http://informahealthcare.com/jmt ISSN: 0309-1902 (print), 1464-522X (electronic) J Med Eng Technol, 2014; 38(2): 90–99 ! 2014 Informa UK Ltd. DOI: 10.3109/03091902.2013.872204
INNOVATION
Feedback control of TET system with variable coupling coefficients for a novel artificial anal sphincter 820 Institute, Department of Instrument Science and Engineering, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, PR China Abstract
Keywords
For treating severe faecal incontinence, the authors developed an intelligent artificial anal sphincter system (AASS) equipped with a feedback sensor that utilized a transcutaneous energy transfer system (TETS). To deliver the correct amount of power (i.e. to match the load demand under variable coupling conditions caused by changes in positioning between the coils due to fitting and changes in posture), a regulating method to stabilize output voltage with a closed loop variable-frequency controller was developed in this paper. The method via which the voltage gain characteristics of a voltage-fed series-tuned TETS were derived is also described. The theoretical analysis was verified by the results of the experiment. A numerical analysis method was used as a control rule with respect to the relationship between operating frequency and output voltage. To validate the feedback control rules, a prototype of the TET charging system was constructed, and its performance was validated with the coupling variation between 0.12–0.42. The results show that the output voltage of the secondary side can be maintained at a constant 7 V across the whole coupling coefficient range, with a switching frequency regulation range of 271.4–320.5 kHz, and the proposed controller has reached a maximal end-to-end power efficiency of 67.5% at 1 W.
Artificial anal sphincter, closed-loop control, faecal incontinence, variable coupling coefficient, transcutaneous energy transfer
1. Introduction Faecal incontinence (FI) is a common clinical symptom that seriously affects patients’ quality-of-life (QoL) [1]. Medical science has devoted much attention to anorectal research and has sought solutions for FI. In recent years, an Artificial Bowel Sphincter (ABS) (American Medical Systems, Minneapolis, MN)—which comprises three silastic elements (an inflatable cuff, a pressure-regulating balloon that also functions as a fluid reservoir, and a control pump)—was developed as an alternative for patients with end-stage FI and failure of conventional treatments or permanent colostomy [2]. Despite its simplicity, the ABS still has some limitations. First, patients can’t perceive when to defecate, so they must be trained to evacuate at regular, scheduled times; second, to open the occlusive cuff, patients must repeatedly squeeze and release the bulb of the control pump (placed under the scrotum or the labia major of the vulva), which may eventually damage patients’ skin and possibly become infected; third, because the cuff refills automatically, the time allotted for defecation is determined by the total duration of the refilling and opening of the cuff. Some patients do not have enough time to defecate and develop defecation difficulties after implantation due to the rapid closure of the *Corresponding author. Email: [email protected]
History Received 6 October 2013 Revised 18 November 2013 Accepted 26 November 2013
cuff; lastly, according to some studies, all patients suffer from pressure atrophy to a certain degree. Under such conditions, cuff efficiency diminishes, which may lead to the recurrence of faecal incontinence [3–5]. To overcome these drawbacks, a novel, highly integrated and intelligent artificial anal sphincter system (AASS) is presented. The structure of this system, with sensor feedback, is shown in detail. The key element of the AASS—a voltage-fed series-tuned transcutaneous energy transfer system (TETS)—is then discussed. It enables the transfer of power across the skin without direct electrical connectivity. The secondary coil of the TETS is implanted under the skin, and the primary coil is placed on top of the secondary coil, outside the body. The distance between the transformer windings would be approximately equal to the thickness of the patient’s skin, fatty tissue, and muscle, nominally between 1–2 cm [6]. This spacing cannot be assumed constant; the alignment of the cores and the distance between them would certainly vary during the operation. Variation in distance and misalignment of the coil pair can affect the coupling coefficient k, and change the operating state of the inductive link. However, the inductive power link was expected of properly power, regardless of the variable k, was transfer to the secondary circuit in order to reduce power loss and the possibility of tissue damage from overheating. Previous studies reported that there were two main methods of regulating power in TETS based on
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L. Ke*, G. Yan, S. Yan, Z. Wang, and Z. Liu
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DOI: 10.3109/03091902.2013.872204
magnitude and frequency control strategies. The power delivered to the load may be modulated by the magnitude control that varies the input voltage to the primary power inverter [7]. However, due to the mismatch of the resonant frequency of the secondary resonant circuit and the operating frequency of the external power inverter, a larger input voltage was required for a given power transfer, resulting in increased electromagnetic interference (EMI) and reduced power efficiency overall. In the case of frequency control, the Class-E amplifier may be returned to a better or optimum operating state by varying the operating frequency of the primary power converter to vary the power flow when k changes [8]. However, the frequency adjustment ranges have not yet been determined theoretically. Si et al. [9] developed a variable resonant frequency method to regulate the power flow by changing the effective capacitance of the primary circuit by switching on and off capacitors that were parallel to the primary MOSFETs. However, this method requires that the system has more switching devices and resonant capacitors.
Figure 1. Diagram of the AASS. Figure 2. The novel AASS prototype. (a) IAAS; (b) External transmitter of the TETS and control unit; (c) New sphincter prosthesis cuff with sensor. Inflated ¼ Continence; (d) Deflated ¼ Defecation.
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In this paper, a new closed-loop variable frequency control method is studied in detail, with the aim of keeping the output power constant when k changes. Analytical expression is derived as functions of the voltage gain characteristic GV, the operating frequency f of the driving signal, and the coupling coefficient k. Through numerical analysis, a method was derived as a control rule with respect to the relationship between operating frequency and output voltage. All calculations and control processes were performed with the digital signal controller dsPIC33FJ128 combined with a programmable waveform generator that offers the advantage of reduced switching components and capacitors. Experiments were conducted to validate the theoretical design when k is changed from 0.42 to 0.12 and back to 0.42.
2. The novel artificial anal sphincter system The system block diagram is shown in Figure 1. The new version of an AASS with biosensor feedback powered by TETS is an integrative, modular, remote-controlled sphincter prosthesis that mainly comprises three modules including an intelligent artificial anal sphincter (IAAS, Figure 2A), a TETS and an external controller (Figure 2B). The IAAS is composed of a driver unit, sphincter prosthesis, and an energy-receiving coil. The driver unit integrates the micropump, rechargeable battery, microcontroller circuit, and fluid reservoir in a casing that presently measures 5.5 4.5 2.5 cm (L W H). The mechanical medical micropump of the IAAS can realize bidirectional flow with a maximum flow rate of 8.5 mL min1 and can build backpressure up to 170 kPa. The design of the prosthesis reduces occlusion pressure and allows for low inflation volumes (910.5 mL); operating pressures between 4.05– 7.16 kPa indicate that the risk of ischaemic injury to the bowel is minimal [10]. The sphincter prosthesis cuff and the reservoir are connected with the bidirectional micropump. The sensor inside the cuff can measure the occlusion pressure, and
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perceive the change of enteric cavity pressure indirectly. The microcontroller circuit processes the information from the sensor and compares the pressure to a specified threshold. As soon as the pressure approaches the threshold, an alarm signal is sent out. The patient can push in a normal defecation manner, and control the activity of his/her prosthesis (Figure 2C closed vs Figure 2D open) with the micropump via wireless communication. The diameter of the cuff can be re-designed to accommodate rectums/colons of varying sizes. The occluding cuff pressure and alarm threshold can be altered to function for different levels of continence via the application-specific software. All components of the IAAS are encapsulated in biocompatible-grade silicon so that the device is suitable for implantation. During the process of implantation, the prosthesis cuff is placed around the end of the rectum, the driver unit is fixed in a subcutaneous pouch in the left abdominal wall, and the energy-receiving coil is embedded in a subcutaneous area of the groin and connected to the driver unit by a subcutaneous wire tunnelled through the peritoneum.
Two pairs of MOSFETs driving signals were produced by the programmable waveform generator associated with the full bridge FET driver (HIP4082). The electromagnetic-field generated by the primary coil penetrated the skin and produced an induced voltage in the secondary coil. The induced voltage waveform was rectified by the full bridge rectifier and smoothed by a large capacitor that was connected to the 5 V buck regulator. An integrated Li-ion linear charger and system power path management module BQ24072 was designed, which powered the system while simultaneously and independently charging the battery via TETS. 3.2. TET coils A set of planar spiral coils used in this TETS were designed. They were thin and compact while maintaining good levels of coupling with a wide displacement tolerance. The outer and inner diameters of the primary coil were 48 mm and 16 mm, respectively, with a thickness of 5.6 mm, and a weight of 20 g; the outer and inner diameters of the secondary coil were 35 mm and 5 mm, respectively, with a thickness of 3 mm, and a weight of 6.5 g, as shown in Figure 4. The primary coil
3. TETS architecture 3.1. TETS circuit From the perspective of patient safety and QoL, a TETS is most suitable for powering implantable medical devices. Figure 3 shows a typical voltage-fed full bridge seriesresonant inverter used to power the IAAS. It employed a traditional zero-voltage switching (ZVS) full-bridge DC-AC inverter topology, which comprises a primary coil L1, and a tuning capacitor C2. For compensation on the primary side of a loosely coupling link, parallel compensation can only reduce the output current of the driving circuit; the power transfer ability and the efficiency of the link are not improved. Series compensation together with a full bridge driving circuit can achieve better results [11]; the required primary compensation capacitance was found to be independent of the load if the primary circuit was series compensated [12]. The secondary pick up coil was also series tuned with the lumped inductance L2, a tuning capacitor C2 and a load resistor RL.
Figure 4. Photograph of the fabricated internal control circuit with the receiving coil.
Figure 3. Basic structure of a TETS with frequency modulation.
L1
S2
S1 IS VS S3
C1 S4
C2
+ VO
L2
-
5V Buck regulation
Voltage Detection
Charging manager
rechargeable battery
Microprocessor PIC16F690
Secondary Power Circuit Prosthesis
Sensor
MOSFET Driver Internal transceiver Signal generator Body dsPIC33FJ128 External transceiver Primary Control
433MHz Communication channel
IAAS
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1.2
93
(a) 0.6 R1 R2
0.5 Coupling coefficient (k)
Resistance/Ω
1 0.8 0.6 0.4 0.2 0 100
0.4 0.3 0.2 0.1
200
300
400
0
500
0
5
10
Figure 5. Plot of the ESR of L1 and L2 vs operating frequency.
comprised 50 turns of a twisted bunch of 45 thin Litz wires, each with a diameter of 0.08 mm. The secondary coil comprised 31 turns of a twisted bunch of 14 thin Litz wires (0.08 mm) attached to the surface of the ferrite disk. The parameters of the self-inductance, the specified operating coupling (k) range and their equivalent series resistances (ESR) as a function of frequency should be determined in order to analyse the characteristics of the set of coils. For the set of TET coils used throughout the paper, the self-inductances of the primary and secondary coils were 37.05 mH and 32.92 mH, respectively. The terms R1 and R2 represents the ESR of the primary and secondary coils, respectively. The ESR values were determined by measuring the TET coils in practice with a HIOKI 3532-50 LCR HiTESTER at 25 kHz separations from 100–500 kHz. The resulting ESR values of the TET coils are shown in Figure 5. Our experimental measurements showed that the changes in ESR of the primary and secondary coils over our range of frequencies (265–350 kHz) were 40% and 7%, respectively. TET transfer was based on the mutual magnetic coupling between the coil pair. The k between these two coils was determined by the core material, the number of turns, and the geometry. The coupling and displacement data for the set of TET coils were measured at several points and their relationship is shown in Figure 6. Vertical separation in Figure 6(A) corresponds to the distance between the surface of the coils when they were parallel to each other with their centre points aligned, and Figure 6(B) shows the relationship between the k and the lateral displacement under different vertical separation. Within the effective range, the minimum operating coupling coefficient was 0.12 at any point between a 20 mm vertical separation or a 20 mm lateral displacement at 5 mm separation. Maximum coupling was achieved when the coils were right on top of each other at 5 mm separation and corresponds to a coupling factor of 0.42. This coupling condition was expected to cover reasonable changes in coupling due to surgical placement, posture, patient alignment and differences in body shape. Thus, the specified operating coupling range is 0.12–0.42.
15
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25
Axial separation/mm (b) 0.5
Coupling coefficient (k)
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Frequency/KHz
D=5mm D=10mm D=15mm D=20mm
0.4
0.3
0.2
0.1
0
0
5 10 15 Lateral displacement/mm
20
Figure 6. Coupling coefficient as a function of the displacement for the coil pair. (a) The vertical displacement when the coils are right on top of each other. (b) The lateral displacement under the different distances.
3.3. Analysis of GV against operating frequency A loosely coupled transformer was formed with an inductive link. Figure 7 shows a simplified T-representation model of Figure 3 [13]. To simplify the derivation of the analytical equation parameters, the non-linear secondary circuit was converted to a linear model by transferring the DC load RL to an equivalent AC load Req which represent power dissipation in the DC load, rectified diodes, and filter in Figure 3, where: Req ¼ 8RL =2
ð1Þ
In Figure 7, Z1, Z2 and Z3 represent the impedances at various points; the transfer gain of the voltage is given by the following relationship: Z2 Req VO ð2Þ GV ¼ ¼ jVS j Z1 Z3 where: ðjX1 þ R1 ÞðjXM þ jX2 þ R2 þ Req Þ þjXM ðjX2 þ R2 þ Req Þ Z1 ¼ jXM þ jX2 þ R2 þ Req
Z2 ¼
jXM ðjX2 þ R2 þ Req Þ jXM þ jX2 þ R2 þ Req
ð3Þ
ð4Þ
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C1 + VS -
L1-M
L2-M M
Req
R1
C2 Z2
+ Vo -
RL = 100Ω ＋ RL = 75Ω О
2.5
RL = 50Ω X
2
Z3 GV
Z1
(a) 3
R2
1.5
Figure 7. T equivalent circuit of the proposed TET system. 1
1 X1 ¼ !ðL1 MÞ !C1 1 X2 ¼ !ðL2 MÞ !C2 pffiffiffiffiffiffiffiffiffiffi XM ¼ !M ¼ !k L1 L2
0.5
ð5Þ
0 150
200
250
ð6Þ
300
400
(b) 4.5
ð7Þ
4
RL = 100Ω ＋
3.5
ð8Þ
RL = 75Ω О
3 GV
Where ! is an operating frequency of the converter, M is the mutual inductance between the coil pair, and k is the coupling coefficient. From (3) and (5), expanding (2), the following equation of the dc transfer gain GV for varying operating frequency can be obtained: ( X1 ðX1 þ XM ÞR2 þ ðX2 þ XM ÞR1 2 1þ þ GV ¼ XM XM Req
RL = 50Ω X
2.5 2 1.5 1 0.5 0 220
235
250
265
280
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310
Frequency/KHz
2 )12 X1 þ X2 þ X1 X2 =XM R1 R2 þ Req =XM þ Req
(c) 6 RL = 100Ω ＋ 5
RL = 75Ω О
ð9Þ
RL = 50Ω X
4
Figure 8 compares the analytical results with the measurement results for the changing operating frequency and various RL at three different cases of the coupling coefficient. The solid lines show the analytical values of the GV in equation (9), and the symbolic marks represent the measurement results. The parameters used in the analysis are based on the practical parameters of the components listed in Table 1. Results show that the characteristics of the GV for the three cases are almost identical, except for a small deviation in the high frequency domain (f4f0). Thus, the analytical curves can be used to design and control for the TETS. To regulate the output voltage for varying the k and the load, the feedback variable-frequency control of the output voltage should be designed by selecting the applicable region from among the three different regions of the GV in Figure 8. As shown in Figure 8, the region was divided into three smaller regions: a low-frequency region (†), a middlefrequency region (II) and a high-frequency region (III). The voltage transfer gain did not depend on load in the low- and high-frequency regions. The GV increased linearly as the operating frequency increased in the low-frequency region and decreased linearly in the high-frequency region. In the middle-frequency region, the gain largely depended on the variations of k and the load, and the bandwidth of region II decreased as the k decreased. This indicated that a TET system with a lower coupling coefficient needs more accurate
350
Frequency/KHz
GV
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Z3 ¼ jX2 þ R2 þ Req
3 2 1 0 240
250
260
270
280
290
Frequency/KHz
Figure 8. Plot of transfer dc gain (GV) vs operating frequency for different load. (a) k ¼ 0.42 (D ¼ 5 mm). (b) k ¼ 0.31 (D ¼ 10 mm). (c) k ¼ 0.12 (D ¼ 20 mm).
Table 1. Component values of the TET link. Parameters L1 C1 R1 L2 C2 R2 f0
Values
Notes
37.05 mH 10.408 nF 0.83
32.92 mH 11.788 nF 0.65
256 KHz
Self-inductance of primary coil Primary tuning capacitor ESR of L1 Self-inductance of secondary coil Secondary tuning capacitor ESR of L2 Resonant frequency
frequency control with a higher resolution to achieve equivalent output voltage regulation as compared to a system with a higher coupling coefficient. Taking the ZVS operation into account, the high-frequency region is suggested as a feasible region to control the output voltage for varying the k and the load.
Feedback control for a novel artificial anal sphincter 2
f = 282KHz f = 295KHz
3.5. Feedback controller design The coupling coefficient was affected due to the misalignment of the coil pair. To detect variations in k and regulate the frequency according to the load voltage, a method of numerical analysis with a microprocessor was used to realize the feedback control. In order to simplify the analysis of the proposed regulation method, the primary and secondary ESR of the coil pair and tuning capacitors were neglected, and all
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1
f = 321KHz
0.78
3.4. Switching frequency regulation range Frequency control involves varying the operating frequency of the primary inverter to vary the power delivered to the secondary load. Depending on the actual changes in output voltage, the operating frequency is varied in order to tune or detune the TETS, thereby maintaining a constant output voltage for the secondary power pickup, regardless of the coupling coefficient. To achieve this goal, a feedback signal would have to be transmitted from inside the patient’s body to the primary circuit via RF transmission. This makes use of the already available RF channel used for communication in the IAAS application. The load characteristics of the implantable IAAS are not constant because of the different charge phases including conditioning pre-charge, constant current fast charge and constant voltage tapering. In this design, the charge current was set at between 140 mA (constant current charge) and 60 mA (constant voltage charge), the equivalent load of the implantable system is 50100 ; at 7 V output voltage, this corresponds to 0.5@1 W of power. However, as shown in Figure 8, the GV does not depend on load variation in the high-frequency region of the curves at different cases of the coupling coefficient. Hence, steady-state loading conditions are representative. The average load of RL ¼ 75
was used to perform all feedback design and practical experiments. It was also necessary to determine the range of frequencies required to allow for coupling variations [14]. From Figure 8(A), it can be seen that the starting frequency of the high-frequency region was 321 KHz for k ¼ 0.45; here the GV is 0.78. Thus, this frequency was used as the upper limit of the frequency modulation and the objective GV was set at 0.78 with about a 3% margin (0.750.8). Figure 9 shows the curves of GV as measured at four different cases of the coupling coefficient for RL ¼ 75 . The operating frequencies of these conditions were between 270 and 330 KHz for GV ¼ 0.78. In view of the power consumption and the temperature increase of the coils and components, the output target voltage delivered to the 5 V voltage regulator can range from 6.8–7.2 V over the specified full coupling range of k ¼ 0.12–0.42. Based on the above analysis, the input voltage (VS) of the primary circuit was set to 9 V.
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k = 0.42 k = 0.31 k = 0.21 k = 0.12
f = 272KHz
1.5
GV
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0.5
0 260
275
290
305
320
335
350
Frequency/KHz
Figure 9. Plot of GV vs operating frequency for designed variablefrequency controller, RL ¼ 75 .
of the switches and the input DC voltage were assumed to be ideal. Solving equation (9), the coupling coefficient k as a function of GV and f can be obtained: ( 0 0 ð2X1 X2 þ R2eq =G2V Þ 1 k ¼ pffiffiffiffiffiffiffiffiffiffi 2 ! L1 L2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi912 0 0 0 0 0 2 2 2 2 > ð2X1 X2 þ Req =GV Þ 4 X1 2X2 2 þ Req X1 2 > = > 2 > ; ð10Þ where: 0
X1 ¼ !L1 0
X2 ¼ !L2
1 !C1
ð11Þ
1 !C2
ð12Þ
According to equation (10), once the output voltage was detected via an RF channel, it was compared to a pre-defined objective value (6.8–7.2 V) to calculate the current actual k with the present operating frequency. Then, from equation (10), at a fixed objective output voltage (GV ¼ 0.78), the corresponding frequency with respect to k can be determined by MATLAB (Figure 10). The variation range of k is set to 0.125k50.42, and the variation region of the regulating frequency is 2705f5320. The fitting formula (control rule function) can be expressed as (14) (R2 ¼ 1; RMSE ¼ 0.058). The regulating frequency can be calculated by equation (13) to maintain the output voltage again. All calculations and control processes were performed with the digital signal controller dsPIC33FJ128; they required no complex, sophisticated controllers or other peripheral devices. The frequency resolution of the programmable waveform generator AD9833 was 0.1 Hz with a 25 MHz clock rate, which met the requirements for frequency modulation accuracy. A flow chart representing the voltage regulation procedure is shown in Figure 11. f jGV ¼0:78 ¼ 66:58e2:239k þ 190
ð13Þ
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330
Frequency/KHz
320 310 300 290 280 270 260 0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
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Coupling coefficient (k)
Figure 10. Fitting curve of the regulating operation frequency f with respect to the coupling coefficient k when GV ¼ 0.78. Secondary Compare VO with threshold values No Higher or Lower? Yes Transmitted data
Received data (Vrx) GV = Vrx/9.0 k = fun1( GV, fcurrent )
MOSFETs driver
fregulating= fun2( k )|GV=0.78
Signal generator (AD9833)
Primary
dsPIC33FJ128
Figure 11. Flowchart of close-loop regulation procedure.
4. Experiment verification The practical measurement set-up is shown in Figure 12. The primary coil was fixed at an upholder, and the secondary coil was mounted in a four-dimensional-coordinates moving workbench. The relative position between the coil pair can be randomly adjusted to simulate the actual operational conditions as closely as possible. Practical TETS requires a regulated power of typically 1 W at the IAAS; the power flow controller must overcome variations in TET coil separation and misalignment due to patient movement, which corresponds to variations in coupling coefficient levels between the coil pair. A 75 load was used to approximate performance for the practical experiments. The proposed system can maintain the output at 7 V with a coil separation ranging from 5–20 mm, which corresponds to the best and lowest coupling situation. The practical switching frequency regulation ranged from 271.4–320.5 KHz. These experimental results are in good agreement with the analytical results. The practical circuit waveforms of three different coil separation distances are shown in Figures 13–15 under an
Figure 12. Practical measurement set-up.
input dc voltage of 9 V. In all three practical circuit waveform figures, the top waveform is the switch voltage VS1, the secondary waveform is the voltage across the primary tuning capacitor VC1 and the last waveform is the induced voltage across the secondary capacitor VC2. The operating frequency of the driving signal is 320.5, 279.6 and 271.4 KHz and the VC2 is 4.53, 5.14 and 5.35 V at the minimum (0.12), medium (21) and maximum (0.42) coupling coefficients, respectively. The reflected impedance of the secondary side decreases as the coupling coefficient lowers. Therefore, the primary current becomes large at a low coupling coefficient. Because the voltage of the primary tuning capacitor proportionally increases as the primary current increases, it reaches 60 V at the worst condition (k ¼ 0.12). The maximum operating frequency (320.5 KHz) of the inverter is at maximum coupling condition and the minimum operating frequency (271.4 KHz) is at minimum coupling coefficient. The output current Io2 (VC2/!C2) of the secondary circuit can be maintained at 107 mA due to the variable frequency control; thus, the system was able to maintain 7 V at the load side. Figure 16 shows the measured results of the output voltage at load side, the transfer efficiency and the operating frequency. By detecting the actual output voltage, the closed loop frequency regulation system can automatically adjust the operating frequency of the primary inverter from 320.5 KHz to 271.4 KHz by calculation of equations (10) and (13). This will increase the primary current and the flux density to a required level so that the output voltage of the secondary side can be maintained at a constant 7 V across the whole coupling coefficient range. It is clear that the practical adjusted frequency corresponds well to the analytical frequency range. From Figure 16, when the system operated in a fixed frequency mode, the output voltage changed obviously over the full range of coupling coefficient. In this mode, the ranges of the output voltage were 12.813.72 V and 17.7812.22 V with fixed frequencies of 285 K and 265 K, respectively. A high voltage (17.78 V) and a low voltage (3.72 V) will be induced, which may cause damage due to significant power loss and internal heating. As the coupling coefficient lowers (separation distance increases), the efficiency is also lowered at the same load condition because the primary current is
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DOI: 10.3109/03091902.2013.872204
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Figure 13. Practical circuit waveform, k ¼ 0.42 (TET coil separation distance of 5 mm), f ¼ 320.5 KHz, Io2 ¼ 107.5 mA.
Figure 14. Practical circuit waveform, k ¼ 0.21 (TET coil separation of distance 15 mm), f ¼ 279.6 KHz, Io2 ¼ 107.5 mA.
higher. Furthermore, the output performance and transfer efficiency will be enhanced as the operating frequency, shifting towards the resonant frequency due to a reduction in the imaginary part of equivalent impedance. In Figure 16, the frequency regulation system achieved a maximal end-of-end efficiency of 67.5% compared to 76.5% from the fixed frequency (265 KHz) operation mode. This efficiency can be improved in future experiments by optimizing the coupling efficiency. Moreover, comparing with the fixed operating frequency work mode of 285 KHz, the transfer efficiency of the variable frequency system was less than the ones of the fixed frequency mode when the operating frequency was
more than 285 KHz, which approximately matches to an equivalent axial separation in the range 2–12 mm, and the opposite case appeared when the operating frequency was below 285 KHz, which was in accordance with the above theory.
5. Conclusion A TETS based on a new closed-loop power flow control method has been developed to adaptively send the needed power to the IAAS, regardless of variations in the coupling coefficient and equivalent loading conditions. A prototype of
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J Med Eng Technol, 2014; 38(2): 90–99
Figure 15. Practical circuit waveform, k ¼ 0.12 (TET coil separation of distance 20 mm), f ¼ 271.4 KHz, Io2 ¼ 107.5 mA.
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Acknowledgements 285 KHz
VO/V
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We acknowledge with appreciation the financial support provided by the National Natural Science Foundation of China (No. 31170968).
η/%
80 65
Declaration of interest
50
The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.
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Figure 16. Experimental results of output voltage of secondary circuit (V0), transfer efficiency () and variable frequency (f) vs separation distance. The blue circular symbolic marks and red square symbolic marks represent the fixed operating frequency, 265 KHz and 285 KHz, respectively.
the TET charging system was constructed. The voltage transfer gain was derived from the T-model, and the switching frequency regulation range was determined. The relationship between coupling coefficient, voltage transfer gain and operating frequency was derived, which gave a good prediction of the change in k. Then, the target operating frequency was determined accurately by the control function. The system has reduced the total components compared to those in existing frequency controllers. Experimental results showed that the proposed system can maintain the output voltage of the secondary circuit to be constant across the full ranges of the coupling coefficient variations.
1. Bharucha, A.E., Wald, A., Enck, P., and Rao, S., 2006, Functional anorectal disorders. Gastroenterology, 130, 1510–1518. 2. Edden, Y., and Wexner, S.D., 2009, Therapeutic devices for fecal incontinence: dynamic graciloplasty, artificial bowel sphincter and sacral nerve stimulation. Expert Review of Medical Devices, 6, 307–312. 3. Gallas, S., Leroi, A.M., Bridoux, V., Lefebure, B., Tuech, J.J., and Michot, F., 2009, Constipation in 44 patients implanted with an artificial bowel sphincter. International Journal of Colorectal Disease, 24, 969–974. 4. Mundy, L., Merlin, T.L., Maddern, G.J., and Hiller, J.E., 2004, Systematic review of safety and effectiveness of an artificial bowel sphincter for faecal incontinence. British Journal of Surgery, 91, 665–672. 5. Belyaev, O., Mu¨ller, C., and Uhl, W., 2006, Neosphincter surgery for fecal incontinence: A critical and unbiased review of the relevant literature. Surgery Today, 36, 295–303. 6. Dissanayake, T.D., Hu, P.A., Malpas, S., Bennet, L., Taberner, A., Booth, L., and Budgett, D., 2009, Experimental study of a TET system for implantable biomedical devices. IEEE Transactions on Biomedical Circuits and Systems, 3, 370–378. 7. Si, P., Hu, P.A., Hsu, J.W., Chiang, M., Wang, Y., Malpas, S., and Budgett, D., 2007, Wireless power supply for implantable biomedical device based on primary input voltage regulation. 2nd IEEE Conference on Industrial Electronics and Applications. Harbin, China, 23-25 May, pp. 235–239. 8. Zan, P., Yan, G., Liu, H., Luo, N., and Zhao, Y., 2007, Adaptive transcutaneous power delivery for an artificial anal sphincter
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system. Journal of Medical Engineering & Technology, 33, 136–141. 9. Si, P., Hu, P.A., Malpas, S., and Budgett, D., 2008, A frequency control method for regulating wireless power to implantable devices. IEEE Transactions on Biomedical Circuits and Systems, 2, 22–29. 10. Wong, W.D., Congliosi, S.M., Spencer, M.P., Corman, M.L., Tan, P., Opelka, F.G., Burnstein, M., Nogueras, J.J., Bailey, H.R., Devesa, J.M., Fry, R.D., Cagir, B., Birnbaum, E., Fleshman, J.W., Lawrence, M.A., Buie, W.D., Heine, J., Edelstein, P.S., Gregorcyk, S., Lehur, P.A., Michot, F., Phang, P.T., Schoetz, D.J., Potenti, F., and Tsai, J.Y., 2002, The safety and efficacy of the artificial bowel sphincter for fecal incontinence. Disease of the Colon & Rectum, 45, 1139–1153. 11. Lu, Y., Cheng, K.W.E., Kwok, Y.L., Kwok, K.W., Chan, K.W., and Cheung, N.C., 2007, Gapped air-cored power converter for
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intelligent clothing power transfer. International Conference on Power Electronics and Drive Systems (Bangkok), 27–30 Nov, pp. 1578–1584. 12. Wang, C.S., Covic, G.A., and Stielau, O.H., 2004, Power transfer capability and bifurcation phenomena of loosely coupled inductive power transfer systems. IEEE Transactions on Industrial Electronics, 51, 148–157. 13. Schuder, J.C., Gold, J.H., and Stephenson, H.E.J., 1971, An inductively coupled RF system for the transmission of 1 kW of power through the skin. IEEE Transactions on Biomedical Circuits and Systems, 18, 265–273. 14. Wang, B., Hu, P.A., and Budgett, D., 2012, Power flow control based solely on slow feedback loop for heart pump applications. IEEE Transactions on Biomedical Circuits and Systems, 6, 279–286.
INNOVATION
Feedback control of TET system with variable coupling coefficients for a novel artificial anal sphincter 820 Institute, Department of Instrument Science and Engineering, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, PR China Abstract
Keywords
For treating severe faecal incontinence, the authors developed an intelligent artificial anal sphincter system (AASS) equipped with a feedback sensor that utilized a transcutaneous energy transfer system (TETS). To deliver the correct amount of power (i.e. to match the load demand under variable coupling conditions caused by changes in positioning between the coils due to fitting and changes in posture), a regulating method to stabilize output voltage with a closed loop variable-frequency controller was developed in this paper. The method via which the voltage gain characteristics of a voltage-fed series-tuned TETS were derived is also described. The theoretical analysis was verified by the results of the experiment. A numerical analysis method was used as a control rule with respect to the relationship between operating frequency and output voltage. To validate the feedback control rules, a prototype of the TET charging system was constructed, and its performance was validated with the coupling variation between 0.12–0.42. The results show that the output voltage of the secondary side can be maintained at a constant 7 V across the whole coupling coefficient range, with a switching frequency regulation range of 271.4–320.5 kHz, and the proposed controller has reached a maximal end-to-end power efficiency of 67.5% at 1 W.
Artificial anal sphincter, closed-loop control, faecal incontinence, variable coupling coefficient, transcutaneous energy transfer
1. Introduction Faecal incontinence (FI) is a common clinical symptom that seriously affects patients’ quality-of-life (QoL) [1]. Medical science has devoted much attention to anorectal research and has sought solutions for FI. In recent years, an Artificial Bowel Sphincter (ABS) (American Medical Systems, Minneapolis, MN)—which comprises three silastic elements (an inflatable cuff, a pressure-regulating balloon that also functions as a fluid reservoir, and a control pump)—was developed as an alternative for patients with end-stage FI and failure of conventional treatments or permanent colostomy [2]. Despite its simplicity, the ABS still has some limitations. First, patients can’t perceive when to defecate, so they must be trained to evacuate at regular, scheduled times; second, to open the occlusive cuff, patients must repeatedly squeeze and release the bulb of the control pump (placed under the scrotum or the labia major of the vulva), which may eventually damage patients’ skin and possibly become infected; third, because the cuff refills automatically, the time allotted for defecation is determined by the total duration of the refilling and opening of the cuff. Some patients do not have enough time to defecate and develop defecation difficulties after implantation due to the rapid closure of the *Corresponding author. Email: [email protected]
History Received 6 October 2013 Revised 18 November 2013 Accepted 26 November 2013
cuff; lastly, according to some studies, all patients suffer from pressure atrophy to a certain degree. Under such conditions, cuff efficiency diminishes, which may lead to the recurrence of faecal incontinence [3–5]. To overcome these drawbacks, a novel, highly integrated and intelligent artificial anal sphincter system (AASS) is presented. The structure of this system, with sensor feedback, is shown in detail. The key element of the AASS—a voltage-fed series-tuned transcutaneous energy transfer system (TETS)—is then discussed. It enables the transfer of power across the skin without direct electrical connectivity. The secondary coil of the TETS is implanted under the skin, and the primary coil is placed on top of the secondary coil, outside the body. The distance between the transformer windings would be approximately equal to the thickness of the patient’s skin, fatty tissue, and muscle, nominally between 1–2 cm [6]. This spacing cannot be assumed constant; the alignment of the cores and the distance between them would certainly vary during the operation. Variation in distance and misalignment of the coil pair can affect the coupling coefficient k, and change the operating state of the inductive link. However, the inductive power link was expected of properly power, regardless of the variable k, was transfer to the secondary circuit in order to reduce power loss and the possibility of tissue damage from overheating. Previous studies reported that there were two main methods of regulating power in TETS based on
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magnitude and frequency control strategies. The power delivered to the load may be modulated by the magnitude control that varies the input voltage to the primary power inverter [7]. However, due to the mismatch of the resonant frequency of the secondary resonant circuit and the operating frequency of the external power inverter, a larger input voltage was required for a given power transfer, resulting in increased electromagnetic interference (EMI) and reduced power efficiency overall. In the case of frequency control, the Class-E amplifier may be returned to a better or optimum operating state by varying the operating frequency of the primary power converter to vary the power flow when k changes [8]. However, the frequency adjustment ranges have not yet been determined theoretically. Si et al. [9] developed a variable resonant frequency method to regulate the power flow by changing the effective capacitance of the primary circuit by switching on and off capacitors that were parallel to the primary MOSFETs. However, this method requires that the system has more switching devices and resonant capacitors.
Figure 1. Diagram of the AASS. Figure 2. The novel AASS prototype. (a) IAAS; (b) External transmitter of the TETS and control unit; (c) New sphincter prosthesis cuff with sensor. Inflated ¼ Continence; (d) Deflated ¼ Defecation.
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In this paper, a new closed-loop variable frequency control method is studied in detail, with the aim of keeping the output power constant when k changes. Analytical expression is derived as functions of the voltage gain characteristic GV, the operating frequency f of the driving signal, and the coupling coefficient k. Through numerical analysis, a method was derived as a control rule with respect to the relationship between operating frequency and output voltage. All calculations and control processes were performed with the digital signal controller dsPIC33FJ128 combined with a programmable waveform generator that offers the advantage of reduced switching components and capacitors. Experiments were conducted to validate the theoretical design when k is changed from 0.42 to 0.12 and back to 0.42.
2. The novel artificial anal sphincter system The system block diagram is shown in Figure 1. The new version of an AASS with biosensor feedback powered by TETS is an integrative, modular, remote-controlled sphincter prosthesis that mainly comprises three modules including an intelligent artificial anal sphincter (IAAS, Figure 2A), a TETS and an external controller (Figure 2B). The IAAS is composed of a driver unit, sphincter prosthesis, and an energy-receiving coil. The driver unit integrates the micropump, rechargeable battery, microcontroller circuit, and fluid reservoir in a casing that presently measures 5.5 4.5 2.5 cm (L W H). The mechanical medical micropump of the IAAS can realize bidirectional flow with a maximum flow rate of 8.5 mL min1 and can build backpressure up to 170 kPa. The design of the prosthesis reduces occlusion pressure and allows for low inflation volumes (910.5 mL); operating pressures between 4.05– 7.16 kPa indicate that the risk of ischaemic injury to the bowel is minimal [10]. The sphincter prosthesis cuff and the reservoir are connected with the bidirectional micropump. The sensor inside the cuff can measure the occlusion pressure, and
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perceive the change of enteric cavity pressure indirectly. The microcontroller circuit processes the information from the sensor and compares the pressure to a specified threshold. As soon as the pressure approaches the threshold, an alarm signal is sent out. The patient can push in a normal defecation manner, and control the activity of his/her prosthesis (Figure 2C closed vs Figure 2D open) with the micropump via wireless communication. The diameter of the cuff can be re-designed to accommodate rectums/colons of varying sizes. The occluding cuff pressure and alarm threshold can be altered to function for different levels of continence via the application-specific software. All components of the IAAS are encapsulated in biocompatible-grade silicon so that the device is suitable for implantation. During the process of implantation, the prosthesis cuff is placed around the end of the rectum, the driver unit is fixed in a subcutaneous pouch in the left abdominal wall, and the energy-receiving coil is embedded in a subcutaneous area of the groin and connected to the driver unit by a subcutaneous wire tunnelled through the peritoneum.
Two pairs of MOSFETs driving signals were produced by the programmable waveform generator associated with the full bridge FET driver (HIP4082). The electromagnetic-field generated by the primary coil penetrated the skin and produced an induced voltage in the secondary coil. The induced voltage waveform was rectified by the full bridge rectifier and smoothed by a large capacitor that was connected to the 5 V buck regulator. An integrated Li-ion linear charger and system power path management module BQ24072 was designed, which powered the system while simultaneously and independently charging the battery via TETS. 3.2. TET coils A set of planar spiral coils used in this TETS were designed. They were thin and compact while maintaining good levels of coupling with a wide displacement tolerance. The outer and inner diameters of the primary coil were 48 mm and 16 mm, respectively, with a thickness of 5.6 mm, and a weight of 20 g; the outer and inner diameters of the secondary coil were 35 mm and 5 mm, respectively, with a thickness of 3 mm, and a weight of 6.5 g, as shown in Figure 4. The primary coil
3. TETS architecture 3.1. TETS circuit From the perspective of patient safety and QoL, a TETS is most suitable for powering implantable medical devices. Figure 3 shows a typical voltage-fed full bridge seriesresonant inverter used to power the IAAS. It employed a traditional zero-voltage switching (ZVS) full-bridge DC-AC inverter topology, which comprises a primary coil L1, and a tuning capacitor C2. For compensation on the primary side of a loosely coupling link, parallel compensation can only reduce the output current of the driving circuit; the power transfer ability and the efficiency of the link are not improved. Series compensation together with a full bridge driving circuit can achieve better results [11]; the required primary compensation capacitance was found to be independent of the load if the primary circuit was series compensated [12]. The secondary pick up coil was also series tuned with the lumped inductance L2, a tuning capacitor C2 and a load resistor RL.
Figure 4. Photograph of the fabricated internal control circuit with the receiving coil.
Figure 3. Basic structure of a TETS with frequency modulation.
L1
S2
S1 IS VS S3
C1 S4
C2
+ VO
L2
-
5V Buck regulation
Voltage Detection
Charging manager
rechargeable battery
Microprocessor PIC16F690
Secondary Power Circuit Prosthesis
Sensor
MOSFET Driver Internal transceiver Signal generator Body dsPIC33FJ128 External transceiver Primary Control
433MHz Communication channel
IAAS
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(a) 0.6 R1 R2
0.5 Coupling coefficient (k)
Resistance/Ω
1 0.8 0.6 0.4 0.2 0 100
0.4 0.3 0.2 0.1
200
300
400
0
500
0
5
10
Figure 5. Plot of the ESR of L1 and L2 vs operating frequency.
comprised 50 turns of a twisted bunch of 45 thin Litz wires, each with a diameter of 0.08 mm. The secondary coil comprised 31 turns of a twisted bunch of 14 thin Litz wires (0.08 mm) attached to the surface of the ferrite disk. The parameters of the self-inductance, the specified operating coupling (k) range and their equivalent series resistances (ESR) as a function of frequency should be determined in order to analyse the characteristics of the set of coils. For the set of TET coils used throughout the paper, the self-inductances of the primary and secondary coils were 37.05 mH and 32.92 mH, respectively. The terms R1 and R2 represents the ESR of the primary and secondary coils, respectively. The ESR values were determined by measuring the TET coils in practice with a HIOKI 3532-50 LCR HiTESTER at 25 kHz separations from 100–500 kHz. The resulting ESR values of the TET coils are shown in Figure 5. Our experimental measurements showed that the changes in ESR of the primary and secondary coils over our range of frequencies (265–350 kHz) were 40% and 7%, respectively. TET transfer was based on the mutual magnetic coupling between the coil pair. The k between these two coils was determined by the core material, the number of turns, and the geometry. The coupling and displacement data for the set of TET coils were measured at several points and their relationship is shown in Figure 6. Vertical separation in Figure 6(A) corresponds to the distance between the surface of the coils when they were parallel to each other with their centre points aligned, and Figure 6(B) shows the relationship between the k and the lateral displacement under different vertical separation. Within the effective range, the minimum operating coupling coefficient was 0.12 at any point between a 20 mm vertical separation or a 20 mm lateral displacement at 5 mm separation. Maximum coupling was achieved when the coils were right on top of each other at 5 mm separation and corresponds to a coupling factor of 0.42. This coupling condition was expected to cover reasonable changes in coupling due to surgical placement, posture, patient alignment and differences in body shape. Thus, the specified operating coupling range is 0.12–0.42.
15
20
25
Axial separation/mm (b) 0.5
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D=5mm D=10mm D=15mm D=20mm
0.4
0.3
0.2
0.1
0
0
5 10 15 Lateral displacement/mm
20
Figure 6. Coupling coefficient as a function of the displacement for the coil pair. (a) The vertical displacement when the coils are right on top of each other. (b) The lateral displacement under the different distances.
3.3. Analysis of GV against operating frequency A loosely coupled transformer was formed with an inductive link. Figure 7 shows a simplified T-representation model of Figure 3 [13]. To simplify the derivation of the analytical equation parameters, the non-linear secondary circuit was converted to a linear model by transferring the DC load RL to an equivalent AC load Req which represent power dissipation in the DC load, rectified diodes, and filter in Figure 3, where: Req ¼ 8RL =2
ð1Þ
In Figure 7, Z1, Z2 and Z3 represent the impedances at various points; the transfer gain of the voltage is given by the following relationship: Z2 Req VO ð2Þ GV ¼ ¼ jVS j Z1 Z3 where: ðjX1 þ R1 ÞðjXM þ jX2 þ R2 þ Req Þ þjXM ðjX2 þ R2 þ Req Þ Z1 ¼ jXM þ jX2 þ R2 þ Req
Z2 ¼
jXM ðjX2 þ R2 þ Req Þ jXM þ jX2 þ R2 þ Req
ð3Þ
ð4Þ
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C1 + VS -
L1-M
L2-M M
Req
R1
C2 Z2
+ Vo -
RL = 100Ω ＋ RL = 75Ω О
2.5
RL = 50Ω X
2
Z3 GV
Z1
(a) 3
R2
1.5
Figure 7. T equivalent circuit of the proposed TET system. 1
1 X1 ¼ !ðL1 MÞ !C1 1 X2 ¼ !ðL2 MÞ !C2 pffiffiffiffiffiffiffiffiffiffi XM ¼ !M ¼ !k L1 L2
0.5
ð5Þ
0 150
200
250
ð6Þ
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400
(b) 4.5
ð7Þ
4
RL = 100Ω ＋
3.5
ð8Þ
RL = 75Ω О
3 GV
Where ! is an operating frequency of the converter, M is the mutual inductance between the coil pair, and k is the coupling coefficient. From (3) and (5), expanding (2), the following equation of the dc transfer gain GV for varying operating frequency can be obtained: ( X1 ðX1 þ XM ÞR2 þ ðX2 þ XM ÞR1 2 1þ þ GV ¼ XM XM Req
RL = 50Ω X
2.5 2 1.5 1 0.5 0 220
235
250
265
280
295
310
Frequency/KHz
2 )12 X1 þ X2 þ X1 X2 =XM R1 R2 þ Req =XM þ Req
(c) 6 RL = 100Ω ＋ 5
RL = 75Ω О
ð9Þ
RL = 50Ω X
4
Figure 8 compares the analytical results with the measurement results for the changing operating frequency and various RL at three different cases of the coupling coefficient. The solid lines show the analytical values of the GV in equation (9), and the symbolic marks represent the measurement results. The parameters used in the analysis are based on the practical parameters of the components listed in Table 1. Results show that the characteristics of the GV for the three cases are almost identical, except for a small deviation in the high frequency domain (f4f0). Thus, the analytical curves can be used to design and control for the TETS. To regulate the output voltage for varying the k and the load, the feedback variable-frequency control of the output voltage should be designed by selecting the applicable region from among the three different regions of the GV in Figure 8. As shown in Figure 8, the region was divided into three smaller regions: a low-frequency region (†), a middlefrequency region (II) and a high-frequency region (III). The voltage transfer gain did not depend on load in the low- and high-frequency regions. The GV increased linearly as the operating frequency increased in the low-frequency region and decreased linearly in the high-frequency region. In the middle-frequency region, the gain largely depended on the variations of k and the load, and the bandwidth of region II decreased as the k decreased. This indicated that a TET system with a lower coupling coefficient needs more accurate
350
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Z3 ¼ jX2 þ R2 þ Req
3 2 1 0 240
250
260
270
280
290
Frequency/KHz
Figure 8. Plot of transfer dc gain (GV) vs operating frequency for different load. (a) k ¼ 0.42 (D ¼ 5 mm). (b) k ¼ 0.31 (D ¼ 10 mm). (c) k ¼ 0.12 (D ¼ 20 mm).
Table 1. Component values of the TET link. Parameters L1 C1 R1 L2 C2 R2 f0
Values
Notes
37.05 mH 10.408 nF 0.83
32.92 mH 11.788 nF 0.65
256 KHz
Self-inductance of primary coil Primary tuning capacitor ESR of L1 Self-inductance of secondary coil Secondary tuning capacitor ESR of L2 Resonant frequency
frequency control with a higher resolution to achieve equivalent output voltage regulation as compared to a system with a higher coupling coefficient. Taking the ZVS operation into account, the high-frequency region is suggested as a feasible region to control the output voltage for varying the k and the load.
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f = 282KHz f = 295KHz
3.5. Feedback controller design The coupling coefficient was affected due to the misalignment of the coil pair. To detect variations in k and regulate the frequency according to the load voltage, a method of numerical analysis with a microprocessor was used to realize the feedback control. In order to simplify the analysis of the proposed regulation method, the primary and secondary ESR of the coil pair and tuning capacitors were neglected, and all
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1
f = 321KHz
0.78
3.4. Switching frequency regulation range Frequency control involves varying the operating frequency of the primary inverter to vary the power delivered to the secondary load. Depending on the actual changes in output voltage, the operating frequency is varied in order to tune or detune the TETS, thereby maintaining a constant output voltage for the secondary power pickup, regardless of the coupling coefficient. To achieve this goal, a feedback signal would have to be transmitted from inside the patient’s body to the primary circuit via RF transmission. This makes use of the already available RF channel used for communication in the IAAS application. The load characteristics of the implantable IAAS are not constant because of the different charge phases including conditioning pre-charge, constant current fast charge and constant voltage tapering. In this design, the charge current was set at between 140 mA (constant current charge) and 60 mA (constant voltage charge), the equivalent load of the implantable system is 50100 ; at 7 V output voltage, this corresponds to 0.5@1 W of power. However, as shown in Figure 8, the GV does not depend on load variation in the high-frequency region of the curves at different cases of the coupling coefficient. Hence, steady-state loading conditions are representative. The average load of RL ¼ 75
was used to perform all feedback design and practical experiments. It was also necessary to determine the range of frequencies required to allow for coupling variations [14]. From Figure 8(A), it can be seen that the starting frequency of the high-frequency region was 321 KHz for k ¼ 0.45; here the GV is 0.78. Thus, this frequency was used as the upper limit of the frequency modulation and the objective GV was set at 0.78 with about a 3% margin (0.750.8). Figure 9 shows the curves of GV as measured at four different cases of the coupling coefficient for RL ¼ 75 . The operating frequencies of these conditions were between 270 and 330 KHz for GV ¼ 0.78. In view of the power consumption and the temperature increase of the coils and components, the output target voltage delivered to the 5 V voltage regulator can range from 6.8–7.2 V over the specified full coupling range of k ¼ 0.12–0.42. Based on the above analysis, the input voltage (VS) of the primary circuit was set to 9 V.
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f = 272KHz
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0.5
0 260
275
290
305
320
335
350
Frequency/KHz
Figure 9. Plot of GV vs operating frequency for designed variablefrequency controller, RL ¼ 75 .
of the switches and the input DC voltage were assumed to be ideal. Solving equation (9), the coupling coefficient k as a function of GV and f can be obtained: ( 0 0 ð2X1 X2 þ R2eq =G2V Þ 1 k ¼ pffiffiffiffiffiffiffiffiffiffi 2 ! L1 L2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi912 0 0 0 0 0 2 2 2 2 > ð2X1 X2 þ Req =GV Þ 4 X1 2X2 2 þ Req X1 2 > = > 2 > ; ð10Þ where: 0
X1 ¼ !L1 0
X2 ¼ !L2
1 !C1
ð11Þ
1 !C2
ð12Þ
According to equation (10), once the output voltage was detected via an RF channel, it was compared to a pre-defined objective value (6.8–7.2 V) to calculate the current actual k with the present operating frequency. Then, from equation (10), at a fixed objective output voltage (GV ¼ 0.78), the corresponding frequency with respect to k can be determined by MATLAB (Figure 10). The variation range of k is set to 0.125k50.42, and the variation region of the regulating frequency is 2705f5320. The fitting formula (control rule function) can be expressed as (14) (R2 ¼ 1; RMSE ¼ 0.058). The regulating frequency can be calculated by equation (13) to maintain the output voltage again. All calculations and control processes were performed with the digital signal controller dsPIC33FJ128; they required no complex, sophisticated controllers or other peripheral devices. The frequency resolution of the programmable waveform generator AD9833 was 0.1 Hz with a 25 MHz clock rate, which met the requirements for frequency modulation accuracy. A flow chart representing the voltage regulation procedure is shown in Figure 11. f jGV ¼0:78 ¼ 66:58e2:239k þ 190
ð13Þ
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330
Frequency/KHz
320 310 300 290 280 270 260 0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
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Coupling coefficient (k)
Figure 10. Fitting curve of the regulating operation frequency f with respect to the coupling coefficient k when GV ¼ 0.78. Secondary Compare VO with threshold values No Higher or Lower? Yes Transmitted data
Received data (Vrx) GV = Vrx/9.0 k = fun1( GV, fcurrent )
MOSFETs driver
fregulating= fun2( k )|GV=0.78
Signal generator (AD9833)
Primary
dsPIC33FJ128
Figure 11. Flowchart of close-loop regulation procedure.
4. Experiment verification The practical measurement set-up is shown in Figure 12. The primary coil was fixed at an upholder, and the secondary coil was mounted in a four-dimensional-coordinates moving workbench. The relative position between the coil pair can be randomly adjusted to simulate the actual operational conditions as closely as possible. Practical TETS requires a regulated power of typically 1 W at the IAAS; the power flow controller must overcome variations in TET coil separation and misalignment due to patient movement, which corresponds to variations in coupling coefficient levels between the coil pair. A 75 load was used to approximate performance for the practical experiments. The proposed system can maintain the output at 7 V with a coil separation ranging from 5–20 mm, which corresponds to the best and lowest coupling situation. The practical switching frequency regulation ranged from 271.4–320.5 KHz. These experimental results are in good agreement with the analytical results. The practical circuit waveforms of three different coil separation distances are shown in Figures 13–15 under an
Figure 12. Practical measurement set-up.
input dc voltage of 9 V. In all three practical circuit waveform figures, the top waveform is the switch voltage VS1, the secondary waveform is the voltage across the primary tuning capacitor VC1 and the last waveform is the induced voltage across the secondary capacitor VC2. The operating frequency of the driving signal is 320.5, 279.6 and 271.4 KHz and the VC2 is 4.53, 5.14 and 5.35 V at the minimum (0.12), medium (21) and maximum (0.42) coupling coefficients, respectively. The reflected impedance of the secondary side decreases as the coupling coefficient lowers. Therefore, the primary current becomes large at a low coupling coefficient. Because the voltage of the primary tuning capacitor proportionally increases as the primary current increases, it reaches 60 V at the worst condition (k ¼ 0.12). The maximum operating frequency (320.5 KHz) of the inverter is at maximum coupling condition and the minimum operating frequency (271.4 KHz) is at minimum coupling coefficient. The output current Io2 (VC2/!C2) of the secondary circuit can be maintained at 107 mA due to the variable frequency control; thus, the system was able to maintain 7 V at the load side. Figure 16 shows the measured results of the output voltage at load side, the transfer efficiency and the operating frequency. By detecting the actual output voltage, the closed loop frequency regulation system can automatically adjust the operating frequency of the primary inverter from 320.5 KHz to 271.4 KHz by calculation of equations (10) and (13). This will increase the primary current and the flux density to a required level so that the output voltage of the secondary side can be maintained at a constant 7 V across the whole coupling coefficient range. It is clear that the practical adjusted frequency corresponds well to the analytical frequency range. From Figure 16, when the system operated in a fixed frequency mode, the output voltage changed obviously over the full range of coupling coefficient. In this mode, the ranges of the output voltage were 12.813.72 V and 17.7812.22 V with fixed frequencies of 285 K and 265 K, respectively. A high voltage (17.78 V) and a low voltage (3.72 V) will be induced, which may cause damage due to significant power loss and internal heating. As the coupling coefficient lowers (separation distance increases), the efficiency is also lowered at the same load condition because the primary current is
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Figure 13. Practical circuit waveform, k ¼ 0.42 (TET coil separation distance of 5 mm), f ¼ 320.5 KHz, Io2 ¼ 107.5 mA.
Figure 14. Practical circuit waveform, k ¼ 0.21 (TET coil separation of distance 15 mm), f ¼ 279.6 KHz, Io2 ¼ 107.5 mA.
higher. Furthermore, the output performance and transfer efficiency will be enhanced as the operating frequency, shifting towards the resonant frequency due to a reduction in the imaginary part of equivalent impedance. In Figure 16, the frequency regulation system achieved a maximal end-of-end efficiency of 67.5% compared to 76.5% from the fixed frequency (265 KHz) operation mode. This efficiency can be improved in future experiments by optimizing the coupling efficiency. Moreover, comparing with the fixed operating frequency work mode of 285 KHz, the transfer efficiency of the variable frequency system was less than the ones of the fixed frequency mode when the operating frequency was
more than 285 KHz, which approximately matches to an equivalent axial separation in the range 2–12 mm, and the opposite case appeared when the operating frequency was below 285 KHz, which was in accordance with the above theory.
5. Conclusion A TETS based on a new closed-loop power flow control method has been developed to adaptively send the needed power to the IAAS, regardless of variations in the coupling coefficient and equivalent loading conditions. A prototype of
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J Med Eng Technol, 2014; 38(2): 90–99
Figure 15. Practical circuit waveform, k ¼ 0.12 (TET coil separation of distance 20 mm), f ¼ 271.4 KHz, Io2 ¼ 107.5 mA.
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We acknowledge with appreciation the financial support provided by the National Natural Science Foundation of China (No. 31170968).
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Figure 16. Experimental results of output voltage of secondary circuit (V0), transfer efficiency () and variable frequency (f) vs separation distance. The blue circular symbolic marks and red square symbolic marks represent the fixed operating frequency, 265 KHz and 285 KHz, respectively.
the TET charging system was constructed. The voltage transfer gain was derived from the T-model, and the switching frequency regulation range was determined. The relationship between coupling coefficient, voltage transfer gain and operating frequency was derived, which gave a good prediction of the change in k. Then, the target operating frequency was determined accurately by the control function. The system has reduced the total components compared to those in existing frequency controllers. Experimental results showed that the proposed system can maintain the output voltage of the secondary circuit to be constant across the full ranges of the coupling coefficient variations.
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