in the field of automatic control of the geometry in the arc welding process have been intense in the last four decades. The most representative

and **Table 1** shows the document references analyzed.

*Weld bead width and depth penetration controller with decouples.*

*Automatic Control of the Weld Bead Geometry DOI: http://dx.doi.org/10.5772/intechopen.91914*

them will be described.

**Figure 8.**

**of weld bead**

**processes**

**61**

$$G\_2(z^{-1}) = \frac{K\_2 z^{p\_2}}{1 - a\_2 z^{-1}} \tag{5}$$

where the terms *α*<sup>1</sup> and *α*<sup>2</sup> are related with the sample time (*Ts*) and process time constants *T*<sup>1</sup> and *T*2, as shown in the next equations,

$$a\_1 = e^{-\frac{T\_t}{T\_1}} \tag{6}$$

$$a\_2 = e^{-\frac{T\_t}{T\_2}}\tag{7}$$

then the feedforward transfer function is

$$\frac{\Delta u}{\Delta v} = F F \left( z^{-1} \right) = -\frac{K\_2 z^{-p\_2} (1 - a\_1 z^{-1})}{K\_1 z^{-p\_1} (1 - a\_2 z^{-1})} \tag{8}$$

$$\frac{\Delta u}{\Delta v} = F F \left( z^{-1} \right) = -K\_{FF} z^{\left( p\_1 - p\_2 \right)} \frac{\mathbf{1} - a\_1 \mathbf{z}^{-1}}{\mathbf{1} - a\_2 \mathbf{z}^{-1}} \tag{9}$$

where

$$K\_{FF} = \frac{K\_2}{K\_1} \tag{10}$$

Sometimes only the steady value is compensated, and the dynamic is depreciated in which case the transfer function of the feedforward block is *KFF*. This simplifies the modeling work and the model structure. It is important to note that the dead time in the principal channel must be less or equal than the disturbance channel (*p*<sup>1</sup> ≤ *p*2) for the dynamic compensation to be effective.

If the interactions between loops are considered as disturbances, the same feedforward scheme can be used to decoupling the weld bead width and penetration control loop in our welding process. **Figure 8** shows the block diagram with decouples.

Decouples *FF*<sup>1</sup> and *FF*<sup>2</sup> are designed to minimize the interaction between loops and improve the controller behavior. The calculation of the transfer function of decouples is similar to what is explained in the feedforward transfer function. This strategy is similar to inverse decoupling shown in [21, 22].

#### **Figure 8.**

The feedforward control tries to anticipate the effect of the disturbance (*d*). The

*FFG*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ

<sup>1</sup> � *CG*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ <sup>¼</sup> <sup>0</sup> (1)

<sup>1</sup> � *CG*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ <sup>¼</sup> <sup>0</sup> (2)

*<sup>G</sup>*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ (3)

<sup>1</sup> � *<sup>α</sup>*1*z*�<sup>1</sup> (4)

<sup>1</sup> � *<sup>α</sup>*2*z*�<sup>1</sup> (5)

*<sup>T</sup>*<sup>1</sup> (6)

*<sup>K</sup>*1*z*�*p*<sup>1</sup> <sup>1</sup> � *<sup>α</sup>*2*z*�<sup>1</sup> ð Þ (8)

<sup>1</sup> � *<sup>α</sup>*2*z*�<sup>1</sup> (9)

(10)

control action is applied directly to the control loop drive element, before the disturbance can affect the controlled variable [6, 20]. Eqs. (1) and (2) usually define the necessary conditions to it, while the feedforward model is obtained in Eq. (3).

<sup>Δ</sup>*<sup>v</sup>* <sup>¼</sup> *<sup>G</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> ð Þþ *FFG*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ

*FF* <sup>¼</sup> *<sup>G</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ

*<sup>G</sup>*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> <sup>¼</sup> *<sup>K</sup>*1*z<sup>p</sup>*<sup>1</sup>

*<sup>G</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> <sup>¼</sup> *<sup>K</sup>*2*z<sup>p</sup>*<sup>2</sup>

*α*<sup>1</sup> ¼ *e* �*Ts*

*α*<sup>2</sup> ¼ *e* �*Ts <sup>T</sup>* , <sup>2</sup> (7)

<sup>Δ</sup>*<sup>v</sup>* <sup>¼</sup> *FF z*�<sup>1</sup> ¼ � *<sup>K</sup>*2*z*�*p*<sup>2</sup> <sup>1</sup> � *<sup>α</sup>*1*z*�<sup>1</sup> ð Þ

<sup>Δ</sup>*<sup>v</sup>* <sup>¼</sup> *FF z*�<sup>1</sup> ¼ �*KFFz <sup>p</sup>*1�*<sup>p</sup>* ð Þ<sup>2</sup> <sup>1</sup> � *<sup>α</sup>*1*z*�<sup>1</sup>

*KFF* <sup>¼</sup> *<sup>K</sup>*<sup>2</sup> *K*1

Sometimes only the steady value is compensated, and the dynamic is depreciated in which case the transfer function of the feedforward block is *KFF*. This simplifies the modeling work and the model structure. It is important to note that the dead time in the principal channel must be less or equal than the disturbance

If the interactions between loops are considered as disturbances, the same feedforward scheme can be used to decoupling the weld bead width and penetration control loop in our welding process. **Figure 8** shows the block diagram with decouples. Decouples *FF*<sup>1</sup> and *FF*<sup>2</sup> are designed to minimize the interaction between loops and improve the controller behavior. The calculation of the transfer function of decouples is similar to what is explained in the feedforward transfer function. This

channel (*p*<sup>1</sup> ≤ *p*2) for the dynamic compensation to be effective.

strategy is similar to inverse decoupling shown in [21, 22].

where the terms *α*<sup>1</sup> and *α*<sup>2</sup> are related with the sample time (*Ts*) and process time

If *<sup>G</sup>*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ and *<sup>G</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ are quite close to first-order transfer function with delay,

Δ*y*

as it is shown in

*Welding - Modern Topics*

where

**60**

<sup>Δ</sup>*<sup>v</sup>* <sup>¼</sup> *<sup>G</sup>*<sup>2</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ

Δ*y*

constants *T*<sup>1</sup> and *T*2, as shown in the next equations,

then the feedforward transfer function is

Δ*u*

Δ*u*

<sup>1</sup> � *CG*<sup>1</sup> *<sup>z</sup>*�<sup>1</sup> ð Þ <sup>þ</sup>

*Weld bead width and depth penetration controller with decouples.*

The design and synthesis of PID controllers and fuzzy algorithms in FPGA or microcontroller devices are possible, and the resource consumption is very low, as is shown in [23]. But many other scientific researchers are being developed and tested to solve and improve the control of the welding process. In the next section, some of them will be described.
