Establishment the parasitic oscillation model’s balance control of LA-FSM by using strain controlled electronic hinge

The analysis and establish model for noise in the lever balance control channel is essential for minimize effect of noise to the accuracy of the system. The paper presents methods and analysis results, establishes mathematical models for these parasitic oscillation noises.

Research ESTABLISHMENT THE PARASITIC OSCILLATION MODEL’s BALANCE CONTROL OF LA-FSM BY USING STRAIN CONTROLLED ELECTRONIC HINGE Pham Thanh Ha* Abstract: In the lever balance control channel of the lever amplification force standard machine using strain controlled electronic hings is always exist parasitic oscillation noise The affect of these noises to the accuracy of the lever balance establishing is very significant, affected to establishing accuracy of output Deadweight force The analysis and establish model for noise in the lever balance control channel is essential for minimize effect of noise to the accuracy of the system The paper presents methods and analysis results, establishes mathematical models for these parasitic oscillation noises Keywords: Lever Amplification Force Standard Machine; Electronic hing; Parasitic oscillation noise INTRODUCTION Lever Amplification Force Standard Machine (LA-FSM) is a high-accuracy force measurement standard Extending values of range and improve its accuracy is always a scientific and practical requirement in the field of force measurement Therefore, LA-FSM uses strain controlled electronic hinge is the most potential solution to solve the above requirement To improve the accuracy of LA-FSM using strain controlled electronic hinge, it is necessary to minimize the effect of parasitic oscillation noise in the lever balance control channel, particularly the pendulum noise and bounce-mode noise [1, 2] Therefore, the study and analysis of the mechanism of formation, composition, characteristics and establish mathematical model of parasitic oscillation noise in LA-FSM are very necessary for the problem of building solutions to minimize the effects of noise to the accuracy of the system ANALYSIS AND ESTABLISHMENT OF THE LABOR-INTERACTIVE PATIENT MODEL IN LA-FSM Considering the LA-FSM with the principle of generating force as shown in Fig.1 Lever amplification Long lever arm side strain controlled electronic hinge H3 XL-CT Sort lever arm side KĐĐL H2 H1 Deadweight Force l1 l2 Lever Force m F1 F2 Figure Model of LA-FSM's principle of generating force Journal of Military Science and Technology, Special Issue, No.60A, 05 - 2019 31 Electronics & Automation Where: F1 - the force generated by the Deadweight force generation system; F2 - Arm force to balance arm; H1, H2 and H3 - are three electronic hinge; KDĐL – amplification measures stage of signals from lever unbalance sensor; XL-CT stage of machining processing signals and indicate results 2.1 Establishment of pendulum noise in the Deadweight force system Based on the LA-FSM principle, during operating the Deadweight force generation system has structure of a single pendulum system, thus its oscillating also following the physical rules of a single pendulum system (Figure 2) By analyzing the single pendulum system for Deadweight force system as follows    P  FC  maht (1) (2) P cos  FC  m.aht FC  Where: mv2  mg cos l v  gl cos   cos   FC  3mg cos   mg cos   mg  3cos   cos   (3) (4) Figure A single pendulum system where: m - mass of load; g - gravitational acceleration; l - length of pendulum; α and α0 - deflection angle at any position and at the position of oscillation amplitude; v and v0 - velocity at any position and at the equilibrium position; P weight of load; FC - Deadweight force optical tension (rope tension in the single pendulum system) Considering a single pendulum system with a small amplitude, the oscillation equation of the generating force system has the form s  S cost    , where: S   l - amplitude of oscillation;   g / l - angular frequency of oscillation Since then (4) has the form: FC  mg 3 cos  cos  t     cos   (5) When considering the amount of deviation between apparent gravity (static state) and weight-load tension force (dynamic state) is the component of the force 32 Pham Thanh Ha, “Establishment the parasitic oscillation model’s … electronic hinge.” Research noise caused by the style of pendulum oscillation (referred to as pendulum dynamic noise – FNcl), we can write (6) FNcl  P  FC  mg 1  cos   cos  cos  t    Eq.(6) is also the mathematical model of oscillating parasitic noise in the mechanical form in the Deadweight force generation system Caused α0 and φ are random values with dominant properties, type of pendulum oscillation noise in the Deadweight force generating system is also a random and dominant values 2.2 The interaction and bounce-mode noise model in the Deadweight force generation system Stacking effects of factors: Environmental temperature, force of Acsimet, electromagnetic force, inertial force will make alter the oscillation of the pendulum After analysis and synthesis can take Eq (5) and Eq (6) as follows (7) FC    mg A cos  cos   t     cos   (8) FN    mg 1  cos   A cos  cos   t    where:  2TC  a qE a0   TC  a qE a  (9) A        ;      TC     R m m g  R m m g  In the air the pendulum-type damped oscillation of the Deadweight force generation system, under the combined effect of the above factors, the Eq (7) and Eq (8) can be rewritten as (10) FC   td  mg A  cos  e  k t / cos   td t     cos     td   FN  td  mg  cos  A cos  e where,   td     TC   ktd t /  (11) cos n   td t    (12) cos td t    2 TC  a qE a k td2 l ,     R m m g 4g ktd – damping coefficient Can be rewritten Eq (11) as follows  F N   td  A0  A 2n n 1        6     x   x  x where: A  mg 1  cos x  A 1             ;    1.2 1.2 2.32         n    1  1   x    x  x      ; x  m  0ektd t / n 2  2  A2 n  2mg  1 A  1        n!  1.n  1 1.2.n  1n          Thus, parasitic oscillation noise in the generating force system can be expanded into Fourier series as equation (12) Accordingly, noise is a combination of lowJournal of Military Science and Technology, Special Issue, No.60A, 05 - 2019 33 Electronics & Automation frequency components referred to as pendulum-type vibration, while components with higher frequency are referred to as bounce-mode-type vibration [1, 2] 2.3 Influence, characteristics of parasitic oscillation noise in LA-FSM In LA-FSM, the output Deadweight force of the main system equal to force generated from the Deadweight force generation system is amplified by the ratio of the lever arms QLA = l1/l2, then F2  F1  F1   Q LA (13) With: ΔF1 is the total deviation of the force generated at the Deadweight force generation system When considering the existence of pendulum-type and bounce-mode-type oscillation, the mathematical model of the output force from the lever arm-force transmission system or LA-FSM will be l1  l2 l l cos  td t     2mg cos   F1 N l2 l2 F2 / N  P  F( N   td )1  F1 N   mg l1 A cos  e  ktd t / l2   (14) Where: F(N-Σtd)1 – components of pendulum-type and bounce-mode-type oscillation noise Deadweight force generation of system such as (11); ΔF1-N – deviation or errors caused by difference factors from pendulum-type and bouncemode-type oscillation noise At this time, the generated force component from the lever arm force transmission system is being affected by parasitic oscillation noise can be described as follows l F N   td 2  mg 1  cos   A cos  e  ktd t / cos  td t    (15) l2    The parasitic noise has been amplified to QLA so that it retains the characteristics as non-white random noise (color noise), which has a domination and heavy-tailed distribution noise (HT noise) The effect of parasitic oscillation noise in LA-FSM force generation may be preliminarily evaluated when considering F( N   td ) mg l1 l   cos   A cos  e  ktd t / cos  td t       P.Q LA mg l1 l          cos  A cos  e ktd t / cos td t    (16) Simulating Eq (16) shows that the effect of parasitic oscillation noise is quite big, where the most significant influence is Archimedes and inertial forces Accordingly, when requesting LA-FSM reach to an error less than 2.10-4 without taking into the influence of Archimedes force, or reach to an error less than 1.10-5 without taking into also the effect of inertial force included in the component of this noise is really not feasible Thus, the mathematical analysis of mechanical changes in LA-FSM shows the kinetic model of the parasitic oscillation arising from the system's generating force 34 Pham Thanh Ha, “Establishment the parasitic oscillation model’s … electronic hinge.” Research principle, thereby indicating the mechanism, composition, influence level and characteristics of this parasitic oscillation ESTABLISH THE SIGNAL MODEL IN LA-FSM ’s LEVER BALANCING CONTROL CHANNEL USING STRAIN CONTROLLED ELECTRONIC HINGS 3.1 Momentary forces in lever amplifiers and LA-FSM lever balancing equations Consider LA-FSM with a lever amplifier using strain controlled electronic hinge as shown in Figure [3] With this design, when the lever is imbalance, momentary forces is created at the electronic hinge will create the surface deformation at the rotating center axis of the elastic hinges This distortion is perceived and transformed into corresponding electrical signals by deformed stamp sensors The deformed stamp sensors are used in the diagram to sense the moment component created by the imbalance of the lever Therefore, these signals help to detect the imbalance and then re-establish the balance of the lever LA-FSM's lever balance control model is shown in Figure Ma l1 Mb l2 βc la βa Mc lb βb maht P Fhtb F1 F2 F2 Figure Momentary force in blow amplifier system When the lever is controlled to equilibrium, that is βa → 0, then the bending moment Ma at H1 reaches the value as M a  2mgla cos e  ktd t / cos td t     cos  (17) Considering the curvature of the lever when increasing the load, that is, at the equilibrium but βa = βa0 + βacong(F1) = βacong(F1 ) > Then we have M a  2mgla cos0 e ktdt / cos td t   cos0   mgla sin  acong(F1 ) (18) Journal of Military Science and Technology, Special Issue, No.60A, 05 - 2019 35 Electronics & Automation FN F1 Ma + F2 Mc1 H1 H3 Mc2 Mb H2 u1 u3 KĐĐL XL-CT PC u2 ∆F2 Uđc Lever balancing control channel BTĐB Control by hand ĐCCB ĐKĐC Figure LA-FSM lever balancing model using strain controlled electronic hinge In other words, when the curvature of the load due to the weight of the load is taken into account, the Eq (18) will be a mathematical description of the bending moment component generated at H1 caused by the parasitic vibration and curvature at the equilibrium Similarly, the bending moment Mb is formed at the electron bearing H2 by the radial component of the output load with the arm as the transmission shaft (Figure 3) Therefore, the bending moment Mb can be written as (19) M b  F htb  l b where: lb – the length of the hanging optical beam - the arm force transmission point; Fhtb – The radial force component of the output load caused at the transmission to the test object (due to the sliding effect), which is caculated as follows (20) Fhtb  F2   F2 sin  b where βb – angle of deviation from equilibrium at position H2; ∆F2 - deviation Therefore, the Mb torque moment at H2 can be caculated as follows (21) M b  Fhtb  l b  F2   F2 sin  b  l b When the controlled lever reaches its equilibrium, that is βb → then Mb → However, if the shift of the transmission shaft (due to installation) is considered, that is, at the equilibrium, but βb = βb0 + βblech = βblech > 0, we have (22) M b  F2  F2 l b sin  blech Eq.(22) describes the bending moment component at H2 when the lever is balanced Bending moment Mc formed at H3 electronic hinge from two moments, in which the first moment is caused by the force generated by the load force system with long arm l1, The second moment is caused by the force generated from the transmission system that carries the ratio of the arm to the short arm l2 Accordingly, the bending moment at H3 in this case can be written as follows (23) M c  F1 cos  c  l1  F2   F2 cos  c  l 36 Pham Thanh Ha, “Establishment the parasitic oscillation model’s … electronic hinge.” Research where: βc – angle deviation from equilibrium at position H3; l1 – length of long arm; l2 – the length of the short arm; F1 – force components generated from the load force generation system; F2 – the force generated from the proportional arm force transmission system; ∆F2 – Total deviation and correction amount to achieve the equilibrium In the case if parasitic oscillation noise is considered, that is F1 = P – F(N-Σtd)1 + ΔF1-N, The bending moment at H3 will be (24) M c  P  F( N   td )1   F1 N l1 cos  c  F   F l cos  c When the lever is at the equilibrium, that is βc → then M c  P  F( N   td )1   F1 N l1  F   F l   mgA cos e  ktd t / cos  td t     2mg cos    F1 N l1  F2  F2 l (25) If we consider the system of torque in the lever amplifier system to be flat, when the lever reaches its equilibrium, the lever balancing equation will be formed as follows M  M a  M b  M c  (26) Replace the expressions of the corresponding moments, gives 2mgl a cos e  ktd t / cos  td t     cos    mgl a sin  acong   F2  F2 l b sin  blech   mgA cos e  ktd t / cos td t     2mg cos   F1 N l1  F2  F2 l  (27) We have  2la  Al1    la  l1  cos e ktdt / cos td t     2mg  cos  mg  l2  lb sin blech   l2  lb sin  blech  la l1  mg sin  acong  F1N md  F2  F2 l2  lb sin blech l2  lb sin blech la Fmd  mg sin  acong l  lb sin  blech (28) (29) Where: ΔF1-N-md - Deviation components caused by factors other than parasitic oscillation noise; ΔFmd – The wrong component is caused by distortion of the lever arm (the curve is bent due to the weight of the load) To achieve the equilibrium, the total deviation and correction force at the right arm force transmission system are  2l a  A l1    l a  l1  cos  e  ktd t / cos   td t     mg   cos   mg   l  l b sin  blech   l  l b sin  blech  la l1 l  mg sin  acong  F1 N  md  mg   F2 (30) l  l b sin  blech l  l b sin  blech l2   Thus, the equilibrium of lever and the correcting force to establish lever balance can be determined from the moment equation (30) The accuracy of LA-FSM using electronic hinge will depend on the ability to determine this calibrating force 3.2 The signal in the lever amplifier using strain controlled electronic hinge From the principle of electronic hinge design and system structure implementation, each electronic hinge is attached with deformed stamp circuit Journal of Military Science and Technology, Special Issue, No.60A, 05 - 2019 37 Electronics & Automation which is sensitive to desired deformation In H1 electronic bearings, the deformed bridge circuit is used to ensure the best sensitivity to deformation caused by Ma bending moment Therefore, the sensitivity of the deformed stamp as S1 and the output signal at H1, the imbalance of the lever can be expressed as follows     u1  S1  M a  S1mgl a cos  e  ktd t / cos   td t     cos   S1mgl a sin  a (31) When hit reaches equilibrium, this signal reaches the value of     u1  2S1mgla cos  e ktd t / cos td t     cos  S1mgla sin  acong (32) At the H2 electronic hinge, the deformed bridge circuit is installed to ensure the best sensitivity to the distortions caused by the bending moment Mb Therefore, with the sensitivity of the deformed stamp bridge selected as S2, the electrical signal at the output will be (33) u  S  M b  S F2  F2  sin  b  l b When the lever reaches its equilibrium, this signal has the following value (34) u  S F2  F2 l b sin  blech At H3 electronic hinge, the deformed bridge circuit is installed to ensure the best sensitivity to the deformation caused by bending moment Mc Therefore, with the sensitivity of S3, the output signal at H3 can be written as u3  S3  M c  S3 P  F( N  td )1  F1 N l1 cos  c  F2  F2 l2 cos  c    S mgA cos e  k t / cos  td t     2mg cos    F1 N l1 cos  c  (35)  S3 F2  F2 l cos c td And when reaching equilibrium, this signal will be u  S mgA cos e  k t / cos  td t     2mg cos    F1 N  l1  S F2  F2   l (36) td As described above, the electrical signals received from H1, H2 and H3 carry information about the imbalance or balance of the lever amplifier system, with mathematical models corresponding to expressions from 31 to 36 These signals are amplified, digitized and filtered noise by the optimal method of measuring measurement information as described in Figure u1 Amp Indicators AD H1 u21 H21 u22 Urđk H22 u3 Optimal signal synthesizer and filter H3 Figure Diagram describing blocks of Amplifier and Indicator When the sensitivity coefficients on electronic bearings (including elastic hinges, deformed bridge circuit and Amplifier) are designed to satisfy the equation 38 Pham Thanh Ha, “Establishment the parasitic oscillation model’s … electronic hinge.” Research (14), the processing of these electrical signals allows detecting the imbalance of the lever and provides the corresponding data to control and establish the equilibrium with the moment equation Supposing the synthesis of signals in discrete form is done according to the Equation: u (k ) u (k ) u (k ) x(k )    , (37) S1 S2 S3 Then, the Eq.(37) is identical to Eq (27) in the continuous form The detection and establishment of the equilibrium is carried out according to Eq (37) in discrete form completely similar to Eq (27) in continuous form On the other hand, with the random characteristics and "mutation" of noise, we can consider building the modified Kalman filter algorithm according to Student's t distribution to perform parasitic noise filtering, including pendulum oscillation noise and bounce-mode type in channel balance control [4, 5] This is also the future research to improve the effectiveness of the proposed model, which will be presented in the next paper CONCLUSION In this paper, author proposed a noise model by mathematical analysis of force, torque and signal in the lever balancing control channel with LA-FSM using electronic hinge, thereby showing the mechanism of formation and establishment of parasitic oscillating noise model, including pendulum vibration and bobbing pattern The construction of this noise model will facilitate the study of characteristics and its impact on the accuracy of the system (due to some limitations, the results of this study will be presented in the next paper) Based on the noise model and its characteristics, we can build a filtering algorithm that optimizes the lever balancing control channel to improve the accuracy of LA-FSM One of the most appropriate approaches is using the modified Kalman filter algorithm according to Student's - t distribution REFERENCES [1] Yon-Kyu Park and Dae-Im Kang, Pendulum motion of a Deadweight forcestandard machine, Measurement Science and Technology, Volume 11, Number 12, 2000 - iopscience.iop.org [2] Yon-Kyu Park, Dae-Im Kang, Rolf Kumme and Amritlal Sawla, Investigation of the Dynamic Behaviour of PTB Deadweight force Standard Machines, Proceedings of the 17th International Conference on Force, Mass, Torque and Pressure Measurements, IMEKO TC3, 17-21 Sept 2001, Istanbul, Turkey [3] Lim C K., Bernd G and Thomas A., New developments in lever-amplified force standard machines, Proceedings of XVII IMEKO World Congress, June 22 - 27, 2003, Dubrovnik, Croatia [4] Huang Y, Zhang Y, Li N, Chambers JA Robust Student's t Based Nonlinear Filter and Smoother IEEE Transactions Aerospace and Electronic Systems 2016, 52(5), 2586-2596 Journal of Military Science and Technology, Special Issue, No.60A, 05 - 2019 39 Electronics & Automation [5] Berntorp, K.; Di Cairano, S Approximate Noise-Adaptive Filtering Using Student-t Distributions, TR2018-088 July 13, 2018 TĨM TẮT THIẾT LẬP MƠ HÌNH NHIỄU DAO ĐỘNG KÝ SINH TRONG KÊNH ĐIỀU KHIỂN CÂN BẰNG ĐÒN CỦA LA-FSM SỬ DỤNG GỐI ĐIỆN TỬ ĐIỀU KHIỂN THEO ĐỘ BIẾN DẠNG Trong kênh điều khiển cân đòn máy chuẩn lực tải tỷ lệ cánh tay đòn sử dụng gối điện tử điều khiển theo độ biến dạng tồn nhiễu dao động ký sinh Tác động nhiễu đến độ xác thiết lập cân đòn đáng kể, làm ảnh hưởng đến độ xác thiết lập lực tải đầu Việc phân tích xác lập mơ hình cho nhiễu kênh điều khiển cân đòn cần thiết cho toán giảm thiểu ảnh hưởng nhiễu đến độ xác hệ thống Bài báo trình bày phương pháp kết phân tích, thiết lập mơ hình tốn học cho nhiễu dao động ký sinh Từ khóa: Máy chuẩn lực tải tỷ lệ cánh tay đòn; Gối điện tử; Nhiễu dao động ký sinh Received 29th March 2019 Revised 10th April 2019 Published 15th May 2019 Address: 40 Vietnam Metrology Institute, Hoang Quoc Viet, Cau Giay, Hanoi * Email: hapt@vmi.gov.vn Pham Thanh Ha, “Establishment the parasitic oscillation model’s … electronic hinge.” ... used in the diagram to sense the moment component created by the imbalance of the lever Therefore, these signals help to detect the imbalance and then re-establish the balance of the lever LA-FSM' s... using strain controlled electronic hinge In other words, when the curvature of the load due to the weight of the load is taken into account, the Eq (18) will be a mathematical description of the. .. model by mathematical analysis of force, torque and signal in the lever balancing control channel with LA-FSM using electronic hinge, thereby showing the mechanism of formation and establishment of