A Novel Engineering Method for the Power Flow Assessment in Servoactuated Automated Machinery
A Novel Engineering Method for the Power Flow Assessment in
Servoactuated Automated Machinery
Enrico Oliva1, Giovanni Berselli2*, and Marcello Pellicciari2
1SIR Soluzioni Industriali Robotizzate
Modena, 41012, Italy
2 “Enzo Ferrari” Engineering Department
University of Modena and Reggio Emilia
Modena, 41012, Italy
ABSTRACT
Multipurpose and programmable servoactuated mechanisms may be envisaged as the key technology for
increasing flexibility and reconfigurability of modern automated machinery. Unfortunately, based on the current
stateoftheart, these mechatronic devices are extremely flexible but generally energy intensive, thus
compromising the overall system sustainability. Nonetheless, the system power consumption can be partially
reduced if energy optimality is introduced as a design goal along with the global productivity. Naturally, as a first
step towards the practical implementation of any energyoptimality criterion, the end user should be capable of
predicting the system power flow, including the major sources of energy loss. In this context, this paper firstly
presents a reliable model of a servoactuated mechanism accounting for linkage, electric motor and power
converter behavior. Then, a novel identification method is discussed, which allows the separate determination of
the models parameters by means of noninvasive experimental measures. The method is finally validated by
comparing predicted and actual power flows in a simple mechatronic system, which is composed of a slidercrank
mechanism directly coupled with a positioncontrolled permanent magnet synchronous motor.
1. INTRODUCTION
The reduction of the Energy Consumption in automated production systems is currently becoming a topic of
primary importance for both large manufacturing companies and small/medium enterprises [1]. In particular, a
growing attention has been recently focused on the development of novel methods and tools for the energy
consumption optimization in positioncontrolled Servoactuated Mechanisms (SM) [2] and industrial robot [35],
whose behavior can be improved by either selecting energyefficient components or by simply employing
energyoptimal motions law whenever possible. Naturally, the practical implementation of the aforementioned
energysaving strategies requires a reliable model of the SM power flow, which is the direct consequence of several
interacting factors, namely mechanical system and electric motor dynamics, controller performance, and power
converter architecture. Even though several SM models may be easily found in the literature [6], the numerical
parameters describing the system behavior are usually either unknown, rather inaccurate or covered by confidentiality
agreements. For instance, the numerical parameters describing the mechanical hardware (e.g. link masses and
moments of inertia) can be directly measured if the linkage structure is disassembled. Nonetheless, this procedure
would require extensive time and effort or may also end up being impossible (due, for instance, to warranty issues).
Similarly, the torque constant and the motor efficiency at the nominal operating point can be found in the component
datasheets. However, these data are often very roughly defined and useful only for approximate models, so that
appropriate identification methods become necessary [7]. Within this scenario, the dynamic identification of serial and
parallel mechanisms has been widely studied in the past literature, both in the field of robotics [810] and automated
machinery [11]. In parallel, proper techniques for the identification of accurate electric motor models have been
proposed [12,13]. However, these techniques are rarely integrated into one single identification procedure [14].
In this context, the purpose of the present paper is to outline a simple and fast method for the power flow
assessment in linkage systems actuated by means of a permanent magnet synchronous motor. The proposed method is
based on the separate study of power converter, motor and mechanical hardware, which is possible thanks to the use of
a power meter at the entrance (network side) and exit (motor side) of the converter. In particular, the identification of
a simple SliderCrank (SC) servomechanism is carried out as a case study. First, the mechanism Dynamic Model
(DM), the electric Motor Model (MM) and the Converter Model (CM) are derived in LinearinParameters
formulations. Then, the dynamic parameters are identified, together with the torque constant [15]. Once these
* Corresponding author: Tel.: (+39) 0592026259; Email: giovanni.berselli@unimore.it
Flexible Automation and Intelligent Manufacturing, FAIM2014
parameters are known, also the MM and the CM are identified, focusing on the system power flow. Finally, all the
estimated models are recasted into reliable formulations of ingoing and outgoing converter powers.
2. IDENTIFICATION METHOD
The whole identification process is conceptually summarized in Figure 1 (quantities between blocks simply
represent the outputs and the inputs of the previous and consecutive blocks respectively). Initially, the DM of the
servomechanism is derived, assuming only the SC geometric parameters as known. This model, that describes the
relation between crank position,
, velocity,
̇ , acceleration,
̈ (hereafter referred to as kinematic variables), and
motor current,
, is obtained in an identifiable linearinparameters formulation. The DM is excited using a suitable
trajectory, performed with and without a known payload applied on the slider. The optimal trajectory, whose choice is
explained in Section 4, is requested to comply welldefined constraints on maximum velocities and accelerations.
During the motions, the useful variables are
sampled, employing several measurement
instruments and two different software, namely
TwinCAT and Matlab Data Acquisition
Toolbox. These values are then accurately
processed, as explained in Section 6, and the
experimental kinematic variables and motor
current are obtained. Similarly to [15], the
torque constant and the dynamic parameters are
estimated together. Once these parameters are
identified, the derivation of the motor and power
converter models can begin. The MM and the
CM are derived focusing the attention on the
power flows, as explained in Section 3. Both
MM and CM are excited employing optimal
trajectories, which are enforced without any
payload applied to the slider. The sampled data,
acquired during these motions, are accurately
processed again. The experimental variables are
finally used to estimate both motor and
converter parameters. As far as all the model
parameters are estimated, they are recasted into a
predictive formulation of the ingoing (network
side,
) and outgoing (motor side,
converter powers (see Figure. 2). These
formulations are finally used to forecast the
power flows on a test trajectory different from
the ones used during the estimation phases. In
Section 8, the predictive capability of the
identified models is finally analyzed.
Figure 1. Schematic of the identification method.
Figure 2. SM schematic with measurements and power flows. Figure 3. SC geometric scheme.
A Novel Engineering Method for the Power Flow Assessment in Servoactuated Automated Machinery
3. MODELING
3.1. MECHANISM DYNAMIC MODEL
As previously defined, the dynamic model of the SM describes the motor's quadrature current
as function of
the kinematic variables. The DM is derived in the following identifiable linear formulation:
(
,
̇
,
̈)
(1)
where
is the Dynamic Regression Matrix and
are the Dynamic Parameters.
This expression is obtained employing proper dynamic parameters and making the following assumptions:
• Linear relation between motor torque,
, and motor current,
. Denoting
as the torque constant, this
relation is modeled as:
.
• Simple friction formulations for the crank’s actuated rotational joint and the slider’s prismatic joint:
,
,
(
̇)
,
̇ (2);
,
,
(
̇
)
,
̇
(3)
where
,
,
,
,
,
and
,
are the Coulomb and viscous friction coefficients for crank and slider
respectively, whereas
̇
is the slider velocity (point B in Fig. 3) in the vertical direction
.
• Negligible friction torques for passive rotational joints, namely crankrod and rodslider joints.
Grounding on these suppositions, Eq. 1 is derived employing the EulerLagrange equation, the virtual work
principle, the motor torquecurrent relation, and a proper definition of the dynamic parameters. All the passages that
led to the definition of the DM will not be discussed here for brevity (the interest reader can refer to [8] for further
details of the general method). Nonetheless, it can be verified that the Dynamic Parameters and Dynamic Regression
Matrix can be expressed as:
1
⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡
2
2
2
2
2
,
,
,
,
⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤
(5);
⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡
̈
2
̈
3
2
̈
2
̈
2
̇
2
2
̇
2
2
⁄ 4
2
4
̈
5
3
4
4
̇
2
3
4
̈
4
2
4
3
̇
2
2
2
3
2
4
̈
3
2
8
̈
3
3
4
̈
2
2
4
̈
2
2
4
̈
2
4
̈
3
6
3
̇
2
2
6
3
̇
2
3
4
̇
2
2
4
̇
2
3
2
2
̇
2
2
2
2
̇
2
2
2
2
2
2
(
2
3
⁄ 2)
(
̇)
̇
(
̇)
1
⁄
̇
1
⁄
2
⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤
(6)
where
,
and
are the crank, rod and slider masses,
and
are the crank and rod barycentric inertias,
g is the gravity acceleration,
and
are the known crank and rod lengths,
and
are the unknown distances of
crank and rod center of gravity from the crankframe and crankrod revolute pairs respectively (as shown in Figure 3),
and
stand for the sine and cosine of
, and
is defined as
2
2
sin
2(
).
3.2. MOTOR AND POWER CONVERTER MODELS
The effect of the electric motor on the power flow is modeled considering the main electrical losses. Taking into
account only the copper and iron losses (as defined in [3]), the difference between the outgoing converter power,
,
and the mechanical power,
ℎ, is expressed as:
ℎ
2

̇  (7)
where
are the electrical losses within the electric motor, and
and
are suitable parameters. This
expression is then reformulated stressing the linear structure of the model:
ℎ
(
̇
,
)
(8)
where
and
are referred to as Motor Regression Matrix and Motor Parameters. Similarly to the motor, also the
power converter is modeled considering the main sources of electrical losses. However, in the converter, also the
energy storage in the DCbus capacitor is modeled, such that:
Flexible Automation and Intelligent Manufacturing, FAIM2014
(9)
where
indicates the energy stored inside the capacitor and
indicates the converter electrical losses.
According to experimental evidence, the power converter losses of the specific case study are modeled considering
only the inverter switching losses (as defined in [3]) and a constant loss term. The right hand side terms of Eq. (9) are
then defined as:
; (10);


(11)
where C is the capacitance and
and
suitable parameters. Equation (9) is then expressed as:
̇


⟶
,
,
̇
(12)
where
and
are the Converter Regression Matrix and the Converter Parameters.
3.3. INGOING AND OUTGOING CONVERTER POWERS
First, the mechanical power is obtained by simply multiplying the motor torque,
, by the motor velocity,
.
Exploiting also the linear relation between torque and current, the following equation is obtained:
ℎ
⟶
ℎ
̇
(13)
where
̇ since the SC mechanism is directly coupled to the electric motor (absence of gear reducer).
Once the mechanical power has been defined, the expression of the outgoing converter power is derived
employing the MM. Exploiting Eqs. (7) and (13), the following equation is derived:
ℎ
⟶
̇
2

̇
(14)
Substituting the motor current with its formulation described in Eq. (1), Eq. (14) is rephrased as:
(
,
̇
,
̈
,
,
,
) (15)
obtaining a formulation that depends only on the kinematic variables
,
̇
,
̈ and on the parameters
,
and
.
The formulation of the ingoing converter power is finally derived exploiting Eq. (14) and Eq. (12). Using these
equations, the following formula is achieved:
⟶
̇
2

̇
̇


(16)
By using Eq. (1), the following formulation is then obtained:
,
̇
,
̈
,
,
̇
,
,
,
,
(17)
Unluckily, this formulation does not depend only on the kinematic variables and model parameters, but also on the
capacitor potential difference,
, and its time derivative. Since a reliable formulation of the capacitor voltage has
not been detected yet, it is not currently possible to define a totally predictive formulation of
.
4. DESIGN OF EXPERIMENTS
Proper experiments need to be performed in order to excite adequately all the parameters and to allow an accurate
estimation phase. The DOE phase generally includes three different steps: 1) the choice of a certain trajectory; 2) the
selection of a proper cost function; 3) the derivation of the best trajectory by means of optimization techniques.
Trajectories are parameterized as Finite Fourier Series:
(
)
0
sin
cos
ℎ
=
1
(18)
where the number of harmonics
ℎ is set to 5 and the fundamental frequency
is set to 1 rad/s.
A Novel Engineering Method for the Power Flow Assessment in Servoactuated Automated Machinery
As said, the optimal exciting trajectories are selected by minimizing a certain cost function. Different appropriate
cost functions can be chosen [8, pp. 296298]. In the present paper, the Condition Number of the observation matrix W
is minimized:
(
) (19)
where each row of the observation matrix is generally defined as the evaluation of the regression matrix in the
considered time instant. Note that the cost functions of the MM and CM are defined grounding on the knowledge of
the already estimated dynamic parameters and the effect of the capacitor is not included (since a predictive function of
the capacitor voltage is not available).
The optimization step is finally carried out employing the fmincon Matlab function, which allows the enforcement
of the optimization constraints on maximum velocities and accelerations. In particular, these values are set to 30 rad/s
and 300 rad/s2 respectively.
5. DATA ACQUISITION
The employed experimental setup is shown in Figure 4. In particular, the experimental rig is composed of a SC
directly coupled with a Beckhoff AM3072 synchronous motor connected to a Beckhoff AX5112 electrical drive. The
control system is based on TwinCAT software, i.e. the PCbased control platform owned by Beckhoff, connected to
the drive via EtherCAT fieldbus. Positions q are measured using the motor encoder through the TwinCAT software
(with a sampling frequency of 2000 Hz). The capacitor voltage,
, is also provided by the TwinCAT software, with
a sampling frequency of 2000 Hz. A Meetbox power meter [16] is used to measure the ingoing and outgoing converter
powers, through the measurement of 2 currents and 2 voltages for each of these powers, as shown in Figures 3 and 4.
These measurements, together with a trigger signal, are passed to the NI module in the form of analogue signals. The
digital variables are finally obtained employing the Matlab Data Acquisition Toolbox with a sampling frequency of 25
kHz.
6. SIGNAL PROCESSING
The signal processing phase is mainly focused on three different aspects: 1) integration of the measures obtained
using Meetbox and TwinCAT; 2) derivation of all the needed variables from the measured ones; 3) execution of a
good filtering phase.
The integration of the different measures is obtained employing a trigger signal sent from the industrial PC to the
NI module. This signal is processed together with the other Meetbox measures and all the variables are then
synchronized to the TwinCAT ones.
Figure 4. Experimental setup. Power and information flows are highlighted.
Flexible Automation and Intelligent Manufacturing, FAIM2014
With reference to Figure 2, before performing the filtering phase, the outgoing current on the b phase is derived
imposing that the sum of the three currents is null. Then, the quadrature motor current
is obtained employing the
Park transformation [10]. Furthermore, the ingoing and outgoing converter powers are obtained using the Aron
insertion [17, section 3.2] and the following formulas are used:
; (20);
(21)
where
is defined as
,
,
,
,
is defined as
,
,
,
,
indicates
,
,
,
and
is finally
defined as
,
,
,
.
Once these variables are defined, the filtering phase is carried out. The sampled variables
and
and the
derived variables
,
and
are filtered with a lowpass Butterworth filter. The filtering is applied both in
forward and backward direction using the filtfilt Matlab function, thus avoiding to add any phase shift to the signal.
Velocities and accelerations are then derived applying second order central differences to the filtered positions.
Similarly, the capacitor voltage time derivative is derived using the second order central differences. Finally,
exploiting Eq. (13), the mechanical power is computed as:
ℎ
̇
𝐾
(22)
where
is the estimated value of the torque constant, and
̇ and
are the velocity and the filtered motor current
respectively. Henceforth, being
a generic variable, its experimental filtered value will be referred to as
.
7. ESTIMATION
Since the DM, MM and CM are expressed in linear formulations, all the unknown parameters could be identified
using simple linear regression techniques. The proposed method makes use of ordinary unweighted least squares:
𝜽
((
)
−
1
)
+
(23)
where
is the Dependent Variable and (.)+ denotes the Pseudoinverse. As shown in Figure 1, the dynamic parameters
and the torque constant are identified together employing data acquired during the DM exciting trajectory, performed
with and without a known payload attached to the slider. The torque contribution due to the known payload mass,
, is modeled considering the rate on the motor torque owing to the contribution of a slider mass equaling the
payload. Performing a few simple computations, the following equation is found:
,
̇
,
̈
,
with
,
1
2
,
2
2
,
3
,
4
(24)
The motor current rate due to the payload,
, is then obtained simply dividing
by the torque constant
.
By adding the payload contribution to the dynamic model of Eq. (1), the following relation is found:
,
̇
,
̈
,
with (25)
,
̇
,
̈
,
(
,
̇
,
̈)
,
,
̇
,
̈
,
and
1
⁄
where
and
are the regression matrix and the parameters of the Loaded Dynamic model. Both dynamic
parameters and torque constant are then identified using the following formula:
𝜽
,
̇
,
̈
,
+
(26)
where
,
̇
,
̈
and
are the vectors of experimental variables and
is the payload mass vector, whose
elements are set to zero when the payload is not mounted.
Similarly, the motor and converter parameters are estimated employing the experimental measures obtained during
their exciting trajectories. The following formulas are used:
𝜽
[
(
̇
,
)]
+(
ℎ
) (27);
𝜽
,
,
̇
+(
) (28)
A Novel Engineering Method for the Power Flow Assessment in Servoactuated Automated Machinery
8. RESULTS
The identified models are validated verifying their predictive accuracy on a test trajectory different from the ones
employed during the identification process. The test trajectory, shown in Figure 5, consists in several motions
featuring a trapezoidal speed profile and performed between some randomly chosen points. During these trajectories,
carried out without any payload, the predicted values are obtained using the following formulations:
,
̇
,
̈
,
𝜽
,
,
𝜽
(29);
,
̇
,
̈
,
,
̇
,
𝜽
,
,
𝜽
,
𝜽
(30)
being
,
̇
,
̈
,
and
̇
the experimental values and
𝜽
,
,
𝜽
,
𝜽
the estimated parameters. It is important to
notice that, while the outgoing converter power can be predicted once the kinematic variables are known, the ingoing
converter power formulation depends on the capacitor voltage and its time derivative. Therefore, the model in Eq. (30)
cannot be used to fully predict the ingoing converter power given a certain trajectory. Nevertheless, both motor,
,
and power converter,
,
electrical losses can be predicted employing:
2

̇

;
with
(
,
̇
,
̈
)
𝜽
(31)
where
,
̇
,
̈
are the experimental kinematic variables and
𝜽
,
,
,
,
are the estimated parameters.
Figure 6 shows the predicted and experimental ingoing and outgoing powers during the test trajectory, where also the
influence of the predicted electrical losses is highlighted.
Figure 5. Test trajectory. The test trajectory consists in 9 speed trapezoidal motions, with jerk limitations, passing through 8
randomly chosen motor angles. The waiting time between different motions is set to zero.
Figure 6. Experimental,
and
, and predicted,
and
, ingoing and outgoing converter powers concerning the test
trajectory. Predicted motor,
, and power converter,
, electrical losses (red dashed lines).
Flexible Automation and Intelligent Manufacturing, FAIM2014
9. CONCLUSION AND FUTURE WORKS
In this paper, a novel identification method for the power flow assessment of a slidercrank SM has been proposed.
The strength of this new method stands in the capability of identifying dynamic, motor and power converter
parameters by performing only simple and fast experiments. While the simplicity of the linear structure of the
identified models results in a substantial gain in the computational speed, the predictive capability of the derived
models is nonetheless excellent. In practice, the proposed models and identification method can be employed as a base
for the development of energy optimization methods, which usually require reliable predictive formulations of the SM
power losses. Future works will concern the formulation of a predictive model for the capacitor voltage, thus
achieving a fully predictive model of the ingoing converter power, and the application of the method to the
identification of energy losses in multi degreesoffreedom SM such as industrial robots.
ACKNOWLEDGEMENTS
The research leading to these results has received funding from the European Community‘s seventh framework
programme under grant agreement no. 609391 (AREUS  Automation and Robotics for EUropean Sustainabile
manufacturing).
REFERENCES
[1] E. Westkämper, “The Objectives of Manufacturing Development,” in Towards the ReIndustrialization of Europe, Springer,
2014, pp. 23–37.
[2] M. Pellicciari, G. Berselli, F. Balugani, D. Meike, and F. Leali, “On designing optimal trajectories for servoactuated
mechanisms through highly detailed virtual prototypes,” in IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics
(AIM), 2013, pp. 1780–1785.
[3] C. Hansen, J. Oltjen, D. Meike, and T. Ortmaier: “Enhanced approach for energyefficient trajectory generation of
industrial robots” in 2012 IEEE Int. Conf. on Automation Science and Engineering (CASE), 2012, pp. 1–7.
[4] D. Meike, M. Pellicciari, G. Berselli, “Energy Efficient Use of MultiRobot Production Lines in the Automotive Industry:
Detailed System Modeling and Optimization”, IEEE Transaction on Automation Science and Engineering, Vol. PP,
Issue:99, pp. 1–12, 2013.
[5] D. Meike, M. Pellicciari, G. Berselli, A. Vergnano, L. Ribickis. “Increasing the Energy Efficiency of MultiRobot Production
Lines in the Automotive Industry”. IEEE CASE, Int. Conf. on Automation Science and Engineering, pp. 1–6, 2012.
[6] B. K. Bose, Modern Power Electronics and AC Drives. Prentice Hall, 2002.
[7] L. Ljung, System Identification: theory for the user (second edition). Prentice Hall, 1999.
[8] W. Khalil and E. Dombre, Modeling, Identification and Control of Robots. Kogan Page Science, 2004.
[9] J. Swevers, W. Verdonck, and J. De Schutter: “Dynamic Model Identification for Industrial Robots,” IEEE Control Systems,
vol. 27, no. 5, pp. 58–71, 2007.
[10] E. Oliva, G. Berselli, and F. Pini: “Dynamic Identification of Industrial Robots from LowSampled Data,” Applied
Mechanics and Materials, vol. 328, pp. 644–650, Jun. 2013.
[11] J. Ha, R. Fung, K. Chen, and S. Hsien: “Dynamic modeling and identification of a slidercrank mechanism,” Journal of
Sound and Vibration, vol. 289, pp. 1019–1044, Feb. 2006.
[12] N. Urasaki, T. Senjyu, and K. Uezato: “Influence of all losses on permanent magnet synchronous motor drives,” in 26th
Annual Conference of the IEEE Industrial Electronics Society (IECON), 2000, pp. 1371–1376.
[13] M. Tenerz, “Parameter Estimation in a Permanent Magnet Synchronous Motor,” PhD thesis, Linköping, 2011.
[14] M. G. Robet: “Decoupled identification of electrical and mechanical parameters of synchronous motordriven chain with an
efficient CLOE method,” in 2013 8th IEEE Conference on Industrial Electronics and Applications (ICIEA), 2013, pp. 1780–
1785.
[15] M. Gautier and S. Briot: “New method for global identification of the joint drive gains of robots using a known payload
mass,” in 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2011, pp. 3728–3733.
[16] http://www.irsweb.it/MeetBOX.html (accessed January 10, 2014).
[17] J. G. Webster, Electrical Measurement, Signal Processing, and Displays. CRC Press, 2003.