combined temperature and force control for robotic friction stir

COMBINED TEMPERATURE AND FORCE CONTROL FOR
ROBOTIC FRICTION STIR WELDING
Axel Fehrenbacher1, Christopher B. Smith2, Neil A. Duffie1, Nicola J. Ferrier1,
Frank E. Pfefferkorn1, Michael R. Zinn1*
1Department of Mechanical Engineering, University of Wisconsin – Madison, USA
2Friction Stir Link, Inc., Brookfield, WI, USA
* corresponding author
e-mail: [email protected]
phone: 608/263-2893
ABSTRACT
Use of robotic friction stir welding (FSW) has gained in popularity as robotic systems can
accommodate more complex part geometries while providing high applied tool forces required
for proper weld formation. However, even the largest robotic FSW systems suffer from high
compliance as compared to most custom engineered FSW machines or modified CNC mills. The
increased compliance of robotic FSW systems can significantly alter the process dynamics such
that control of traditional weld parameters, including plunge depth, is more difficult. To address
this, closed-loop control of plunge force has been proposed and implemented on a number of
systems. However, due to process parameter and condition variations commonly found in a
production environment, force control can lead to oscillatory or unstable conditions and can, in
extreme cases, cause the tool to plunge through the workpiece. To address the issues
associated with robotic force control, the use of simultaneous tool interface temperature control
has been proposed. In this paper, we describe the development and evaluation of a closed-loop
control system for robotic friction stir welding that simultaneously controls plunge force and tool
interface temperature by varying spindle speed and commanded vertical tool position. The
controller was implemented on an industrial robotic FSW system. The system is equipped with a
custom real-time wireless temperature measurement system and a force dynamometer. In
support of controller development, a linear process model has been developed that captures the
dynamic relations between the process inputs and outputs. Process validation identification
experiments were performed and it was found that the interface temperature is affected by both
spindle speed and commanded vertical tool position while axial force is affected primarily by
commanded vertical tool position. The combined control system was shown to possess good
command tracking and disturbance rejection characteristics. Axial force and interface
temperature was successfully maintained during both thermal and geometric disturbances and
thus weld quality can be maintained for a variety of conditions in which each control strategy
applied independently could fail. Finally, it was shown through the use of the control process
model, that the attainable closed-loop bandwidth is primarily limited by the inherent compliance
of the robotic system, as compared to most custom engineered FSW machines, where
instrumentation delay is the primary limiting factor. These limitations did not prevent the
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Zinn - MANU-12-1357 – Page 1 implementation of the control system, but are merely observations that we were able to work
around.
1. INTRODUCTION
Friction stir welding (FSW) was invented at The Welding Institute (TWI) in the UK in 1991
[1]. This relatively new, solid-state joining process differentiates itself from many other welding
processes by not melting the workpiece. As a result, the joining process generates excellent
joint properties, is energy efficient, environment friendly, and versatile.
The basic concept of FSW can be described as follows: a non-consumable rotating FSW
tool with a specially designed shoulder and probe is pressed against the base metal surface,
while a vertical downward force is applied (Figure 1). Due to friction between the rotating tool
and the workpiece and plastic deformation of the workpiece, the temperature in the weld zone
increases. The generated heat is usually not sufficient to melt the material, however, the
workpiece is softened in the area around the probe and the deformation resistance (i.e., yield
strength) of the base material decreases. The tool is traversed along the weld interface to mix
the joining members in a forging action along the joining line to create a weld in the solid state.
Friction stir welding results in intense plastic deformation and temperature increase in the weld
zone, which leads to a significant microstructural evolution without typically causing phase
changes [2,3].
Friction stir welding was initially applied to aluminum alloys but welding of other materials
such as copper, titanium and magnesium alloys as well as steels and nickel alloys have been
investigated [3]. Friction stir welding is also identified as a technology that can be used to join
dissimilar alloys and metals. By maintaining the weld below the solidus temperature, minimal
pre- and post-processing, excellent weld strength and ductility and environmentally friendly
nature, the process enables cost reductions in many industrial applications and allows the
joining of materials considered not weldable by fusion processes (e.g., highly alloyed 2XXX and
7XXX series aluminum). Friction stir welding has developed numerous potential applications in
aerospace, automotive, railway, shipbuilding, construction and other areas [2,3].
Vertical force
FSW Tool
Translation
Rotation
Advancing Side
Shoulder
Leading Edge
Trailing Edge
Probe
Retreating Side
Figure 1: Schematic of the FSW process. 2. MOTIVATION
During FSW, numerous parameters and conditions can vary that affect weld quality.
Changing conditions include different mechanical and thermal properties of the workpiece
(Figure 2 a) and changes in the thermal capacity of the workpiece (Figure 2 b). Furthermore,
variations in the thickness of the workpiece (Figure 2 c) affect the relative position of the tool
Zinn - MANU-12-1357 – Page 2
shoulder to the workpiece surface and can cause voids or extensive flash. The FSW process
can be sensitive to these variations, which usually are present in a production environment;
hence, there is a significant need to control the process to assure high quality. In addition,
robotic FSW presents unique challenges not present in most custom engineered FSW
machines. In particular, the inherent compliance of robotic manipulators makes it difficult to
control plunge depth and often necessitates the use of force control or other strategies to
maintain weld quality.
Weld
(a)
FSW Tool
(b)
FSW Tool
(c)
Figure 2: Schematics of (a) varying workpiece properties, (b) varying workpiece geometry and (c) varying
workpiece thickness.
Workpiece variability, including changes in thermal constraints, material properties and
geometry, as well as robotic manipulator compliance variability due to changes in robotic
configuration, could be addressed through complex calculations beforehand, (i.e., an open-loop
algorithm). However, this would only be effective if the variations (disturbances) to the FSW
process could be well characterized a priori. This would add significant cost due to the
metrology required for every workpiece and the need to calibrate the stiffness of the robotic
manipulator over its complete workspace and would make the system inflexible. Workpiece
variability can also be addressed through a closed-loop control strategy that allows flexible use
under a wide range of conditions that do not have to be known beforehand.
Previous work showed that temperatures at the tool shoulder-workpiece interface can be
measured in real-time and can be utilized as a feedback signal for closed-loop control of
temperature, which can help maintain weld quality [4,5]. Cederqvist et al. [6] also implemented
temperature control algorithms for the welding of copper canisters. A cascaded control
algorithm with PI controllers was developed that determines the power input requirement and
maintains the tool temperature within a process window. Ross and Sorensen [7] also employ a
cascaded controller for temperature control for friction stir processing of low-carbon steel with
the goal of increasing the tool life. Relationships between temperature and weld quality have
been reported in the literature for FSW: Peel et al. found that weld properties are dominated by
the heat input (temperature) in welding aluminum 5083 [8]. Gratecap et al. found a qualitative
influence of weld temperatures on weld quality [9]. Simar et al. observed effects of the weld
heat input (by varying the travel speed) on the microstructure and the mechanical properties of
the weld [10].
Force control, during which the axial tool position (z-axis) is adjusted to maintain a
constant axial welding force, has proven to be a successful technology. When developing a
robotic FSW system, Smith [11] experienced problems with the robot’s inherent lack of stiffness.
He found that welding with a force control algorithm produces higher quality welds than without
force control. Von Strombeck et al. [12] also developed force control algorithms to overcome
stiffness issues with robotic FSW. Zäh and Eireiner [13] proposed that constant welding
conditions, i.e., a constant axial force, is required during welding to ensure a uniform weld
quality. They implemented force controlled welding and presented welds with a constant axial
force. Oakes et al. [14] developed a dynamic process model relating the travel speed, spindle
Zinn - MANU-12-1357 – Page 3
speed and plunge depth to the axial force and implemented a force controller that tracks both
constant and sinusoidal desired forces.
Both temperature and force control can help in maintaining the weld quality during the
presence of inherent process disturbances. However, each control method has their limitations.
One possible way to implement temperature control is to change the spindle speed (or travel
speed) to adjust the energy input to the weld while welding at a constant plunge depth. This
strategy would fail in situations where the workpiece thickness changes as illustrated in Figure 2
c because proper contact of the tool shoulder and the workpiece cannot be maintained. On the
other hand, when welding under axial force control only, by adjusting the vertical tool position,
the system might fail in certain situations. Welding over a workpiece of varying thermal
capacitance affects the rate at which heat flows away from the weld zone, and can cause
changes in stir zone temperature (Figure 2 a and b), affecting weld quality. In many cases, this
change in temperature cannot be compensated for when welding solely under force control.
An example of a scenario in which simultaneous temperature and axial force control
would be beneficial is when welding close to the edge of a workpiece or going around a corner
(Figure 3). Heat generated by the FSW process is not able to conduct away from the weld zone
as quickly as the tool approaches the corner (one direction of heat dissipation is removed),
which causes the stir zone and region around it to overheat. Under force control alone, the
resulting material softening can lead to the tool shoulder plunging well below the workpiece
surface and creating unacceptable welds [15].
Weld
FSW Tool
Workpiece
Figure 3: Schematic of welding around a workpiece corner.
For these reasons, it would be beneficial to combine the two control methods, so that
during robotic friction stir welding both a certain temperature and a specified axial force is
maintained. To the authors’ knowledge, such a combined control system has not been
demonstrated on a robotic FSW system to date.
3. APPROACH
Closed-loop temperature and force control of robotic FSW requires real-time weld temperature
and force measurements as well as a valid, calibrated process model from which the control
design can be established. In our implementation, force measurements were provided by a 3axis force dynamometer placed below the weld specimen while temperature measurements
were acquired with a custom wireless tool-embedded temperature measurement system. The
process model was developed through a set of characterization experiments. The following
section details the approach in regards to each of these areas.
Zinn - MANU-12-1357 – Page 4
3.1 Temperature Measurement
Ideally, weld zone temperatures are measured, which is not possible without significant
effort. For this reason, another location, close to or on the boundary of the weld zone, must be
measured. In this work, an approach is chosen that uses thermocouples embedded into the
tool, together with a wireless system to transmit the data. This approach was originally reported
in [4] but is repeated here for clarity.
In general, the FSW tool is made of a material of relatively low thermal diffusivity (e.g.,
highly alloyed tool steel), as compared to an aluminum workpiece material (which is friction stir
welded most commonly). It is therefore desirable to place the thermocouples as close to the
tool-workpiece interface as possible to minimize the time delay associated with heat flow through
the tool. In this work, we are making use of through holes to enable direct contact of the tip of
the thermocouples with the workpiece material - in this case an aluminum alloy that has a very
high thermal diffusivity.
Two 0.8 mm diameter through holes were fabricated using electrical discharge machining
(EDM) into the tool shank (Figure 4). One 7.1 mm deep hole exits on the shoulder, 3.4 mm from
the outer edge of the shoulder. Another, 17 mm deep hole was made that exits on the side of
the probe (location of thread of the tool), 1.2 mm from the bottom of the probe, in order to obtain
temperatures further down in the weld. The two through holes are located at the same angular
position.
The smallest possible off-the-shelf, sheathed, ungrounded, type K thermocouple was
chosen to reduce the temperature response time (sheath diameter 0.25 mm, part no. TJ36CAXL-010U by Omega Corp.). The two thermocouples were inserted into the through holes and
secured with high temperature thermocouple cement (maximum service temperature 1426 °C).
The thermocouple sheaths are in direct contact with the workpiece material during welding as
there is no thermocouple cement between the tip of thermocouple assembly and workpiece
material.
Since the tool is rotating at high speed, a wireless data transmission system is used to
transmit the temperature measurements in real-time (i.e., without significant delays) to a
stationary data acquisition (DAQ) and control system. Figure 5 provides a schematic of the
overall wireless DAQ system, illustrating the main components. Figure 6 and Figure 7 show a
photograph of the instrumented tool holder and a close-up view of the FSW tool with the
embedded thermocouples, respectively. For the various spindle speeds used in this study (1700
rpm to 2900 rpm) and a sample rate of 333 Hz, the system can capture 7 to 12 temperature
measurements per rotation of the tool (angular resolution of 31 to 52 degrees). More detailed
information can be found in [4].
The instrumented tool holder has been successfully operated for a weld length of over 7
m using a single set of thermocouples without failure. Another, similar, tool has been used
flawlessly for a weld length of over 22 m. A failure that would occur during a weld could be
detected by additional algorithms. In that case the thermocouple or tool would have to be
replaced.
Zinn - MANU-12-1357 – Page 5
44°
Rotation
Axis
N
S
37°
FSW Tool
with two
Thermocouples
Stationary Magnet
Hall Effect
Sensor
Shoulder
Probe
1.2 mm
3.4 mm
Power Supply
(Battery)
Signal
Conditioning
Figure 4: Schematic of through hole locations for
the thermocouples on the FSW tool (not to scale,
section view). The thermocouples are exposed at
the tool-workpiece interface.
Figure 6: Photograph of assembled instrumented
tool holder for FSW.
R8
Tool Holder
Transmitter
Stationary
DAQ
Receiver
Rotating Assembly
Figure 5: Schematic illustrating the main
components of the wireless DAQ system used for
FSW.
Figure 7: Close-up view of FSW tool showing the
exposed thermocouples at the shoulder-workpiece
and probe-workpiece interfaces.
3.2 Force Measurement
Welding forces were measured using a 3-axis force dynamometer (Kistler model 9265A),
which is cooled during and in between experiments using a constant temperature bath at room
temperature. The spindle torque is recorded through a serial interface (Modbus communication
protocol) from the spindle motor servo drive (Control Techniques model FM-3DN). Custom data
acquisition, logging and control software (developed using National Instruments LabVIEW™) is
running on a laptop and communicates with the robot controller through a serial interface.
Compared to the robot controller, the software on the laptop offers a powerful programming
environment, fast processing, various interfaces to connect other devices, and real-time plotting,
to name a few. Based on the measured temperature and axial force, the control software
determines spindle speed and vertical tool position adjustments, which are sent to the robot.
Custom code was added to Friction Stir Link’s StirWareTM software (programmed in ABB’s
Rapid), which runs on the robot controller and receives and processes the adjustments. The
setup is able to manipulate both spindle speed and vertical tool position adjustments
simultaneously. The spindle speed and vertical tool position commands were limited to protect
the experimental hardware from damage (1700 rpm to 2900 rpm and 7 mm to 18 mm, for
spindle speed and tool position, respectively).
Force measurements are sampled at 2500 Hz. The sampling rate for the temperature
measurements is 333 Hz. Spindle torque is available at approximately 5 Hz. Spindle speed and
vertical tool position commands are sent at 20 Hz to the robot controller, where they are updated
Zinn - MANU-12-1357 – Page 6
at approximately 10 Hz. The schematic of the signal flow of the measurement and control
system is shown in Figure 8.
Figure 8: Signal flow schematic of experimental testbed.
3.3 Dynamic Process Model
The closed-loop controller developed in this work is model-based and, hence, a dynamic
process model needs to be established. Other reasons for obtaining a process model are the
ability to better understand the process dynamics, to get a basic insight into the physics
governing the process and to help explain the limitations of the system. The process is
represented by a multi-input-multi-output (MIMO) system including two inputs: the commanded
spindle speed ω*tool(t) and the commanded vertical tool position z*tool(t) and two outputs: the
interface temperature tint(t) and the axial force fz(t).
The closed-loop controller is designed in a way that cross-coupling effects are
decoupled, i.e., nulled (see section 3.4). For the purpose of model development it is assumed at
this point that no cross-coupling exists. This allows the development of two individual models.
First, a model relating the commanded spindle speed to the interface temperature is introduced.
Next, a model relating the commanded vertical tool position to the axial force is discussed.
Finally, a combined MIMO model, using the two previous models with additional coupling terms,
is presented.
Prior system identification work of the welding process indicated that a first order model
with pure delay (gain Kp,T, time constant τp,T and delay ∆Tp,T) could be used to represent the
dynamic relation between commanded spindle speed and measured shoulder interface
temperature for FSW on a CNC mill [4]. The 1st order system model is given in equation (1) and
(2) in the time and frequency domain (Laplace domain), respectively. In that work, the process
model was identified using frequency domain techniques. While providing good process model
and parameter identification, frequency domain identification can be time consuming. In this
work, we rely on the earlier process model identification and focus on parameter identification,
Zinn - MANU-12-1357 – Page 7
assuming that the same process model type is also suitable for the robotic setup. As such, time
domain identification, via examination of time history response to step inputs, is used to
determine the model parameters that describe the relationship between commanded spindle
speed and measured shoulder interface temperature. Equation (1) represents the system
behavior in the time domain and equation (2) in transfer function notation in the Laplace domain.
 p ,T
d

t int (t )  t int (t )  K p ,T tool
(t  T p ,T )
dt
K p ,T Tp ,T s
Tint ( s )

e
 tool ( s )  p ,T s  1
(1)
(2)
The relation between commanded vertical tool position z*tool(t) and measured axial force
fz(t) is modeled using a simple analytical, lumped parameter model of the system as illustrated in
Figure 9. The single degree of freedom (DOF) model consists of one mass m, two springs with
stiffness k and two dampers with damping factor c. The springs represent the flexibility of the
robotic manipulator and the workpiece while the dampers add damping to the system behavior.
Only displacements and forces perpendicular to the workpiece surface (i.e., parallel to the tool
axis) are considered in this model. ztool(t) represents the actual vertical position of the tool. The
differential equation that governs the physics of the simple model is given in equation (3). The
force fz(t) is measured using a dynamometer and is related to the actual vertical tool position as
shown in equation (4). A higher DOF model with more degrees of freedom could be chosen, but
the described simple model is believed to capture the main dynamics of the system. The model
is not intended to predict actual numerical values, but rather used to gather qualitative
information about the system and to guide control system design.
Figure 9: Schematic of simple analytical 1‐DOF lumped parameter model m
d2
d
d 

z (t )  2c z tool (t )  2kz tool  c z tool
(t )  kz tool
(t )
2 tool
dt
dt
dt
f z (t )  c
d
ztool (t )  kztool (t )
dt
(3)
(4)
Using equations (3) and (4) and applying a Laplace transform yields the transfer function
relating the measured axial force and the commanded vertical tool position:
Zinn - MANU-12-1357 – Page 8
Fz ( s )
(cs  k ) 2


Z tool
( s ) ms 2  2cs  2k
(5)
Equation (5) can also be expressed in terms of time domain parameters using a gain Kp,F, a
damping ratio ζp, a natural frequency ωp,n and a time constant τp,z associated with a zero of the
transfer function. These parameters can then easily be correlated with experimental data.
K p , F ( p , z s  1) 2
Fz ( s)


Z tool
( s) s 2  2 p p ,n s   p2 ,n
(6)
Step response tests have been performed previously by Zhao et al. to identify nonlinear
process models for the use in axial force control via plunge depth adjustments [16]. We are also
estimating the model parameters by examination of the time history response to step inputs.
During some welds, oscillations of the tool and robot arm were observed at approximately 0.6 to
0.8 Hz due to the low stiffness of the robotic manipulator. The occurrence of these oscillations is
dependent on the orientation of the robotic end effector, the heat input (low travel speeds are in
favor of the oscillations) and other factors. The frequency of the oscillations was not correlated
with the spindle speed or its harmonics and thus is assumed to be a resonance frequency of the
system and was used to determine the undamped natural frequency of the model. We suspect
that the observed oscillations reveal the resonance frequency of the system (1st mode) but this
cannot be independently verified. The observed oscillations may not be the dominant mode in
regards to our simplified model, i.e. may not be a mode aligned with the direction of the applied
force. The simplified mechanical model used in this work is restricted to forces and
displacements in the vertical direction only. We have chosen to use this assumption to estimate
the mechanical system model parameters, as this results in a conservative estimate of the
model resonance frequency (i.e. lower in frequency) and thus a controller designed based on
this model will result in a more robust controller. Stiffness and mass properties vary as a
function of the configuration of the robotic manipulator and were determined for the particular
configuration used in this work.
Both inputs of the MIMO model are assumed to affect both outputs, resulting in a
dynamic cross-coupling of the system as illustrated in the block diagram in Figure 10. The
cross-coupling terms are introduced to capture the dynamic coupling between the thermal and
mechanical process models. The coupling terms are cast as input-equivalent disturbances and
are directly related to the controlled process outputs. For example, the measured force, Fz, was
found to have an effect on the interface temperature, Tint, equivalent to a scaled change in
spindle speed. Here it is likely that plunge force directly affects the torque applied to the spindle
(acting as a disturbance torque to the spindle speed controller) which in turn results in a change
in the spindle speed. In this case, the spindle speed closed-loop controller dynamics are
significantly faster that the thermal process model dynamics. As such, the coupling between
force and temperature can ignore the spindle speed controller dynamics.
The governing equations of the system shown in Figure 10, expressed in the Laplace
domain, are shown in equations (7) and (8). The combined MIMO model contains the two
individual models as described above and two cross-coupling gains Kp,Z and Kp,Ω.
Zinn - MANU-12-1357 – Page 9
 tool (s ) 
K


p ,T
Tint (s)
Tp,T s
p ,T
s 1
e
K p ,Z
K p,

Z tool
(s )  
K p ,F ( p , z s  1) 2
F z (s )
Tp,F s
s 2  2 p p ,n s   p2 ,n
e
Figure 10: Block diagram of multi-input-multi-output dynamic process model with dynamic cross-coupling.
Tint ( s) 
Fz ( s ) 
K p ,T
 p ,T s  1
e
 T p ,T s
K p , F ( p , z s  1) 2
s  2 p p ,n s  
2
2
p ,n

e

tool
( s )  K p , Fz ( s )
 T p , F s
Z

tool

( s)  K p , zTint ( s)
(7)

(8)
The parameters of both the temperature and the force model were estimated empirically
for the given setup on the robotic FSW system using step response tests and the System
Identification Toolbox in MATLAB™. Assuming linearity enables the use of the principle of
superposition for parameter estimation, i.e., one input was held constant while the other was
varied in steps, observing both outputs.
The estimated model parameters based on
experiments are summarized in Table 1.
As noted above, the model structure for the temperature model was derived from [4],
whereas the model structure for the force model was developed using the mechanical model
discussed in this section. The model parameters were determined by performing step response
experiments. Example plots of experimental data of those step response tests are illustrated in
Figure 11, which shows sections of two welds: (a) Changing the spindle speed in a step from
1900 rpm to rpm and observing both outputs and (b) changing the vertical tool position from 9
mm to 10.5 mm and observing both outputs. By examining the plots, the first and second order
model structure of the temperature and the force model, respectively, can be seen. The figure
also shows that for our setup and parameter ranges, there is no significant effect of the spindle
speed on the axial force, except a change in the amplitude of the axial force oscillations due to
the tool rotation.
The process time delays are comparable to each other (400 ms and 300 ms) and are a
result of communication delays between the control system and the robot, internal delays in the
robot and delays resulting from the wireless transmission of the temperature measurements. It
was found that the vertical tool position has a significant effect not only on the axial force but
also on the interface temperature ( K p ,  0.5rpm / N ), i.e., a change of 1 N in axial force has
the same effect on the interface temperature as a variation in spindle speed by 0.5 rpm. On the
other hand, the spindle speed affects the interface temperature, but the influence on the axial
Zinn - MANU-12-1357 – Page 10
force is negligible ( K p ,Z  0mm / C ). This may not be in agreement with previous research
[17,18], but is valid on the given welding machine, setup, workpiece alloy and input parameter
range investigated here. Although no definite explanation can be named at this point, the
flexibility of the robot manipulator is believed to be a reason for the insensitivity of the axial force
with respect to the spindle speed. Unlike stiffer welding setups (e.g. those using c-frame gantry
systems), where plunge depth is held constant by the stiff supporting structure, a robotic welding
system does not maintain constant plunge depth but, instead, acts as a compressed spring.
Variations in material height (e.g. due to the softening of the material during welding) do not
have a significant effect on measured axial force because the resulting deflections are modest
as compared to the effective compression of the robotic manipulators supporting structure. In
order to help investigate this phenomenon further, a position sensing system could be added to
measure the actual vertical tool position during welding.
Table 1: Estimated model parameters Parameter
Estimated Value
Unit
K p ,T
0.04
°C/rpm
 p,T
0.04
s
T p ,T
0.4
s
K p ,Z
0
mm/°C
K p ,
0.5
rpm/N
K p , F  p2,n
500
N/mm
 p, z
0.07
s
ωp,n
0.2
0.7
Hz
T p, F
0.3
s
Temperature
CrossCoupling
Interface Temp. [C]
ζp
550
540
530
520
66.5
67
67.5
Time [s]
68
68.5
520
500
50.5
51
Time [s]
51.5
52
50.5
51
Time [s]
51.5
52
3500
5000
4500
4000
3500
3000
66.5
540
50
Axial Force [N]
Axial Force [N]
Interface Temp. [C]
Force
67
67.5
Time [s]
68
68.5
3000
2500
2000
1500
50
(a)
(b)
Figure 11: Example welds used for model parameter estimation for (a) changing the spindle speed from 1900
rpm to 1700 rpm and (b) changing the vertical tool position from 9 mm to 10.5 mm.
Zinn - MANU-12-1357 – Page 11
-1
10
-2
10
Kp,T
(2  p,T)-1
-3
10
-2
10
Magnitude [N/mm]
Magnitude [ C/rpm]
Using the parameter estimates found above, the open-loop frequency response plots of
the model are generated and are shown in Figure 12. The bandwidth of both processes is
similar and both systems experience significant phase lags at higher frequencies due to the time
delays. The peak in the magnitude of the force model is due to the underdamped characteristics
of the system.
-1
10
0
10
Frequency [Hz]
1
10
2
10
2
2
Kp,F p,z
p,n
-2
10
-1
10
0
10
Frequency [Hz]
1
10
2
10
0
Phase [deg]
Phase [deg]
Oscillatory Mode
10
0
-90
-180
Phase lag due to
time delay
-270
-360
-2
10
-2
Kp,F p,n
3
10
-1
10
0
10
Frequency [Hz]
1
10
-90
-180
-270
-360
-2
10
2
10
(a)
p,n
-1
10
0
10
Frequency [Hz]
Phase lag due to
time delay
1
10
2
10
(b)
Figure 12: Frequency response plot of open-loop process model of (a) output interface temperature relative
to commanded spindle speed and (b) output axial force relative to commanded vertical tool position.
3.4 Closed-Loop Controller
Based on the open-loop process model found in section 3.3, a closed-loop controller is
designed in the frequency domain. Two integral controllers are chosen for simplicity and to
eliminate any steady-state errors. This choice is strongly suggested from the open-loop
frequency response of the system model. With the significant time delays, which introduce large
phase lags, there is little hope of achieving closed-loop bandwidths above the break (or
resonant) frequencies. The use of the integral controllers, with cross-over frequencies placed
below the break (or resonant) frequencies, provides good phase margin and sufficient gain
stabilization (i.e., attenuation) of the resonant mode) to ensure a robust controller. Each
controller is introduced independently assuming no cross-coupling. The temperature controller
is discussed first, then the force controller. Finally, both controllers are combined including static
decoupling.
Successful closed-loop control of the shoulder interface temperature has been previously
implemented on a CNC mill [4]. An integral controller with gain Kc,T was used, which determines
spindle speed adjustments. The same measurement and control system is transferred to the
robotic FSW testbed in this work. Figure 13 shows the block diagram of the interface
temperature control system, for which either the shoulder or probe interface temperature can be
used as the feedback signal. The controller gain (20 rpm/°C) was determined utilizing the
developed process model, resulting in a gain margin of 13 dB and a phase margin of 70 degrees
and an estimated closed-loop bandwidth of 0.2 Hz. This results in a reasonable tradeoff
between sufficient stability and good performance. Figure 14 shows magnitude and phase of
the compensated open-loop system Tint ( s ) / ET ( s ) and Figure 15 shows magnitude and phase

of the compensated closed-loop system Tint ( s) / Tint ( s) .
Zinn - MANU-12-1357 – Page 12
T int ( s ) 
ET (s )
Kc,T
 tool (s )
K p ,T
 p ,T
s

e
s 1
Tp ,T s
Tint (s)
0
10
Gain Margin 13 dB
C
-2
10
-4
10
-2
10
-1
10
0
10
Frequency [Hz]
1
10
2
Magnitude [ C/ C]
Magnitude [ C/ C]
Figure 13: Block diagram of closed-loop interface temperature control system adjusting spindle speed.
10
Phase [deg]
Phase [deg]
B
-2
10
-2
10
-1
0
10
1
10
10
0
-90
-270
-1
10
Frequency [Hz]
0
-180
0
10
Phase Margin 70 deg
-360
-2
10
-1
10
0
10
Frequency [Hz]
1
10
2
10
Figure 14: Simulated compensated open-loop
frequency response of interface temperature control
system.
-90
-180
-270
-360
-2
10
B
-1
0
10
1
10
10
Frequency [Hz]
Figure 15: Simulated closed-loop frequency
response of interface temperature control system.
Closed-loop control of axial force by vertical tool position adjustments has not been
implemented on our previous testbed (CNC mill) due to system limitations (i.e., lack of ability to
adjust the vertical tool position in real-time), but has been employed previously by other
researchers [11–14]. Figure 16 shows the block diagram of the axial force control system
implemented in this work. The same controller structure was used as in the temperature control
system presented above. The controller gain (0.001 mm/N) was determined utilizing the
developed process model, resulting in a gain margin of 7 dB, a phase margin of 84 degrees and
an estimated closed-loop bandwidth of 0.1 Hz. Figure 17 shows magnitude and phase of the
compensated open-loop system Fz ( s ) / E F ( s ) and Figure 18 shows magnitude and phase of the
compensated closed-loop system Fz ( s ) / Fz ( s ) .
F z (s )


EF (s)
Kc, F
s

Z tool
(s )
K p ,F ( p , z s  1) 2
s 2  2 p p ,n s   p2 ,n
e
 T p ,F s
Fz (s)
Figure 16: Block diagram of closed-loop axial force control system with vertical tool position as control
input.
Zinn - MANU-12-1357 – Page 13
Gain Margin 7 dB
C
-1
10
0
10
Frequency [Hz]
1
2
10
Magnitude [N/N]
Magnitude [N/N]
0
10
-1
10
-2
10
-3
10
-4
10
-2
10
10
-1
10
B
-2
10
-2
-1
10
0
10
1
10
10
Frequency [Hz]
0
0
Phase [deg]
Phase [deg]
0
10
-90
-180
Phase Margin 84 deg
-270
-360
-2
10
-1
10
0
10
Frequency [Hz]
1
2
10
10
-90
-180
B
-270
-2
-1
10
0
10
1
10
10
Frequency [Hz]
Figure 17: Simulated compensated open-loop
frequency response of axial force control system.
Figure 18: Simulated closed-loop frequency
response of axial force control system.
In order to combine the interface temperature and axial force control systems, both
controllers are implemented in parallel using the same gains as found previously. Because the
two processes are dynamically cross-coupled, as shown in section 3.3, a decoupling structure is
added, shown in the block diagram of the overall control system in Figure 19. As a
consequence of placing the closed-loop bandwidth of the system below the process model
break frequency, the controller only needs to decouple the static gain of the process coupling

model, simplifying the implementation. The static decoupling gains used are K p , Z  0 mm / rpm

and K p ,  250 rpm / mm . The former gain is chosen to be zero because no significant effect of
spindle speed on the axial force was observed. The latter decoupling gain improves the
performance of the control system because the undesired effect of the vertical tool position on
the interface temperature is nulled through this feed-forward element.
Controller
T int ( s ) 
ET (s )
Kc,T
Process
Static Decoupling

s



 tool (s ) 
K


 K p ,Z
p ,T
p ,T
s 1
e
  T p ,T s
K p,Z
K p,

 K p,
F z (s )


EF (s)
Kc,F
Tint (s)



Z tool
(s )  
K p ,F ( p , z s  1) 2
s  2 p p ,n s  
2
s
2
p ,n
e
Tp ,F s
Fz ( s )
Figure 19: Block diagram of combined closed-loop interface temperature and axial force control system
using both spindle speed and vertical tool position as control inputs.
Zinn - MANU-12-1357 – Page 14
4. EXPERIMENTAL PROCEDURE
Welding experiments were performed on a robotic FSW system (Friction Stir Link, Inc.
RobostirTM system using an ABB IRB 7600 robot with an S4C+ robot controller). The spindle
motor’s (Control Techniques model MH-8500) maximum power rating was 9.95 kW, the rated
torque was 31.6 Nm and the maximum speed was 3000 rpm. On the given setup, a gear ratio of
1:2.83 was utilized between the motor and the spindle, resulting in a maximum spindle speed of
8500 rpm and maximum torque of 11.2 Nm. The tool travel angle was held constant at 3
degrees by using an angled fixture with the spindle orientated vertically. A FSW tool made of
H13 tool steel with a concave shoulder and a threaded, conical probe with three flats was used.
The tool shoulder diameter was 15 mm, the probe diameter was tapered from 7.0 mm to 5.2 mm
and the probe length was 4.7 mm (measured from the outer edge of the shoulder). The tool
rotation direction was always counterclockwise. The tools were machined in house on a 5-axis
mill-turn center (Mori Seiki NT1000/W). 170 mm long bead-on-plate welding was performed on
extruded 6.35 mm thick 6061-T6 aluminum workpieces (102 mm by 203 mm). All welds are
partial penetration welds. An 8 mm thick low carbon steel backing plate was used under the
workpieces unless otherwise noted.
5. RESULTS AND DISCUSSION
5.1 Process Dynamics
Figure 20 shows the measured interface temperatures at the shoulder and probe location
and the measured forces during a weld under position control with a constant spindle speed of
2000 rpm, a constant travel speed of 300 mm/min and a step change in commanded vertical tool
position from 10.5 mm to 11.0 mm in the first half of the weld traverse. The temperature
measurement approach chosen in this work captures the dynamics of the process very well,
because the thermocouple sheaths are in direct contact with the aluminum workpiece at the toolworkpiece interface. The measured temperatures are not constant, but rather oscillating as the
tool traverses under constant operating conditions as seen in Figure 20. The frequency of these
oscillations is found to match the frequency of the spindle rotation, i.e., the thermocouple is
capturing temperature variations through 360 degrees of the tool rotation. For the weld shown in
Figure 20, the amplitude of the shoulder and probe interface temperature is 3 °C and 6 °C,
respectively, and the amplitude of the axial force is 750 N. More information about the
temperature dynamics captured with this measurement strategy can be found in [19], and a
calibration of the measurements is presented in [20]. The amplitudes of the oscillations
observed in the three welding forces (also at the same frequency as the spindle rotation rate)
are larger than those observed with the same workpiece/tool combination on a CNC mill setup
[19], which is one indication of a higher flexibility of the robotic system compared to the stiffer
CNC mill.
Zinn - MANU-12-1357 – Page 15
0
20
30
Tool retracts
Change in vertical
tool position
200
Traverse starts
400
Plunge starts
Interface Temperatures [ C]
600
Shoulder
Probe
6061 solidus
40
50
Time [s]
60
70
80
40
50
Time [s]
60
70
80
6
Forces [kN]
Lateral
Traverse
Axial
4
2
0
20
30
Figure 20: Measured interface temperatures and forces when welding 6.35 mm thick 6061-T6 with a constant
spindle speed of 2000 rpm, constant travel speed of 300 mm/min and a step in commanded vertical tool
position from 10.5 mm to 11.0 mm (at 48 s).
The closed-loop control system is only enabled during the weld traverse, hence all
subsequent figures will only show the weld traverse for simplicity.
5.2 Closed-Loop Control of Interface Temperature
In order to verify the control system’s performance, command tracking experiments were
performed (Figure 21), in which the desired probe temperature was varied sinusoidally with a 10
°C amplitude and a frequency of 0.2 Hz. As mentioned in section 3.2, the spindle speed limits
were 1700 rpm and 2900 rpm, and the limits of the tool position were 7 mm and 18 mm. It can
be seen that the spindle speed is adjusted by the controller and the measured probe interface
temperature also various sinusoidally at the same frequency. Because the system operates right
at the closed-loop bandwidth, there is a significant phase lag of approximately 90 degrees. This
matches the result from the simulation of 83 degrees (Figure 15). Due to the higher
communication delays (400 ms) present on the robotic system (the delay on the CNC mill was
found to be only 85 ms), the phase lag of the control system implemented on the CNC mill is
only approximately 40 degrees (same workpiece and command trajectory). The closed-loop
performance could be increased using more sophisticated controller structures if needed, but the
performance of the given system is likely to be acceptable for many applications. The
magnitude ratio of the measured temperature compared to the commanded temperature is
approximately 0.8 on the robotic system (matching the result from the simulation of 0.74, Figure
15) and approximately 1.3 on the CNC mill. Disturbance rejection properties of the temperature
control system have been demonstrated previously on the CNC mill and can be found in [4].
Zinn - MANU-12-1357 – Page 16
Figure 21: Command tracking of closed-loop interface temperature control system using a sinusoidal
command with 10 °C amplitude and frequency of 0.2 Hz. Constant commanded vertical tool position 10.5 mm.
Constant travel speed of 360 mm/min. Feedback of probe interface temperature.
5.3 Closed-Loop Control of Axial Force
Axial Force [kN]
The performance of the axial force control system was evaluated and is shown in Figure
22 for command tracking of steps in desired force magnitude of 500 N. It can be seen that the
vertical tool position is adjusted appropriately and that the system follows the commands well
with no steady-state error, no overshoot and a closed-loop time constant of approximately 0.9 s.
6
5
Measured
Desired
4
11.5
11
40
45
Time [s]
50
F-control
enabled
Vertical Tool Position [mm]
35
55
Command
10.5
35
40
45
Time [s]
50
55
Figure 22: Command tracking of closed-loop axial force control system using step commands of 500 N
magnitude. Constant spindle speed 2300 rpm. Constant travel speed of 360 mm/min.
In order to evaluate the disturbance rejection properties of the axial force control system,
ramp disturbances were introduced into the system by adding a vertical offset to the
programmed end point of the weld. In Figure 23 it can be seen that the axial forces increase or
decrease significantly (positive and negative offset, respectively) when no axial force control is
utilized. This can lead to a significant degradation in weld quality as seen in the photographs of
the weld surfaces (Figure 24). When employing axial force control, the vertical tool position is
adjusted by the controller, which leads to proper tool shoulder-workpiece contact, a constant
Zinn - MANU-12-1357 – Page 17
6
4
30
Vertical Tool Position
Command [mm]
Axial Force [kN]
No Control
With Control
Desired
8
35
40
Time [s]
45
50
55
11
10
9
No Control
With Control
8
7
30
35
40
45
50
55
Vertical Tool Position
Command [mm]
Axial Force [kN]
axial force and a substantial improvement in weld quality while encountering the ramp
disturbance.
6
4
2
0
16
14
No Control
With Control
Desired
35
40
45
Time [s]
50
55
50
55
No Control
With Control
12
10
35
(a)
40
45
(b)
Figure 23: Disturbance rejection of closed-loop axial force control system using an (a) 3 mm positive and (b)
5 mm negative ramp disturbance. Constant spindle speed 2300 rpm. Constant travel speed of 360 mm/min.
Plunge depth too deep
Plunge depth too shallow: Voids
(a)
(b)
Figure 24: Photographs of weld surfaces related to Figure 23. Top: No control, bottom: With axial force
control. (a) 3 mm positive ramp disturbance, (b) 5 mm negative ramp disturbance.
5.4 Combined Closed-Loop Control of Interface Temperature and Axial Force
The combined temperature and force control system is first evaluated in terms of
command tracking (Figure 25). Initially a constant axial force of 4.5 kN is commanded with a
weld travel speed of 300 mm/min. After approximately 20 seconds, the axial force command is
decreased and increased in discrete steps over a 7 second interval. During the complete weld
the desired interface temperature is held constant. The vertical tool position is automatically
decreased, then increased to achieve the desired axial force. Changing the vertical tool position
also affects the temperatures, so the controller increases and then decreases the spindle speed
in order to compensate for the changed heat generation through different vertical tool positions.
At the end of the weld, the desired interface temperature is increased in steps while the axial
force command was held constant, which caused the controller to increase the spindle speed
and hold the vertical tool position approximately constant (negligible effect of spindle speed on
axial force).
Zinn - MANU-12-1357 – Page 18
Axial Force [kN]
540
520
35
40
45
50
Time [s]
55
60
1800
enabled
T-control
2000
Command
35
40
45
50
Time [s]
55
60
4
65
Measured
Desired
3
65
2400
2200
5
35
14
12
40
45
50
Time [s]
55
60
40
45
50
Time [s]
55
60
65
F-control
enabled
Shoulder
Pin
Desired (Pin)
Vertical Tool Position [mm]
Interface
Temperature [ C]
Spindle Speed [rpm]
620
600
580
560
Command
10
35
(a)
65
(b)
Figure 25: Command tracking of combined closed-loop interface temperature and axial force control system.
(a) Temperature part, (b) force part (same weld). Constant travel speed of 300 mm/min. Feedback of probe
interface temperature.
600
Axial Force [kN]
Shoulder
580
Pin
Desired (Pin)
560
540
520
45
50
55
Time [s]
60
3000
Command
2500
2000
1500
45
50
55
Time [s]
60
65
Measured
Desired
5
4
3
65
45
Vertical Tool Position [mm]
Spindle Speed [rpm] Interface Temperature [ C]

In order to further test the control system for simultaneous command tracking, both
sinusoidal temperature and force commands were used (Figure 26). The desired probe
interface temperature varied at 0.1 Hz with an amplitude of 15 °C and the desired axial force
varied at 0.1 Hz with an amplitude of 500 N and a phase shift of 90 degrees. It can be seen that
the combined control system performs well by simultaneously adjusting spindle speed and
vertical tool position to track both the temperature and force commands. The phase lag for the
temperature is approximately 60 degrees (44 degrees from the simulation, Figure 15) and about
50 degrees for the axial force (53 degrees from the simulation, Figure 18).
50
55
Time [s]
60
65
11
10
Command
9
45
(a)
50
55
Time [s]
60
65
(b)
Figure 26: Simultaneous command tracking of combined closed-loop interface temperature (a) and axial
force (b) control system (same weld). 0.1 Hz sinusoidal commands for both interface temperature (15 °C
amplitude) and axial force (500 N amplitude). Constant travel speed of 300 mm/min. Feedback of probe
interface temperature.
Zinn - MANU-12-1357 – Page 19
5
4
3
2
Measured
Desired
30
35
40
45
Time [s]
50
55
60
40
45
Time [s]
50
55
60
18
16
14
12
10
Command
F-control
enabled
Vertical Tool Position [mm]
Axial Force [kN]
The combined temperature and force control system is also applied in a scenario with a
ramp disturbance (5 mm negative ramp) as described in section 5.3 while simultaneously
commanding a desired interface temperature (Figure 27). The vertical position of the tool is
automatically adjusted throughout the weld in order to maintain a proper tool shoulder-workpiece
contact, resulting in a constant axial force. Meanwhile, the desired interface temperature is
changed in 10 °C steps, resulting in the controller adjusting the spindle speed to alter heat
generation.
30
(a)
35
(b)
Figure 27: Command tracking of temperature (a) and disturbance rejection of force (b) of combined closedloop interface temperature and axial force control system (same weld). Step commands in interface
temperature of 10 °C magnitude. 5 mm negative ramp disturbance for axial force. Constant travel speed of
300 mm/min. Feedback of probe interface temperature.
A final scenario to evaluate the combined control system is the application of a step
disturbance to the temperature by welding over two backing plates of very different thermal
diffusivities as illustrated in Figure 27 and simultaneously applying a ramp disturbance to the
force (3 mm negative ramp disturbance). To simulate a change in workpiece geometry or
properties, welds were performed over a set of two different backing plates of significantly
different thermal diffusivities. Titanium and copper with dimensions of 102 mm x 76 mm x 12.7
mm were selected for their significantly different thermal diffusivities but similar stiffness.
Backing plates of various materials have also been utilized for thermal management during
welding in order to improve the hardness of the resulting weld, particularly in the heat affected
zone (HAZ) [21,22].
Figure 28: Schematic of different backing plates to affect thermal boundary conditions.
The desired probe interface temperature was held constant at 550 °C and the desired
axial force was held constant at 4 kN. The results are shown in Figure 29 and it can be seen
that when no temperature or force control is used, the interface temperature decreases by over
Zinn - MANU-12-1357 – Page 20
Axial Force [kN]
80 degrees over the copper backing plate as compared to the titanium backing plate due to the
higher thermal diffusivity and hence heat loss out of the weld zone. The temperature starts to
decrease approximately 2 s (i.e., 10 mm) before the backing plate interface is crossed, which
indicates that the heat flow out of the weld zone is already affected by the copper backing plate
at that location. The axial force decreases throughout the whole weld due to the weld end point
intentionally programmed 3 mm above the workpiece. When employing the combined control
system, the controller increases the spindle speed initially and increases the vertical tool position
throughout the weld. This successfully maintains the desired temperature and force as
compared to the scenario when no control is used and weld quality is substantially improved as
seen in the weld surfaces in Figure 30. There is a brief drop in probe interface temperature just
before the backing plate interface, which is due to the limited response characteristics of the
control system (see section 5.5). The probe temperature is dropping by 27 °C, even when using
the control system, however, the probe temperature is only outside a ± 10 °C window for 1.7 s.
This brief drop is not believed to have any significant effect on the weld quality since the
temperature stayed at all times within a temperature window previously determined to result in
acceptable weld quality [5]. The chosen setup with the different backing plates also represents
a rather extreme change of thermal boundary conditions, which is rarely found in practice. After
crossing the backing plate interface, the commanded spindle speed continues to rise and then
levels off, because most heat is being conducted from the weld zone into the backing plate at
the center of the copper backing plate. Towards the beginning and end of the copper backing
plate, there is less heat conducted out of the weld zone due to the material boundaries to
titanium and air with much lower thermal diffusivities than copper.
5
4
3
No Control
2
Vertical Tool Position
Command [mm]
1
With Control
Desired
40
45
14
13
Ti Cu
50
Time [s]
55
60
55
60
Ti Cu
No Control
With Control
12
11
10
40
(a)
45
50
(b)
Figure 29: Simultaneous disturbance rejection of combined closed-loop interface temperature (a) and axial
force (b) control system (same weld). Welding over different backing plates (step disturbance for
temperature) and 3 mm negative ramp disturbance for axial force. Constant travel speed of 300 mm/min.
Feedback of probe interface temperature.
Zinn - MANU-12-1357 – Page 21
Plunge depth too shallow and temperature too low: Voids
(a)
(b)
Figure 30: Weld surfaces when welding over different backing plates and applying a 3 mm negative ramp
disturbance for axial force. (a) No control, (b) with combined temperature and force control.
5.5 Limitations
The performance of the robotic FSW closed-loop temperature and force control is directly
related to the achievable closed-loop bandwidth. The higher the bandwidth, the faster the
closed-loop system can respond to commands or reject disturbances. As such, it is important to
understand which system characteristics are responsible for the limitations in control bandwidth.
The major limitations on the given system are time delays and the low stiffness of the robotic
manipulator.
Time delays are caused by communication delays between the laptop that runs the
control laws and the robot controller, internal delays in the robotic FSW system (e.g.,
communication to spindle motor drive) and transmission delays of the measured temperatures.
These delays are inherent to the given system and could be slightly reduced if needed by
employing more advanced hardware and software. We are not attempting to modify the process
dynamics, our goal is rather to reject disturbances and model uncertainties. For this reason, an
integral controller were chosen – where the integral gain was selected to achieve a cross-over
frequency below the process break frequency. A proportional term could have been included,
but only when using a modest gain due to the delay. The closed-loop bandwidth must very likely
remain below the process break frequency to maintain stability with a high level of control
robustness (against model parameter variation). In the interest of simplicity, only the integral
term was kept. In order to better cope with these delays, an advanced controller structure could
be implemented, e.g., a Smith predictor (assuming the delay does not change significantly). The
effect of the time delay on the open-loop process model relating commanded vertical tool
position to axial force is illustrated in the frequency response plot in Figure 31 (a). It can be
seen that the magnitude is not affected by the delay, but that a frequency dependent phase lag
is added. A time delay always reduces the system stability and limits the achievable bandwidth
of a system.
This approach is initial work in establishing combined temperature and force control on
robotic friction stir welding systems. The authors believe that the general model structure should
be appropriate for most robotic systems or other systems with a lack of compliance. As in many
process control applications, some form of model parameter identification would be required for
other test beds with alternate FSW machines, tooling, fixtures, workpieces, etc., either through
explicit experiments or indirectly through tuning of control gains. As such, the structure and
approach are general to these types of systems with some tuning required.
The industrial robot used in this work is designed for a variety of manufacturing tasks,
most of them require higher tool center point (TCP) velocities and lower loads as compared to
most FSW applications. The inherent robot flexibility causes deflections in the serial robot
linkages during FSW, resulting in position errors. E.g., in order to achieve a plunge depth of
approximately 5 mm, the tool position must be commanded to be approximately 11 mm below
the workpiece surface. The robot’s compliance was estimated to be in the order of 1 mm/kN, as
Zinn - MANU-12-1357 – Page 22
2000
1000
500
200
100
40 -2
10
10
-1
0
10
Frequency [Hz]
10
1
2
Magnitude [N/mm]
Magnitude [N/mm]
compared to the CNC mill which has a compliance of 0.05 mm/kN [23]. Figure 31 (b) shows the
effect of varying stiffness on the open-loop process model relating commanded vertical tool
position to axial force. It can be seen that for a higher stiffness, the natural frequency of the
robotic manipulator increases. As a result, the phase lag associated with the resonance is
pushed to a higher frequency and the maximum possible stable closed-loop bandwidth is
increased.
10
-90
-270
-360 -2
10
1000
100
40 -2
10
10
-1
0
10
Frequency [Hz]
10
1
2
10
0
Phase [deg]
Phase [deg]
0
-180
Increasing stiffness
10000
Increasing delay
No delay
Delay = 0.0833s
Delay = 0.1667s
Delay = 0.25s
Delay = 0.333s
10
-1
0
10
Frequency [Hz]
10
1
2
10
-90
-180
-270
Increasing stiffness
Stiffness = 0.5*k
Stiffness = 1*k
Stiffness = 2*k
Stiffness = 5*k
Stiffness = 10*k
-360 -2
10
(a)
10
-1
0
10
Frequency [Hz]
10
1
2
10
(b)
Figure 31: Frequency response plot of open-loop process model of axial force relating to commanded
vertical tool position when (a) varying the time delay and (b) varying the stiffness.
In order to further examine the effect of time delays and compliance, both delay and
stiffness were varied and the maximum achievable crossover frequency was computed such that
the closed-loop system maintains stability. Figure 32 plots the maximum achievable crossover
frequency as a function of time delay and natural frequency. As shown in Figure 31, the natural
frequency is directly related to stiffness. It can be seen that the time delay in combination with
the natural frequency (stiffness) affects the maximum crossover frequency and hence closedloop bandwidth and system performance. For low natural frequencies (as experienced on the
robotic system), the low stiffness is the dominating limitation and the time delay only plays a
minor role. On setups with a high stiffness (such as a CNC mill), the time delay is the mayor
limitation. For systems with low delays the stiffness has an important effect on the performance
whereas for higher delays the delay becomes dominant. On the current setup (shown in Figure
32 in the lower right hand corner), both the delay and the compliance should be reduced in order
to improve the performance of the control system.
Zinn - MANU-12-1357 – Page 23
Maximum Crossover Frequency [Hz]
4
CNC mill
4
Natural Frequency [Hz]
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
Robot used
in this work
1
1
0
0.05
0.1
0.15
Time Delay [s]
0.2
0.25
Figure 32: Maximum achievable crossover frequency (Hz) when varying the stiffness (i.e., natural frequency)
and time delay.
Loop update rates are also a limitation. In our system, internal interrupts in the robot
controller and bus communication to the spindle motor servo drive are executed at
approximately 10 Hz and are not able to run faster because communication to external devices
has lower priorities than motion and safety tasks in the given robot control architecture. This
time discretization contributes additional equivalent delay equal to approximately one half of the
effective sample rate. In addition, the response of the actuators (spindle motor and robotic arm
drive system) is limited, as well as the rate of change of the actuators due to restricted power
being available to these devices. The outputs of the actuators are also limited to a certain range
based on their design specifications.
6. SUMMARY
We have demonstrated the successful development and evaluation of a closed-loop
control system for robotic friction stir welding (FSW) that controls plunge force and tool interface
temperature by varying spindle speed and commanded vertical tool position. The simultaneous
control of temperature and plunge force is necessitated by the unique characteristics of robotic
friction stir welding – primarily the significant increase in compliance as compared to most
custom engineered FSW machines. The system developed was implemented on an industrial
robotic FSW system equipped with a custom real-time wireless temperature measurement
system and plunge force sensor. The combined control system was shown to possess good
command tracking and disturbance rejection characteristics over a range of operating scenarios.
It was demonstrated, through the use of the control process model described here, that the
attainable closed-loop bandwidth of the robotic system is primarily limited by the inherent
compliance of the robotic system, as compared to most custom engineered FSW machines,
where instrumentation delay is the primary limiting factor. The developed system was
successfully implemented albeit the described limitations and is believed to have many potential
applications for production in industrial settings.
7. ACKNOWLEDGMENTS
Partial support of this work by the Department of Mechanical Engineering and the
College of Engineering at the University of Wisconsin - Madison, the Wisconsin Alumni
Research Foundation Technology Development RA, a Wisconsin Innovation & Economic
Zinn - MANU-12-1357 – Page 24
Development Research Program (IEDR) and the U.S. National Science Foundation under
contract CMMI-0824879 is gratefully acknowledged. The Mori Seiki NT1000/W is an equipment
loan from the Machine Tool Technology Research Foundation. The authors would like to thank
Lee Cerveny of Friction Stir Link, Inc. and Edward Cole, Joshua Schmale, Madhu Vadali, Eric
Meunier and Justin Morrow at the University of Wisconsin - Madison and Amir Assi and Ingrid El
Helou at the American University of Beirut (Lebanon) for their help.
8. NOMENCLATURE
CNC
Cu
DAQ
DOF
EDM
FSW
MIMO
TCP
Ti
Computer numerical control
Copper
Data acquisition
Degree of freedom
Electrical discharge machining
Friction stir welding
Multi input multi output
Tool center point
Titanium
c
EF
ET
fz, Fz
F*z
k
Kc,F
Kc,T
Damping constant [N/(m/s)]
Axial force error [N]
Temperature error [°C]
Measured axial force [N]
Desired axial force [N]
Stiffness constant [N/m]
Force controller gain [mm/N]
Temperature controller gain [rpm/°C]
Process gain (force) [N(rad/s)2/mm]
Kp,F
Kp,T
Kp,Z
Kp,Ω
m
tint, Tint
T*int
ztool ,ztool
z*tool ,z*tool
∆Tp,F
∆Tp,T
ζp
p,z
p,T
ωB
ωC
ωp,n
ω*tool, Ω*tool
Process gain (temperature) [°C/rpm]
Cross-coupling gain [mm/°C]
Cross-coupling gain [rpm/N]
Mass [kg]
Measured interface temperature [°C]
Desired interface temperature [°C]
Actual vertical tool position [mm]
Commanded vertical tool position [mm]
Process delay (force) [s]
Process delay (temperature) [s]
Damping ratio [-]
Time constant (zero, force) [s]
Time constant (pole, temperature) [s]
Closed-loop bandwidth [Hz]
Crossover frequency [Hz]
Natural frequency [rad/s]
Commanded spindle speed [rpm]
Zinn - MANU-12-1357 – Page 25
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