Optimal design and modeling of tactile resistive and capacitive sensors interfaces used in modern mechatronics

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1 ROMANIAN JOURNAL OF INFORMATION SCIENCE AND TECHNOLOGY Volume 20, Number 4, 2017, Optimal esign an moeling of tactile resistive an capacitive sensors interfaces use in moern mechatronics Anghel CONSTANTIN National Institute of Research an Development in Mechatronics an Measurement Technique, Bucharest, Romania Abstract. In one of my wier stuies about the best choice of sensors that can be place on the soles in multiple positions of the foot charge points, for real-time calibrate measuring of groun reaction forces (GRF) uring human walking, has been approache the problem of optimal interfacing with the ata acquisition system from tensorestive tactile sensors an one capacitive sensors. The aim of wier project was to calculate the real energetic consumption uring gait as mechanical work of horizontal projection component of GRF. The paper presents the main problems an relate solutions obtaine by PSPICE an LAPLACE moelling an simulation. Thus, for the tactile sensors it is showe an original interfacing circuit with multiple avantages an for the capacitive sensors also an original circuit base on a capacitor-frequency converter with a linear characteristic obtaine by using an equivalent negative capacitance. Key-wors: PSPICE conuctance moel; tactile sensor interface; negative capacitance; LAPLACE analysis. 1. Introuction This paper presents recent research about the optimal esign of an interface between the transucer element an the analog circuit in orer to use the output signal by one analog to igital converter. There were analyze two types of sensors: tactile tensoresistive force sensor an capacitive sensor [1]. Thus, there is continue an original iea (patente by author [2]) an an electronic schematic topology which is iscusse in another article [3]. Base on practical observations, it was esigne an optimize schematic using PSPICE simulation with complex moels that approximates the real working environment.

2 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics 401 Also, there is escribe an original metho of linearization using a negative capacitance calculate base on the LAPLACE analysis of the one auxiliary circuit ae to the main oscillator. This auxiliary circuit, calle Neutroyne is a neutralization circuit an it provies a negative capacitance that compensates the parasitic one. The result is a signal with linear frequency, epening on the force or pressure applie. This linearization metho can be use in a variety of other applications: mechatronic systems, walking analysis, micro-electromechanical systems (MEMS) [4, 5]. 2. The tactile sensor The tactile resistive force sensors provie by Tekscan Company-USA type FlexiForce A was teste. The tactile sensor is mae by laminating two flexible an polyester/polyamie thin films (thickness: inch), each of them being covere with a silver film which serves as a conuctor an play the role of electroes that efine the geometry of the sensitive area in the shape of a circle. Between the two circular silver electroes is inserte a pressure sensitive layer mae out of special ink. When the sensor is unloae, its resistance is very high (1 5 MΩ) an proportional with pressure applie is the inverte value of the resistance (conuctance) [6]. These sensor are fabricate with elastic material in four layers, as showe in the Fig. 1, an they consist of: layer of electrically insulating plastic; an active area which consists of a pattern of conuctors, which is connecte to the leas on the tail to be connecte with the interface circuit; a plastic glue between the two layers, aligne with the active area; flexible substrate coate with a thick polymer conuctive film, aligne with the active area. This polymer is very often replace by a layer of ink. Fig. 1. Tactile sensor structure (elaminate) [7] (color online). The FlexiForce type has better force sensing properties, linearity, hysteresis, rift, an temperature sensitivity than any other thin-film force sensors. The active sensing area is a iameter circle at the en of the sensor. The entire sensing area of the FlexiForce sensor is treate

3 402 Anghel Constantin as a single contact point. For this reason, the applie loa shoul be istribute evenly across the sensing area to ensure accurate an repeatable force reaings [6]. There are many ways to integrate the FlexiForce sensor into an application. One way is to incorporate it into one force-to-voltage circuit optimize an presente below using a PSPICE moeling for it. 3. PSPICE moeling of the tactile sensor For an optimal esign of the interface circuit, there were investigate multiple circuits topologies for simulation an moeling of components with values as close to reality as physical circuit. Thus, for the sensor was esigne a moel base on linear sources in orer to create a voltage controlle conuctance (1/R). This allows the complex simulations an analysis such as the step response (transient analysis), linearity, frequency response, Monte Carlo analysis an others. The symbol for voltage controlle conuctance is shown in Fig. 2. Where: CTRL+ an CTRL represents the connections for control voltage use in range 0 10V, an G1, G2 are the two connections of the controlle conuctance with real range of the sensor use. Fig. 2. Symbol for Voltage Controlle Conuctance(color online). The moel for voltage controlle conuctance is presente in the stanar PSPICE irective in Table 1: Table 1. The PSPICE moel coe ************ Voltage controlle conuctance *************** ****PSPICE MODEL SUBCIRCUIT***** *CONDUCTANCE noe 1, 2,CONTROL noe 4, 5* ***********************************************.SUBCKT VCConuctance ERES 1 3 VALUE = {I (VSENSE)*500K/ (V (4, 5) )} VSENSE 3 2 DC 0V.ENDS VCConuctance

4 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics Circuit Simulations an Results The circuit from Fig. 3 shows the initial circuit use for simulation. For a goo common moe noise rejection an a linear response with conuctivity variation of sensor, an original configuration base on an instrument amplifier was use, but the sensor is place instea of the common resistor which classically establishes the gain. Fig. 3. The initial circuit with cable parasitic capacitance moels(color online). Actually, it is the classically instrumentation amplifier to which were ae new components such as parasitic capacitances of the connections wires between the sensor an the circuit (C6) an between the output of the circuit circle as Part A an the input of the circuit U1B from Part C. The U1B an U1C are place remotely, they are connecte with U1B, with a twiste pair ribbon cable which has parasitic capacitances (C3, C4 an C5) with values about 20 30nF, moele as part B. Fig. 4 shows the step transient response of the sensor pressure signal in the N range. The resistors values were calculate so that the maximum output signal oes not excee 2.5V accoring with the maximum allowable in the input of the analogue to igital converter. Fig. 5 shows the result of the AC frequency analysis simulation. From the behavior of AC analysis it can be observe that the circuit has a transfer function similar with the LPF type with a cutoff frequency approximately 10KHz, but the simulations are revealing an instability at zero loa forces (equivalent resistance of the sensor has high values 2MOhms) by the occurrence of a parasitic oscillation with a frequency aroun 300KHz. Analyzing the reasons of the unwante oscillations occurring in the case of small pushing forces (very small conuctance an very high resistance of the sensor) it was foun that the OPAMP oes not accept at the output capacitive loas higher than 100pF (From the atasheet of use operational amplifier) [8]. The measure value of the cable capacitance is aroun of nf units an can be reuce using the same simple methos. A goo solution is the topological placement of the R3 an R6 resistors near the U1A an U1C amplifier output of section A, which continues with the cable wires (section B) to the input of the U1B amplifier in section C. The new topology of the circuit has been moele an simulate as shown in Fig. 6. Fig. 7 shows the step transient response result after simulations of the new circuit in which the unwante oscillations isappear even at the very high resistance of the tactile sensor.

5 404 Anghel Constantin Fig. 4. Transient step response (color online). Fig. 5. The AC analysis of circuit from Fig. 3 (color online). Fig. 6. Optimal topologies of the interface circuit (color online).

6 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics 405 The symmetry of the input circuit also ensures the symmetry of the rise an fall times of the output signal [9]. Fig. 7. Simulation results of Transient Step response (color online). The instrumentation circuit which is splitte in two parts is one of the original ieas for the analog signals that are place remotely in a ifferential moe with multiple avantages erive from it. The input circuit is symmetric, it is place near the sensor, the ifferential outputs are transmitte at 1m istance an this operation improves global signal to noise ratio. Another goo iea is to place the resistors R3 an R6 near the outputs of the amplifiers from Part A an, so, the capacitance of ribbon cable forms an RC low pass filter. Fig. 8 shows the AC analysis simulation results, which means a characteristic frequency of the global interface circuit an a tactile transucer. The missing of the oscillations an the overshoot is obvious here. In general, the frequency behaviour of the sensor is equivalent to one LPF with Cutoff Frequency aroun 46KHz. This is a very goo result about the ynamically response which is relative to one tactile sensor with a tensoresistive ink. Fig. 8. Simulation results of AC Analysis response (color online).

7 406 Anghel Constantin 5. The capacitive sensor In moern applications of mechatronics the MEMS technology has been rapily integrate an is expecte to evelop as a future specialty being use in a wie range of applications in meical research [5, 10]. The capacitive elements are among the most common electrical effects of MEMS technology either as esirable elements or as parasitic effects [10]. Capacitance is the ability of a capacitor to store an electrical charge. A common form name as parallel plate capacitor an the capacitance is efine by relations C = Q / V, where C is the capacitance relate by the store charge Q at a given voltage V. If the istance between the two electroes or their effective area changes, the capacitance of the evice changes accoringly. So, the capacitive elements can be use as sensors to measure a wie range of mechanical an physical properties [11]. For example, they are utilize as force sensors or isplacement sensors [12, 13]. Base on CMOS (Complementary Metal-Oxie-Semiconuctor) technologies, simple oscillators can be built to achieve capacitance-frequency converters. A multitue of research papers have been evote to improving the linearity an overall stability performance of these types of capacitive sensors. 6. Analysis of plate capacitor geometry errors In Fig. 9 shows a simplifie planar capacitor with non-parallel parallelepipe plates. Fig. 9. Geometrical parameters of non-parallel plate capacitor (color online). If we note with C the capacitance between the plates of charge capacitor with +Q an Q (after a bias uner a voltage V). Base on notation presente in Fig. 9 an after same integral calculation steps, we obtain the relation (1) [14, 15]: C = ε 0ε r l (1 tan(α) ln + L ) sinα (1) Were ε 0 an ε r is the absolute an relative permittivity of material between plates. For verification of the result accoring with ieal parallel plate capacitance classical formula can be write (2): lim α 0 C α = lim α 0 ε 0 ε r l ln(1+ L sinα) tanα L Hospital ======= ε 0 ε r l lim α 0 L cos α 1+ L sin α 1+tan 2 (α) = ε 0ε r l L = ε0εrll (2)

8 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics 407 In relation (1) if α = 0 then can be write the Taylor general approximation (3) with the variable x = 0: Or if applie in (1) then obtain (4): ln(1 + x) = x (3) C α = ε 0 ε r l tan(α) L sin α = ε 0ε r S cos α (4) If notate with err the capacitance error than ieal parallel plate value C ieal = ε0εrs then can be write (5): err = C ieal C α = C ieal (1 cos α) (5) In Table 1 is represente the value of calculate error with relation (6) from angle between 0 to 45 egree: err[%] = C ieal C α C ieal 100 (6) Table 2. The calculate values of error α cos(α) err[%] In the Fig. 10 is showe the curve error from the ieal capacitor accoring to the angle α. For practical implementation accoring with the Fig.11, I use a very classically oscillator which is schematic with a CMOS NAND gate type CD4093 (Schmitt Trigger) circuit which is showe below with schematic presente in Fig. 12 [17]. Without external RC elements, the Schmitt Trigger Gate can be assimilate with an amplifier with supra-unitary gain. So, the RC components create a elaye reaction an the output will not have a stable state, but will become unstable. The waveforms in points A an B are shown in Fig. 13.

9 408 Anghel Constantin Fig. 10. Error curve in percent (color online). Fig. 11. Practical implementation of capacitive sensor (color online). Fig. 12. The classically topology of Schmitt Trigger oscillator (color online).

10 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics 409 Fig. 13. The waveform of the input V A an output V B (color online). In orer to calculate the oscillation perio T we must solve the following ifferential equation see the expressions (7), (8), (9): Which leas to: When T 1 2 i c t + R i c = U 0 (7) c 0 RC i c t + i c = U 0 C or i c t + 1 RC i c = U 0 R i c = U 0 R e t RC or uc = U 0 1 e t RC (9) (8) { uc = V T + U 0 = V OL u c = V T U 0 = V OH (10) By solving the equation system (10) above results the expression of Perio T as (11): T = t 1 + t 2 (11) From (12) an (13) we can notice that (14): ( VDD V ) T t 1 = RC ln V DD V T + ( VT ) + t 2 = RC ln V T (12) (13) T = k 1 RC an C = ε 0 S T = k 1 R ε 0 S (14) Where in expressions (12) an (13) the VDD is the rain power supply voltage an the VT an VT+ is the Schmitt Trigger threshol voltage. The k1 epens on VDD, VT an VT+, it also

11 410 Anghel Constantin has a thermal coefficient of variation with temperature. If consier the general plate capacitive formula, the frequency freq is calculate in relations (15), (16) an (17) [16]. freq = 1 T = k 1 R ε 0 S an = 0 (15) Where is the capacitor layer isplacement proportional with applie force F (16). = k 2 F (16) freq = k 1 R ε 0 S K 2 k 1 R ε 0 S F = f 0 K F (17) Where, from relations (17) result the relations (18). f 0 = k 1 R ε 0 S an K = K 2 k 1 R ε 0 S Theoretically, the variation shoul be linear, but in a real system the parasitic capacitances that occur are not negligible. The CMOS NAND GATE atasheet [17] says the input capacitance is 5pF, but the useful capacitance for isk type armatures with a 20 mm iameter an the istance 0 = 1mm is C0 4,7pF, which is very close to the parasitic one an also we must a the capacitance of the mechanical system, which leas us to reconsier the relation (17) as follows relations (19) an (20): (18) freq = 1 T = 1 ( ) = ε k 1 R 0 S + C 0 P = ( k 1 R 1 ε 0 S+C p( 0 k 2 F ) 0 K 2 F ) ( k 1 R 1 ε 0 S+C p( 0 ) 0 ) = (19) freq = ( 0 k 1 R ε 0 S+C p ( 0 k 2 F ) ) ( k 2 K 1 R ε 0 S+C p ( 0 k 2 F ) ) F (20) We can notice that both f0 an K epen on F, but in a very non-linear way because of parasitic capacitance C p. Experimental results obtaine with R=2MΩ are presente an the characteristic being almost parabolic. The solution for native linearization is an electronic compensation of a parasitic capacitance using a neutroyne circuit for achieving a negative capacitance. If there were analyze the equivalent impeance at the input of the circuit showe in Fig. 14, where G is assimilate with one ipothetic gain factor, to be eterminate in orer to obtain a negative capacitance. Taking into account Kirchhoff s law an LAPLACE formalism, we obtain (21) an (22). i = i 1 + i 2 (21)

12 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics 411 sc e u = sc 1 u + sc 2 (Gu u) (22) Fig. 14. The negative capacitance circuit using Laplace analysis (color online). If: Then: C 1 = C 2 (23) C e = C 1 (1 G) (24) If assuming (23) we obtain (24). The amplifier from the Fig. 14 must provie a zero phase shift on the entire banwith of the transucer an a high impeance input. These requirements can be achieve using a phase-equalize broaban amplifier with irect coupling an gain G=3, such as the schematic shown in Fig. 15. The parasitic capacitance that must be compensate is aroun 6pF, so we select C2 such that C2(1-G) = 6pF. So the results are C2=3pF. We choose C =2.2pF to be uner the critical values an G is set using a potentiometer Rv. 7. Experimental results The experimental results reporte here were obtaine uring research an are base on measurements taken after practical implementation of the original circuit with the schematic iagram shown in Fig. 15 [1, 3]. Base on relation (20) an after some calculus, the frequency of the oscillator can be written as (17). Where F is the applie force an freq is the frequency. Practically, after a few measurements an ajusting of the gain G by the potentiometer Rv can be obtaine the maximum linearity without instability an then can be consiere that negative reactance is assimilate as an equivalent C e = Cp. The tests were mae using the testing evice for tension/compression moel Hounsfiel H10KT having a loa cell with the measuring omain 1 10kN. The loaing parts use provie an uniform istribution of the loa on the sensor sensible area. In the same time, it was measure the output frequency using a Velleman Frequency Counter moel DVM13MFC2U.

13 412 Anghel Constantin Fig. 15. The schematic use in experimental research (color online). Measurements effectuate in the Metrology Laboratory of the National Institute for Mechatronics from Bucharest shows that the output frequency response becomes linear with a force applie, as showe in Fig. 16. Fig. 16. The equivalent capacitance (Ce) an the linearity influence of K (color online). If C e = Cp the relation of frequency variation with applie force is very close to relations (17) an (18): The relation above was valiate experimentally an the linearization of the response was confirme for the use transucer, after the linearization with the metho escribe above. The experimental results are base on the practical implementation of the schematic e-

14 Optimal esign of resistive an capacitive sensors interfaces use in moern mechatronics 413 scribe in Fig. 15 which yiele the following values of the constants (that are corresponing with theoretical calculations): f0=278 khz an K = 695 Hz/N [1, 3]. The circuit presente works well in an application for measuring groun reaction forces uring human walking. 8. Conclusions By complex moeling of the real elements of electronic circuits use in sensors interface esign, there can be obtaine a goo optimization an a conclusion about the behavioral response of the sensors. After these simulations, there were reveale important aspects of ynamic behavior an there was propose an optimal variant of the interface circuit as a non-typically topology instrumentation ifferential amplifier spitte in two parts, one near to the sensor, an the secon far from the sensor an close to an A/D converter of the ata acquisition system. Also, we escribe a circuit for ensuring a negative capacitance in orer to neutralize the parasitically one. The iea of negative capacitance can be applie on a large variety of electronic circuits that use amplifiers, oscillators an interfacing for capacitive circuits mae by hybri technology or by integrating into MEMS technology [6, 7]. From the tests mae with the two types of sensors resulte that resistive tactile sensors may be use to measure the GRF on the groun in more points of the foot sole, in goo conitions of linearity an repeatability, while the capacitive sensors may be use specially to measure the pressure an not to measure the real force value evelope by the foot uring gait. References [1] ANGHEL V. Constantin, GHEORGHE I. Gheorghe, Stuy of piezoresistive an capacitive tactile sensors moeling an simulation for the best linearity with applications in moern microelectronics an walking analysis, in: IEEE Conference Publications, International Semiconuctor Conference (CAS), IEEE Proceeings 2017, pp [2] ANGHEL Constantin, DUMITRU Sergiu, Patent no / 08 August 2007, in: OSIM, BPOI no. 9/2009, Bucharest, Romania, pp [3] ANGHEL Constantin, GHEORGHE Ion Gheorghe, CMOS transucer with linear response using negative capacitance for the force measurement in human walking analysis with applications in MEMS an NEMS technologies, in: Springer Lecture Notes on Electrical Engineering, pp , [4] GHEORGHE Ion Gheorghe, ANGHEL Constantin, DUMITRU Sergiu, Microingineria Mems & Nems Inteligente, Eitura CEFIN, Bucureti, Romania, pp. 52, [5] T. FUJITA, K. MASAKI, F. SUZUKI, AND K. MAENAKA, Wireless MEMS sensing system for human activity monitoring, in: Proceeings of IEEE/ICNE International Conference on Complex Meical Engineering, pp , [6] FLEXIFORCE, FlexiForce Sensor A201 User Manual (Rev I), at: efaultfiles/resources/flexiforce%20sensors%20revi.pf, pp. 10. [7] Open Music Labs Analog an Digital Technique, Force Sensitive Resistors (FSRs), at: Figure 9. [8] Datasheet, TL084ACD, at: pp.25 26, 2004.

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