- Email: [email protected]
Study of a linear actuator with a hybrid core using sensorless position control
Journal Pre-proof Study of a Linear Actuator with a Hybrid Core using Sensorless Position Control Jose´ Alberto (Validation) (Investigation)Writingoriginal draft) (Visualization), Fernando J.T.E. Ferreira (Supervision) (Conceptualization) (Methodology) (Writing - review and editing), An´ıbal T de Almeida (Resources) (Funding acquisition) (Supervision) (Writing - review and editing)
PII:
S0924-4247(19)32141-7
DOI:
https://doi.org/10.1016/j.sna.2020.111919
Reference:
SNA 111919
To appear in:
Sensors and Actuators: A. Physical
Received Date:
28 November 2019
Revised Date:
30 January 2020
Accepted Date:
25 February 2020
Please cite this article as: Alberto J, Ferreira FJTE, de Almeida AT, Study of a Linear Actuator with a Hybrid Core using Sensorless Position Control, Sensors and Actuators: A. Physical (2020), doi: https://doi.org/10.1016/j.sna.2020.111919
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.
Study of a Linear Actuator with a Hybrid Core using Sensorless Position Control José Alberto, Fernando J. T. E. Ferreira, and Aníbal T. de Almeida 1
Institute of Systems and Robotics, Department of Electrical and Computer Engineering, University of Coimbra, Polo II, 3030-
290 Coimbra, Portugal
Jo
ur na
lP
re
-p
ro
of
Graphicala abstract
of ro -p re lP ur na Jo Highlights •
Study on a tubular linear actuator with a hybrid core, composed by a permanent magnet and a ferromagnetic to increase force density.
•
Sensorless position detection using the variation of the coil current ripple with the variation of the core position.
•
Actuator prototype composed by a coil connected to a converter fed by a DC source and controlled by a PWM signal.
•
Positioning control strategy experimentally tested for constant position and constant load force.
Abstract— In this paper, a study of a tubular linear actuator with a hybrid core is presented. Through a finite-element analysis software and force measurements it is shown that by using a hybrid core combining a permanent magnet and a ferromagnetic material, higher force density can be achieved compared to the utilization of a ferromagnetic core alone. Also, by keeping the ferromagnetic part, the sensorless detection of the core position is possible. A simple position control strategy is proposed, using the inductance variation to indirectly detect the position of the core, in which the duty cycle of the PWM voltage is changed to compensate variations of position or load force. In order to test the novel hybrid core and
of
the proposed control strategy, a prototype was built. The experimental results clearly demonstrate the advantages and
ro
applicability of the hybrid core in linear actuators.
Introduction
re
1.
-p
Keywords - Linear actuators; electromagnetic analysis; finite element analysis; sensorless control; linear motors.
In the past, several studies have been made on different types of linear motors and actuators [1–6]. Although they can be used in numerous applications, one of the most interesting and high potential applications is on biomedical actuators [7]. More
lP
specifically, the utilization of motors for prosthetics limbs or exoskeletons has been under research lately [8–10]. In [11], a tubular linear motor with a ferromagnetic core designed to replace a human tendon or muscle is proposed. This type of linear motor can be used in a modular configuration (e.g. multiple coils and/or multiple cores), it has a simple structure and it is easy to control.
ur na
Furthermore, other manufacturing methods for motors and actuators, such as PCB windings [4,12] or additive manufacturing (3D printing) [13–16], allow a fast and economic design and construction of the device, as well as the adjustment of its characteristics to its final application. In this way, these methods can be appropriate for biomedical applications in which the device needs to be scaled according to the patient's requirements.
In [11] a study is made regarding the variation of the maximum force generated with the variation of the geometrical and electrical parameters of the tubular linear motor with a ferromagnetic core. However, as it is known, linear motors using permanent
Jo
magnets have higher force density values regarding those using a ferromagnetic core. Consequently, the utilization of ferromagnetic materials combined with permanent magnets to increase force density has been used in several types of motors and actuators [17–19]. On the other hand, by using a permanent magnet (PM) alone, it is not possible to detect the position of the core through the variation of inductance as proposed in [11]. In order to overcome this drawback, a hybrid core combining a PM and a ferromagnetic material would allow the linear motor to achieve higher force density without losing its ability to detect the position through the variation of the inductance of the coil, avoiding the use of position sensors. In this paper, a tubular linear actuator with a hybrid core is proposed (Fig. 1), as well as a simple positioning control strategy. The actuator is simulated using the finite-element analysis software Flux 2D in order to assess the force generated. Then, using the variation of the inductance and consequently the variation of the current ripple to indirectly detect the position of the core, a position control strategy is proposed. Finally, an experimental setup was built so that the advantages of using a hybrid core and the
proposed control strategy could be tested.
2.
of
Fig. 1- Structure of the proposed actuator with a hybrid core.
Linear Actuator with Hybrid Core
ro
2.1. Finite Element Simulations
The actuator was simulated using the 2D finite-element analysis/method (FEA/FEM) software Flux 2D, to compare the force
-p
generated by the linear actuator with a ferromagnetic core and with a hybrid core. The simulation was of the type Magnetostatic
re
and axisymmetric. The parameters used for the simulations were those from the coil used in the experiments (Table I).
Table I
Value 5.5 mm 7.5 mm (2 x 18) mm2 18 mm 3500
ur na
Parameter Inner radius Outer radius Section Length Number of turns
lP
Coil parameters used for the simulations.
Regarding the dimensions of the core, the dimensions of the two core types are those used in the experimental setup and are represented in Fig. 2:
Hybrid core: 6-mm diameter; 20-mm length the PM part and 18-mm length the ferromagnetic part;
Ferromagnetic core: 6-mm diameter; 38-mm length.
Jo
In Fig. 2, screenshots of the simulations made with FEA/FEM software Flux 2D are shown: the ferromagnetic part is marked with the black colour, the PM part with the red colour, and the coil with pink colour. The white line that divides the blue (air medium where the magnetic field is calculated) and the grey area represents the symmetry axis.
(a)
(b)
Fig. 2- Simulations with FEA/FEM software Flux 2D considering: (a) a ferromagnetic core; (b) a hybrid core. The ferromagnetic part is marked
of
with the color black and the PM part with the color red; the pink region represents the coil. As it is an axisymmetric simulation, the symmetry
lP
re
-p
ro
axis is the white line dividing the blue and the grey areas (the blue area represents the area where the magnetic field was calculated).
(a)
(b)
Fig. 3 - Simulations with FEA/FEM software Flux 2D of the cases considered in this study: (a) magnetic fields produced by the coil (blue
ur na
arrows) and by the PM (yellow arrows) have opposite directions; (b) magnetic fields have the same direction.
The proposed sensorless method relies on the variation of the inductance of the coil and consequently on the variation of the current ripple with the position of the core, as in [11]. In order to identify the case where a higher variation of the current ripple occurs, two situations were simulated for the hybrid core: (i) the magnetic fields generated by the coil and PM are in the same direction (Fig. 3b); (ii) the magnetic fields generated by the coil and PM are in opposite directions (Fig. 3a). These magnetic field simulations were made with FEA/FEM software Flux 2D, and in Fig. 3, the magnetic fields generated by the coil and the PM are
Jo
represented by blue and yellow arrows, respectively. Using the Flux 2D Transient simulation type, with a DC-DC buck converter like the one described later in this paper, fed with a 30 V DC source, with a switching frequency of 1 kHz, the variation on the current ripple for different positions of the core was simulated for both cases. The core position is given by the distance between the geometric centers of the coil and of the core, meaning that the core position is zero when the core is aligned with the coil. This was done considering the characteristics of the materials used in the tested prototype (permanent magnet: Eclipse Magnetics N808 Neodymium Magnet; ferromagnetic: Fair-Rite 78 ROD). The results are shown in Fig. 4
Fig. 4- Simulations with FEA/FEM software Flux 2D of the variation of the current ripple of the coil (p.u.), considering the cases represented in Fig. 2, when the magnetic fields generated by the coil and the PM have the same direction or opposite directions.
Therefore, as seen in Fig. 4, the variation of the current ripple is higher when the coil magnetic field is opposite to the one generated by the PM. This can be explained by the fact that in this way the ferromagnetic core is further away from the saturation
of
point. Afterwards, using the Flux 2D Magnetostatic simulation type, a comparison between the force generated using the two types of core (ferromagnetic and hybrid) was made, considering a constant current of 125 mA or -125 mA feeding the coil. The values of
lP
re
-p
ro
the force were determined for different positions of the core. The results are shown in Fig. 5.
Fig. 5- Force generated by the linear actuator for different positions of the core and for the two different core types.
As seen in Fig. 5, the maximum force generated with the hybrid core (0.63 N for the opposite direction and 0.66 N for the same
ur na
direction) is 3.5 to 3.7 larger than the one generated with the ferromagnetic core (0.18 N) for the same core section and length, thus showing the advantage of using a hybrid core. As the maximum force is approximately the same for the two hybrid core cases, it was decided to use the magnetic field generated by the coil in opposition to that of the PM, due to the higher variation of the current ripple, leading to a more accurate position detection. Then, the current was varied from 65 mA to 125 mA and the force was calculated for different core positions. The results are
Jo
shown in Fig. 6.
Fig. 6- Force generated by the linear actuator with the hybrid core for different values of the current.
As described in Fig. 6, it can be seen that by adjusting the current it is possible: (i) to keep the same position and change the generated force or (ii) change the generated force and keep the same position. The experimental results for these two operating modes will be presented later in the paper. 3. Sensorless positioning control
The circuit of the linear actuator consists of a coil connected to a DC-DC buck converter controlled by a PWM signal and fed
ro
of
by a DC voltage supply as shown in Fig. 7.
-p
Fig. 7- Scheme of the DC-DC buck converter used for the experimental setup.
It is known that the force applied on the core will be proportional to the square of the current flowing through the coil [11].
lP
value of the duty cycle, 𝐷𝑐 , of the PWM signal:
re
Moreover, in steady state (t >> coil) and neglecting the variation of inductance over time, the average current, 𝐼𝑎𝑣𝑔 , depends on the
(1)
The change of the position of the ferromagnetic part of the core will cause a variation of the inductance of the coil. When the
ur na
coil is fed with a PWM voltage, the current ripple Δ𝐼 will depend on the inductance of the coil, as referred in [11]:
(2)
Jo
where 𝑉𝑑𝑐 is the value of the DC voltage that is feeding the converter, 𝐷𝑐 is the duty cycle, R is the intrinsic resistance of the coil, T is the period of the PWM signal, L represents the inductance of the coil and d is the position of the core. So, for a fixed value of DC voltage, duty cycle and period, a higher value of inductance will cause a lower ripple while a lower inductance will result in a higher ripple. As each position of the core corresponds to a certain value of inductance, by measuring the current ripple and duty cycle, the real position of the core can be measured, according to (2). This can be done using a lookup-table experimentally created in which each pair of values of duty cycle and current ripple correspond to a certain position of the core. Then, using the difference between the reference position and the measured position, the duty cycle and consequently the average current and the force applied to the core can be increased or decreased, until the reference position is achieved. The proposed control strategy is represented in Fig. 8.
of ro
Fig. 8 – Control strategy used for core positioning.
-p
4. Experimental Results 4.1. Description of the Experimental Setup
re
As shown in Fig. 9a, an experimental setup was built to test the linear motor and the respective positioning control strategy. A commercial coil was used (MA 22 24 DC H), which was connected to a DC-DC converter (Fairchild FNA40860). The converter
lP
is controlled with the PWM signals generated from the PWM signal generator (NI-9401). The current and its ripple are measured with a Current Probe (Tektronix A622 AC/DC) connected to a data acquisition module (NI-9215). Both NI-9401 and NI-9215 were connected to a real-time control system (NI cRIO-9074) and the control strategy was implemented using the software LabView. The input DC and control supply voltages are generated using a triple power supply (Aim-TTi EX354RT). In Fig. 9b,
Jo
ur na
the ruler used for core position measurements is shown.
(a)
Fig. 9- Details of (a) the setup used for experiments and (b) the ruler used for position measurements.
(b)
As a core, five Neodymium permanent magnets (Eclipse Magnetics N808) with 6 mm diameter and 4 mm length each one together with a ferromagnetic (Fair-Rite 78 ROD) with 6 mm diameter and 18 mm length were used (shown in Fig. 10a). In order to measure the position of the core using the ruler shown in Fig. 9b, a small metal rod with a position mark was added to the core, as shown in Fig. 10b.
of
(a) (b) Fig. 10- (a) Hybrid core used for the experimental setup and (b) core with a metal rod with position mark for position measurements.
Using the experimental setup described in Fig. 8a, two cases were tested: (i) the reference position is changed, and the load force is kept constant; (ii) the reference position is kept constant and the requested load force is changed. In this way, two possible
ro
situations regarding the utilization of this actuator for biomedical applications as prosthetic limbs are tested: the first could represent
4.2. Experimental Results
re
4.2.1. Comparison between Hybrid and Ferromagnetic Core
-p
a moving empty hand and the second could be an example of a hand holding a heavier object.
In order to experimentally compare the maximum force that could be generated using the same linear actuator with ferromagnetic
lP
or hybrid cores, a Sauter FK 10N Digital Force Gauge was used. Then, the force generated with the hybrid core (Fig. 9a) and with a Fair-Rite 78 ROD with 6-mm diameter and 38-mm length, for different values of the current was measured and recorded. The
Jo
ur na
results are shown in Fig. 11.
Fig. 11-Comparison of the maximum force generated with hybrid and ferromagnetic cores, for different values of the current in the actuator.
Analyzing the results described in Fig. 11, it can be concluded that, with the same geometric dimensions, the force generated with a hybrid core goes up to 3.6 times the force generated with a ferromagnetic core, thus confirming the advantage of using a hybrid core, previously demonstrated with the finite-element analysis.
4.2.2. Positioning Control
In order to test the proposed control method described in Fig. 8, a fixed DC voltage of 30 V, a switching frequency of 1 kHz and a value of Δ𝐷𝑐 = 0.006 were considered. In Fig. 12, an example of the PWM voltage and current in the coil for two different
(a)
(b)
of
positions of the core and for a duty cycle of 0.5 is shown.
ro
Figure 12 - Example of the measured PWM voltage and current in the coils, considering the DC voltage equal of 30 V and a duty cycle of 0.5 for two different positions of the core: (a) ferromagnetic part outside the coil; (b) the ferromagnetic part inside the coil.
-p
The position detection was tested by measuring the distance from the center of the coil using the ruler shown in Fig. 8b. As it
ur na
lP
re
can be seen in Fig. 13, the position can be detected with good accuracy compared to the measured position.
Fig. 13- Comparison between the measured position and the estimated position for different values of the duty cycle.
Then, the duty cycle of the PWM signal was varied in order to compensate variations of the reference position (Fig. 14) and load force (Fig. 15).
As it can be seen in Figs. 14 and 15, the control method proposed can, through the incremental or decremental variation of the
Jo
duty cycle, compensate for the variations of the requested load force or of the reference position, thus proving its applicability for biomedical applications. Although the response of the control method is slower than other control methods typically used in electromechanical actuators, such as those described in [20–22], it is simpler to implement and it is fast enough for biomedical applications, such as prosthetic limbs. The measured value of the average current is slightly lower than that determined with (1). For example, in Fig. 14, at 20 seconds the duty cycle is 0.7 and the average current is 104 mA, and for the same conditions the value calculated with (1) is 109 mA. This could be explained with the increase of the equivalent resistance of the coil due to the heating in the coil and the utilization of a high switching frequency. Moreover, this type of linear actuator could also be used for low-cost variable aperture electric valves in which an incremental variation of position is required.
ro
of
(a)
re
-p
(b)
(c)
lP
Fig. 14- Experimental results of the position control considering a fixed load force of 0.09 N with (a) the variation of the reference position; (b)
(a)
Jo
ur na
the variation of the duty cycle of the PWM voltage; (c) the variation of the average current in the coil.
(b)
ro
of
(c)
(d)
Fig. 15- Experimental results of the position control considering a requested position of 19 mm with (a) the variation of the load force; (b) the
-p
variation of the duty cycle of the PWM voltage; (c) measured average current in the coil; (d) the variation of the estimated and requested position when the load is changed.
re
5. Conclusions and Future Work
In this paper, a study on a tubular linear actuator with a hybrid core, composed by a PM and a ferromagnetic part, is presented.
lP
By detecting the position through the variation of the inductance caused by the change of the position of the core, a control strategy is proposed where the duty cycle of the PWM voltage is controlled in order to generate the necessary average current in the coil and force in the core. Using a prototype built with a coil connected to a converter fed by a DC source and controlled by a PWM signal, the control strategy was successfully tested for two cases: the first, where the position is varied and the load force is kept
ur na
constant, and the second where the load force is varied, and the position is kept constant. The numerical and experimental results demonstrate that this control strategy can effectively be applied to this type of linear actuators and that with the hybrid core a higher force density is obtained. The simple construction of this type of linear actuator makes it an inexpensive alternative for actuators used in biomedical applications, such as prosthetic limbs. Furthermore, this type of actuator can be used for the fabrication of servo electric valves with intermediate positions. The developed solution is scalable and can be miniaturized for very small dimensions.
Jo
These actuators could be used in modular systems where they are combined to increase the total force generated or have a greater range of positions. Regarding future work, the control strategy will be improved in order to be more precise and to have a faster response to load force or requested position variations.
Author credit
José Alberto: Validation; Investigation; Writing- Original draft preparation; Visualization; Fernando J T E Ferreira: Supervision; Conceptualization, Methodology; Writing - Review & Editing ; Aníbal T de Almeida: Resources; Funding acquisition; Supervision; Writing - Review & Editing Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
of
This work was performed in the framework of the project “MATIS-Materiais e Tecnologias Industriais Sustentáveis” (ref.: CENTRO-01-0145-FEDER-000014), co-financed by the European Regional Development Fund (FEDER), through the “Programa
ro
Operacional Regional do Centro” (CENTRO2020).
References
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
-p
re
[5]
lP
[4]
ur na
[3]
I. Boldea, Linear electromagnetic actuators and their control: A review, EPE J. 14 (2004) 43–50. D.B. Hiemstra, G. Parmar, S. Awtar, Performance tradeoffs posed by moving magnet actuators in flexure-based nanopositioning, IEEE/ASME Trans. Mechatronics. 19 (2014) 201–212. J. Zheng, J. Chen, Y. Huang, P. Zheng, B. Du, The simulation design of parameters optimization on tubular linear motor with optimal output force, in: 2016 IEEE Adv. Inf. Manag. Commun. Electron. Autom. Control Conf. (IMCEC), IEEE, 2016: pp. 770–774. L.-Y. Hsu, G.-J. Yan, M.-C. Tsai, Novel flexible printed circuit windings for slotless linear motor design, in: 2010 Int. Conf. Electr. Mach. Syst. (ICEMS), IEEE, 2010: pp. 1578–1582. J. Wang, D. Howe, Design optimization of radially magnetized, iron-cored, tubular permanent-magnet machines and drive systems, IEEE Trans. Magn. 40 (2004) 3262–3277. G. Baoming, A.T. de Almeida, F.J.T.E. Ferreira, Design of transverse flux linear switched reluctance motor, IEEE Trans. Magn. 45 (2009) 113–119. J.-F. Llibre, N. Martinez, P. Leprince, B. Nogarede, Analysis and modeling of linear-switched reluctance for medical application, in: Actuators, Multidisciplinary Digital Publishing Institute, 2013: pp. 27–44. M.I. Awad, A. Abouhossein, B. Chong, A.A. Dehghani-Sanij, R. Richardson, D. Moser, S. Zahedi, Investigation into Energy Efficiency and Regeneration in an Electric Prosthetic Knee, in: Springer, Cham, 2017: pp. 613–618. A. Zoss, H. Kazerooni, Design of an electrically actuated lower extremity exoskeleton, Adv. Robot. 20 (2006) 967–988. P. Wattanasiri, P. Tangpornprasert, C. Virulsri, Design of Multi-Grip Patterns Prosthetic Hand with Single Actuator, IEEE Trans. Neural Syst. Rehabil. Eng. (2018) 1–1. J. Alberto, F.J.T.E. Ferreira, A.T. De Almeida, Study and Design of a Small-Diameter Tubular Linear Motor for Biomedical Applications, in: 2018 XIII Int. Conf. Electr. Mach., IEEE, 2018: pp. 1691–1697. X. Wang, C. Li, F. Lou, Geometry Optimize of Printed Circuit Board Stator Winding in Coreless Axial Field Permanent Magnet Motor, in: 2016 IEEE Veh. Power Propuls. Conf., IEEE, 2016: pp. 1–6. L. Li, B. Post, V. Kunc, A.M. Elliott, M.P. Paranthaman, Additive manufacturing of near-net-shape bonded magnets: Prospects and challenges, Scr. Mater. 135 (2017) 100–104. B. Cox, M. Saari, B. Xia, E. Richer, P.S. Krueger, A.L. Cohen, Fiber Encapsulation Additive Manufacturing: Technology and Applications Update, 3D Print. Addit. Manuf. 4 (2017) 116–119. Y. Yan, J. Moss, K.D.T. Ngo, Y. Mei, G.-Q. Lu, Additive manufacturing of toroid inductor for power electronics applications, IEEE Trans. Ind. Appl. 53 (2017) 5709–5714. F. Lorenz, J. Rudolph, R. Wemer, Design of 3D Printed High Performance Windings for Switched Reluctance Machines, in: 2018 XIII Int. Conf. Electr. Mach., 2018. J. Garcia-Amorós, Garcia-Amorós, Jordi, Linear Hybrid Reluctance Motor with High Density Force, Energies. 11 (2018) 2805. P. Andrada, B. Blanque, E. Martinez, M. Torrent, J. Garcia-Amoros, J.I. Perat, New linear hybrid reluctance actuator, in: 2014 Int. Conf. Electr. Mach., IEEE, 2014: pp. 585–590. Y. Hasegawa, K. Nakamura, O. Ichinokura, Basic consideration of switched reluctance motor with auxiliary windings and permanent magnets, in: 2012 XXth Int. Conf. Electr. Mach., IEEE, 2012: pp. 92–97. J. Han, H. Wang, G. Jiao, L. Cui, Y. Wang, Research on Active Disturbance Rejection Control Technology of Electromechanical Actuators, Electronics. 7 (2018) 174. M. Zhou, D. Mao, M. Zhang, L. Guo, M. Gong, A Hybrid Control with PID–Improved Sliding Mode for Flat-Top of Missile Electromechanical Actuator Systems, Sensors. 18 (2018) 4449. M.D.S. Hasan, A. El Hafni, R. Kennel, Position control of an electromagnetic actuator using model predictive control, in: Proc. - 2017 IEEE Int. Symp. Predict. Control Electr. Drives Power Electron. Preced. 2017, Institute of Electrical and Electronics Engineers Inc., 2017: pp. 37–41.
Jo
[1] [2]
Authors’ Biographies José Alberto, born in Coimbra, Portugal. Obtained his Master Degree (MSc) in Electrical Engineering, Energy branch at University of Coimbra. He pursued his PhD degree in Electrical Engineering at the University of Bologna, Italy, during which time he was a visiting scholar at CIRCE - Research Center for Energy Resources and Consumption in Zaragoza, Spain. He is currently a Post-Doctoral Fellow at the Institute of Systems and Robotics at the University of Coimbra. His research interests include Wireless Power Transfer, Resonator Arrays, Inductive Charging, Linear Motors and Actuators.
of
Fernando J. T. E. Ferreira received the Ph.D. in electrical engineering in 2009, from the University of Coimbra, Coimbra, Portugal. He is currently a Professor in the Department of Electrical and Computer Engineering, University of Coimbra. He has been a Researcher in the Institute of Systems and Robotics, University of Coimbra, and has participated in several European projects dealing with electric motor technologies. He is the author/coauthor of more than 150 papers published in international journals and conference records. He received the Best Paper Award at the 2001 IEEE/IAS ICPS, and the Best Poster Presentation Award at the 2010 ICEM.
Jo
ur na
lP
re
-p
ro
Aníbal T. de Almeida received the Ph.D. degree in electrical engineering from Imperial College, University of London, London, U.K. He is currently a Professor with the Department of Electrical and Computer Engineering, University of Coimbra, Coimbra, Portugal. He is the Director of the Institute of Systems and Robotic. He has coauthored six books on energy industrial automation and energy efficiency and more than 300 papers published in international journals and conference proceedings and presented at meetings. He has coordinated six European projects. He is a Distinguished Lecturer of the Industrial Applications Society of IEEE.
PII:
S0924-4247(19)32141-7
DOI:
https://doi.org/10.1016/j.sna.2020.111919
Reference:
SNA 111919
To appear in:
Sensors and Actuators: A. Physical
Received Date:
28 November 2019
Revised Date:
30 January 2020
Accepted Date:
25 February 2020
Please cite this article as: Alberto J, Ferreira FJTE, de Almeida AT, Study of a Linear Actuator with a Hybrid Core using Sensorless Position Control, Sensors and Actuators: A. Physical (2020), doi: https://doi.org/10.1016/j.sna.2020.111919
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.
Study of a Linear Actuator with a Hybrid Core using Sensorless Position Control José Alberto, Fernando J. T. E. Ferreira, and Aníbal T. de Almeida 1
Institute of Systems and Robotics, Department of Electrical and Computer Engineering, University of Coimbra, Polo II, 3030-
290 Coimbra, Portugal
Jo
ur na
lP
re
-p
ro
of
Graphicala abstract
of ro -p re lP ur na Jo Highlights •
Study on a tubular linear actuator with a hybrid core, composed by a permanent magnet and a ferromagnetic to increase force density.
•
Sensorless position detection using the variation of the coil current ripple with the variation of the core position.
•
Actuator prototype composed by a coil connected to a converter fed by a DC source and controlled by a PWM signal.
•
Positioning control strategy experimentally tested for constant position and constant load force.
Abstract— In this paper, a study of a tubular linear actuator with a hybrid core is presented. Through a finite-element analysis software and force measurements it is shown that by using a hybrid core combining a permanent magnet and a ferromagnetic material, higher force density can be achieved compared to the utilization of a ferromagnetic core alone. Also, by keeping the ferromagnetic part, the sensorless detection of the core position is possible. A simple position control strategy is proposed, using the inductance variation to indirectly detect the position of the core, in which the duty cycle of the PWM voltage is changed to compensate variations of position or load force. In order to test the novel hybrid core and
of
the proposed control strategy, a prototype was built. The experimental results clearly demonstrate the advantages and
ro
applicability of the hybrid core in linear actuators.
Introduction
re
1.
-p
Keywords - Linear actuators; electromagnetic analysis; finite element analysis; sensorless control; linear motors.
In the past, several studies have been made on different types of linear motors and actuators [1–6]. Although they can be used in numerous applications, one of the most interesting and high potential applications is on biomedical actuators [7]. More
lP
specifically, the utilization of motors for prosthetics limbs or exoskeletons has been under research lately [8–10]. In [11], a tubular linear motor with a ferromagnetic core designed to replace a human tendon or muscle is proposed. This type of linear motor can be used in a modular configuration (e.g. multiple coils and/or multiple cores), it has a simple structure and it is easy to control.
ur na
Furthermore, other manufacturing methods for motors and actuators, such as PCB windings [4,12] or additive manufacturing (3D printing) [13–16], allow a fast and economic design and construction of the device, as well as the adjustment of its characteristics to its final application. In this way, these methods can be appropriate for biomedical applications in which the device needs to be scaled according to the patient's requirements.
In [11] a study is made regarding the variation of the maximum force generated with the variation of the geometrical and electrical parameters of the tubular linear motor with a ferromagnetic core. However, as it is known, linear motors using permanent
Jo
magnets have higher force density values regarding those using a ferromagnetic core. Consequently, the utilization of ferromagnetic materials combined with permanent magnets to increase force density has been used in several types of motors and actuators [17–19]. On the other hand, by using a permanent magnet (PM) alone, it is not possible to detect the position of the core through the variation of inductance as proposed in [11]. In order to overcome this drawback, a hybrid core combining a PM and a ferromagnetic material would allow the linear motor to achieve higher force density without losing its ability to detect the position through the variation of the inductance of the coil, avoiding the use of position sensors. In this paper, a tubular linear actuator with a hybrid core is proposed (Fig. 1), as well as a simple positioning control strategy. The actuator is simulated using the finite-element analysis software Flux 2D in order to assess the force generated. Then, using the variation of the inductance and consequently the variation of the current ripple to indirectly detect the position of the core, a position control strategy is proposed. Finally, an experimental setup was built so that the advantages of using a hybrid core and the
proposed control strategy could be tested.
2.
of
Fig. 1- Structure of the proposed actuator with a hybrid core.
Linear Actuator with Hybrid Core
ro
2.1. Finite Element Simulations
The actuator was simulated using the 2D finite-element analysis/method (FEA/FEM) software Flux 2D, to compare the force
-p
generated by the linear actuator with a ferromagnetic core and with a hybrid core. The simulation was of the type Magnetostatic
re
and axisymmetric. The parameters used for the simulations were those from the coil used in the experiments (Table I).
Table I
Value 5.5 mm 7.5 mm (2 x 18) mm2 18 mm 3500
ur na
Parameter Inner radius Outer radius Section Length Number of turns
lP
Coil parameters used for the simulations.
Regarding the dimensions of the core, the dimensions of the two core types are those used in the experimental setup and are represented in Fig. 2:
Hybrid core: 6-mm diameter; 20-mm length the PM part and 18-mm length the ferromagnetic part;
Ferromagnetic core: 6-mm diameter; 38-mm length.
Jo
In Fig. 2, screenshots of the simulations made with FEA/FEM software Flux 2D are shown: the ferromagnetic part is marked with the black colour, the PM part with the red colour, and the coil with pink colour. The white line that divides the blue (air medium where the magnetic field is calculated) and the grey area represents the symmetry axis.
(a)
(b)
Fig. 2- Simulations with FEA/FEM software Flux 2D considering: (a) a ferromagnetic core; (b) a hybrid core. The ferromagnetic part is marked
of
with the color black and the PM part with the color red; the pink region represents the coil. As it is an axisymmetric simulation, the symmetry
lP
re
-p
ro
axis is the white line dividing the blue and the grey areas (the blue area represents the area where the magnetic field was calculated).
(a)
(b)
Fig. 3 - Simulations with FEA/FEM software Flux 2D of the cases considered in this study: (a) magnetic fields produced by the coil (blue
ur na
arrows) and by the PM (yellow arrows) have opposite directions; (b) magnetic fields have the same direction.
The proposed sensorless method relies on the variation of the inductance of the coil and consequently on the variation of the current ripple with the position of the core, as in [11]. In order to identify the case where a higher variation of the current ripple occurs, two situations were simulated for the hybrid core: (i) the magnetic fields generated by the coil and PM are in the same direction (Fig. 3b); (ii) the magnetic fields generated by the coil and PM are in opposite directions (Fig. 3a). These magnetic field simulations were made with FEA/FEM software Flux 2D, and in Fig. 3, the magnetic fields generated by the coil and the PM are
Jo
represented by blue and yellow arrows, respectively. Using the Flux 2D Transient simulation type, with a DC-DC buck converter like the one described later in this paper, fed with a 30 V DC source, with a switching frequency of 1 kHz, the variation on the current ripple for different positions of the core was simulated for both cases. The core position is given by the distance between the geometric centers of the coil and of the core, meaning that the core position is zero when the core is aligned with the coil. This was done considering the characteristics of the materials used in the tested prototype (permanent magnet: Eclipse Magnetics N808 Neodymium Magnet; ferromagnetic: Fair-Rite 78 ROD). The results are shown in Fig. 4
Fig. 4- Simulations with FEA/FEM software Flux 2D of the variation of the current ripple of the coil (p.u.), considering the cases represented in Fig. 2, when the magnetic fields generated by the coil and the PM have the same direction or opposite directions.
Therefore, as seen in Fig. 4, the variation of the current ripple is higher when the coil magnetic field is opposite to the one generated by the PM. This can be explained by the fact that in this way the ferromagnetic core is further away from the saturation
of
point. Afterwards, using the Flux 2D Magnetostatic simulation type, a comparison between the force generated using the two types of core (ferromagnetic and hybrid) was made, considering a constant current of 125 mA or -125 mA feeding the coil. The values of
lP
re
-p
ro
the force were determined for different positions of the core. The results are shown in Fig. 5.
Fig. 5- Force generated by the linear actuator for different positions of the core and for the two different core types.
As seen in Fig. 5, the maximum force generated with the hybrid core (0.63 N for the opposite direction and 0.66 N for the same
ur na
direction) is 3.5 to 3.7 larger than the one generated with the ferromagnetic core (0.18 N) for the same core section and length, thus showing the advantage of using a hybrid core. As the maximum force is approximately the same for the two hybrid core cases, it was decided to use the magnetic field generated by the coil in opposition to that of the PM, due to the higher variation of the current ripple, leading to a more accurate position detection. Then, the current was varied from 65 mA to 125 mA and the force was calculated for different core positions. The results are
Jo
shown in Fig. 6.
Fig. 6- Force generated by the linear actuator with the hybrid core for different values of the current.
As described in Fig. 6, it can be seen that by adjusting the current it is possible: (i) to keep the same position and change the generated force or (ii) change the generated force and keep the same position. The experimental results for these two operating modes will be presented later in the paper. 3. Sensorless positioning control
The circuit of the linear actuator consists of a coil connected to a DC-DC buck converter controlled by a PWM signal and fed
ro
of
by a DC voltage supply as shown in Fig. 7.
-p
Fig. 7- Scheme of the DC-DC buck converter used for the experimental setup.
It is known that the force applied on the core will be proportional to the square of the current flowing through the coil [11].
lP
value of the duty cycle, 𝐷𝑐 , of the PWM signal:
re
Moreover, in steady state (t >> coil) and neglecting the variation of inductance over time, the average current, 𝐼𝑎𝑣𝑔 , depends on the
(1)
The change of the position of the ferromagnetic part of the core will cause a variation of the inductance of the coil. When the
ur na
coil is fed with a PWM voltage, the current ripple Δ𝐼 will depend on the inductance of the coil, as referred in [11]:
(2)
Jo
where 𝑉𝑑𝑐 is the value of the DC voltage that is feeding the converter, 𝐷𝑐 is the duty cycle, R is the intrinsic resistance of the coil, T is the period of the PWM signal, L represents the inductance of the coil and d is the position of the core. So, for a fixed value of DC voltage, duty cycle and period, a higher value of inductance will cause a lower ripple while a lower inductance will result in a higher ripple. As each position of the core corresponds to a certain value of inductance, by measuring the current ripple and duty cycle, the real position of the core can be measured, according to (2). This can be done using a lookup-table experimentally created in which each pair of values of duty cycle and current ripple correspond to a certain position of the core. Then, using the difference between the reference position and the measured position, the duty cycle and consequently the average current and the force applied to the core can be increased or decreased, until the reference position is achieved. The proposed control strategy is represented in Fig. 8.
of ro
Fig. 8 – Control strategy used for core positioning.
-p
4. Experimental Results 4.1. Description of the Experimental Setup
re
As shown in Fig. 9a, an experimental setup was built to test the linear motor and the respective positioning control strategy. A commercial coil was used (MA 22 24 DC H), which was connected to a DC-DC converter (Fairchild FNA40860). The converter
lP
is controlled with the PWM signals generated from the PWM signal generator (NI-9401). The current and its ripple are measured with a Current Probe (Tektronix A622 AC/DC) connected to a data acquisition module (NI-9215). Both NI-9401 and NI-9215 were connected to a real-time control system (NI cRIO-9074) and the control strategy was implemented using the software LabView. The input DC and control supply voltages are generated using a triple power supply (Aim-TTi EX354RT). In Fig. 9b,
Jo
ur na
the ruler used for core position measurements is shown.
(a)
Fig. 9- Details of (a) the setup used for experiments and (b) the ruler used for position measurements.
(b)
As a core, five Neodymium permanent magnets (Eclipse Magnetics N808) with 6 mm diameter and 4 mm length each one together with a ferromagnetic (Fair-Rite 78 ROD) with 6 mm diameter and 18 mm length were used (shown in Fig. 10a). In order to measure the position of the core using the ruler shown in Fig. 9b, a small metal rod with a position mark was added to the core, as shown in Fig. 10b.
of
(a) (b) Fig. 10- (a) Hybrid core used for the experimental setup and (b) core with a metal rod with position mark for position measurements.
Using the experimental setup described in Fig. 8a, two cases were tested: (i) the reference position is changed, and the load force is kept constant; (ii) the reference position is kept constant and the requested load force is changed. In this way, two possible
ro
situations regarding the utilization of this actuator for biomedical applications as prosthetic limbs are tested: the first could represent
4.2. Experimental Results
re
4.2.1. Comparison between Hybrid and Ferromagnetic Core
-p
a moving empty hand and the second could be an example of a hand holding a heavier object.
In order to experimentally compare the maximum force that could be generated using the same linear actuator with ferromagnetic
lP
or hybrid cores, a Sauter FK 10N Digital Force Gauge was used. Then, the force generated with the hybrid core (Fig. 9a) and with a Fair-Rite 78 ROD with 6-mm diameter and 38-mm length, for different values of the current was measured and recorded. The
Jo
ur na
results are shown in Fig. 11.
Fig. 11-Comparison of the maximum force generated with hybrid and ferromagnetic cores, for different values of the current in the actuator.
Analyzing the results described in Fig. 11, it can be concluded that, with the same geometric dimensions, the force generated with a hybrid core goes up to 3.6 times the force generated with a ferromagnetic core, thus confirming the advantage of using a hybrid core, previously demonstrated with the finite-element analysis.
4.2.2. Positioning Control
In order to test the proposed control method described in Fig. 8, a fixed DC voltage of 30 V, a switching frequency of 1 kHz and a value of Δ𝐷𝑐 = 0.006 were considered. In Fig. 12, an example of the PWM voltage and current in the coil for two different
(a)
(b)
of
positions of the core and for a duty cycle of 0.5 is shown.
ro
Figure 12 - Example of the measured PWM voltage and current in the coils, considering the DC voltage equal of 30 V and a duty cycle of 0.5 for two different positions of the core: (a) ferromagnetic part outside the coil; (b) the ferromagnetic part inside the coil.
-p
The position detection was tested by measuring the distance from the center of the coil using the ruler shown in Fig. 8b. As it
ur na
lP
re
can be seen in Fig. 13, the position can be detected with good accuracy compared to the measured position.
Fig. 13- Comparison between the measured position and the estimated position for different values of the duty cycle.
Then, the duty cycle of the PWM signal was varied in order to compensate variations of the reference position (Fig. 14) and load force (Fig. 15).
As it can be seen in Figs. 14 and 15, the control method proposed can, through the incremental or decremental variation of the
Jo
duty cycle, compensate for the variations of the requested load force or of the reference position, thus proving its applicability for biomedical applications. Although the response of the control method is slower than other control methods typically used in electromechanical actuators, such as those described in [20–22], it is simpler to implement and it is fast enough for biomedical applications, such as prosthetic limbs. The measured value of the average current is slightly lower than that determined with (1). For example, in Fig. 14, at 20 seconds the duty cycle is 0.7 and the average current is 104 mA, and for the same conditions the value calculated with (1) is 109 mA. This could be explained with the increase of the equivalent resistance of the coil due to the heating in the coil and the utilization of a high switching frequency. Moreover, this type of linear actuator could also be used for low-cost variable aperture electric valves in which an incremental variation of position is required.
ro
of
(a)
re
-p
(b)
(c)
lP
Fig. 14- Experimental results of the position control considering a fixed load force of 0.09 N with (a) the variation of the reference position; (b)
(a)
Jo
ur na
the variation of the duty cycle of the PWM voltage; (c) the variation of the average current in the coil.
(b)
ro
of
(c)
(d)
Fig. 15- Experimental results of the position control considering a requested position of 19 mm with (a) the variation of the load force; (b) the
-p
variation of the duty cycle of the PWM voltage; (c) measured average current in the coil; (d) the variation of the estimated and requested position when the load is changed.
re
5. Conclusions and Future Work
In this paper, a study on a tubular linear actuator with a hybrid core, composed by a PM and a ferromagnetic part, is presented.
lP
By detecting the position through the variation of the inductance caused by the change of the position of the core, a control strategy is proposed where the duty cycle of the PWM voltage is controlled in order to generate the necessary average current in the coil and force in the core. Using a prototype built with a coil connected to a converter fed by a DC source and controlled by a PWM signal, the control strategy was successfully tested for two cases: the first, where the position is varied and the load force is kept
ur na
constant, and the second where the load force is varied, and the position is kept constant. The numerical and experimental results demonstrate that this control strategy can effectively be applied to this type of linear actuators and that with the hybrid core a higher force density is obtained. The simple construction of this type of linear actuator makes it an inexpensive alternative for actuators used in biomedical applications, such as prosthetic limbs. Furthermore, this type of actuator can be used for the fabrication of servo electric valves with intermediate positions. The developed solution is scalable and can be miniaturized for very small dimensions.
Jo
These actuators could be used in modular systems where they are combined to increase the total force generated or have a greater range of positions. Regarding future work, the control strategy will be improved in order to be more precise and to have a faster response to load force or requested position variations.
Author credit
José Alberto: Validation; Investigation; Writing- Original draft preparation; Visualization; Fernando J T E Ferreira: Supervision; Conceptualization, Methodology; Writing - Review & Editing ; Aníbal T de Almeida: Resources; Funding acquisition; Supervision; Writing - Review & Editing Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
of
This work was performed in the framework of the project “MATIS-Materiais e Tecnologias Industriais Sustentáveis” (ref.: CENTRO-01-0145-FEDER-000014), co-financed by the European Regional Development Fund (FEDER), through the “Programa
ro
Operacional Regional do Centro” (CENTRO2020).
References
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
-p
re
[5]
lP
[4]
ur na
[3]
I. Boldea, Linear electromagnetic actuators and their control: A review, EPE J. 14 (2004) 43–50. D.B. Hiemstra, G. Parmar, S. Awtar, Performance tradeoffs posed by moving magnet actuators in flexure-based nanopositioning, IEEE/ASME Trans. Mechatronics. 19 (2014) 201–212. J. Zheng, J. Chen, Y. Huang, P. Zheng, B. Du, The simulation design of parameters optimization on tubular linear motor with optimal output force, in: 2016 IEEE Adv. Inf. Manag. Commun. Electron. Autom. Control Conf. (IMCEC), IEEE, 2016: pp. 770–774. L.-Y. Hsu, G.-J. Yan, M.-C. Tsai, Novel flexible printed circuit windings for slotless linear motor design, in: 2010 Int. Conf. Electr. Mach. Syst. (ICEMS), IEEE, 2010: pp. 1578–1582. J. Wang, D. Howe, Design optimization of radially magnetized, iron-cored, tubular permanent-magnet machines and drive systems, IEEE Trans. Magn. 40 (2004) 3262–3277. G. Baoming, A.T. de Almeida, F.J.T.E. Ferreira, Design of transverse flux linear switched reluctance motor, IEEE Trans. Magn. 45 (2009) 113–119. J.-F. Llibre, N. Martinez, P. Leprince, B. Nogarede, Analysis and modeling of linear-switched reluctance for medical application, in: Actuators, Multidisciplinary Digital Publishing Institute, 2013: pp. 27–44. M.I. Awad, A. Abouhossein, B. Chong, A.A. Dehghani-Sanij, R. Richardson, D. Moser, S. Zahedi, Investigation into Energy Efficiency and Regeneration in an Electric Prosthetic Knee, in: Springer, Cham, 2017: pp. 613–618. A. Zoss, H. Kazerooni, Design of an electrically actuated lower extremity exoskeleton, Adv. Robot. 20 (2006) 967–988. P. Wattanasiri, P. Tangpornprasert, C. Virulsri, Design of Multi-Grip Patterns Prosthetic Hand with Single Actuator, IEEE Trans. Neural Syst. Rehabil. Eng. (2018) 1–1. J. Alberto, F.J.T.E. Ferreira, A.T. De Almeida, Study and Design of a Small-Diameter Tubular Linear Motor for Biomedical Applications, in: 2018 XIII Int. Conf. Electr. Mach., IEEE, 2018: pp. 1691–1697. X. Wang, C. Li, F. Lou, Geometry Optimize of Printed Circuit Board Stator Winding in Coreless Axial Field Permanent Magnet Motor, in: 2016 IEEE Veh. Power Propuls. Conf., IEEE, 2016: pp. 1–6. L. Li, B. Post, V. Kunc, A.M. Elliott, M.P. Paranthaman, Additive manufacturing of near-net-shape bonded magnets: Prospects and challenges, Scr. Mater. 135 (2017) 100–104. B. Cox, M. Saari, B. Xia, E. Richer, P.S. Krueger, A.L. Cohen, Fiber Encapsulation Additive Manufacturing: Technology and Applications Update, 3D Print. Addit. Manuf. 4 (2017) 116–119. Y. Yan, J. Moss, K.D.T. Ngo, Y. Mei, G.-Q. Lu, Additive manufacturing of toroid inductor for power electronics applications, IEEE Trans. Ind. Appl. 53 (2017) 5709–5714. F. Lorenz, J. Rudolph, R. Wemer, Design of 3D Printed High Performance Windings for Switched Reluctance Machines, in: 2018 XIII Int. Conf. Electr. Mach., 2018. J. Garcia-Amorós, Garcia-Amorós, Jordi, Linear Hybrid Reluctance Motor with High Density Force, Energies. 11 (2018) 2805. P. Andrada, B. Blanque, E. Martinez, M. Torrent, J. Garcia-Amoros, J.I. Perat, New linear hybrid reluctance actuator, in: 2014 Int. Conf. Electr. Mach., IEEE, 2014: pp. 585–590. Y. Hasegawa, K. Nakamura, O. Ichinokura, Basic consideration of switched reluctance motor with auxiliary windings and permanent magnets, in: 2012 XXth Int. Conf. Electr. Mach., IEEE, 2012: pp. 92–97. J. Han, H. Wang, G. Jiao, L. Cui, Y. Wang, Research on Active Disturbance Rejection Control Technology of Electromechanical Actuators, Electronics. 7 (2018) 174. M. Zhou, D. Mao, M. Zhang, L. Guo, M. Gong, A Hybrid Control with PID–Improved Sliding Mode for Flat-Top of Missile Electromechanical Actuator Systems, Sensors. 18 (2018) 4449. M.D.S. Hasan, A. El Hafni, R. Kennel, Position control of an electromagnetic actuator using model predictive control, in: Proc. - 2017 IEEE Int. Symp. Predict. Control Electr. Drives Power Electron. Preced. 2017, Institute of Electrical and Electronics Engineers Inc., 2017: pp. 37–41.
Jo
[1] [2]
Authors’ Biographies José Alberto, born in Coimbra, Portugal. Obtained his Master Degree (MSc) in Electrical Engineering, Energy branch at University of Coimbra. He pursued his PhD degree in Electrical Engineering at the University of Bologna, Italy, during which time he was a visiting scholar at CIRCE - Research Center for Energy Resources and Consumption in Zaragoza, Spain. He is currently a Post-Doctoral Fellow at the Institute of Systems and Robotics at the University of Coimbra. His research interests include Wireless Power Transfer, Resonator Arrays, Inductive Charging, Linear Motors and Actuators.
of
Fernando J. T. E. Ferreira received the Ph.D. in electrical engineering in 2009, from the University of Coimbra, Coimbra, Portugal. He is currently a Professor in the Department of Electrical and Computer Engineering, University of Coimbra. He has been a Researcher in the Institute of Systems and Robotics, University of Coimbra, and has participated in several European projects dealing with electric motor technologies. He is the author/coauthor of more than 150 papers published in international journals and conference records. He received the Best Paper Award at the 2001 IEEE/IAS ICPS, and the Best Poster Presentation Award at the 2010 ICEM.
Jo
ur na
lP
re
-p
ro
Aníbal T. de Almeida received the Ph.D. degree in electrical engineering from Imperial College, University of London, London, U.K. He is currently a Professor with the Department of Electrical and Computer Engineering, University of Coimbra, Coimbra, Portugal. He is the Director of the Institute of Systems and Robotic. He has coauthored six books on energy industrial automation and energy efficiency and more than 300 papers published in international journals and conference proceedings and presented at meetings. He has coordinated six European projects. He is a Distinguished Lecturer of the Industrial Applications Society of IEEE.