State Space Modeling, Simulation and Comparative Analysis of a conceptualised Electrical Control Signal Transmission Cable for ROVs

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1 Sae Space Modeling, Simulaion and omparaive Analysis of a concepualised Elecrical onrol Signal ransmission able for ROVs James Naganda, Deparmen of Elecronic Engineering, Konkuk Universiy, Seoul, Korea Absrac Elecrical signal ransmission cables can be mahemaically modeled eiher by lumped parameers approach or disribued parameers approach depending on he frequency of he signal o be ransmied Unlike high frequency signal ransmission sysems, ow frequency elecrical ransmission cables such as Remoe Operaed Vehicle (ROV) conrol signal cables (ehers) can be modeled using lumped parameer approach In his paper, we model, simulae and analyse he behaviour of a concepualised elecrical cable ha is used o ransmi low frequency elecrical conrol signals We concepualise a cable as if resisance, capaciance and inducance are placed a paricular disinc poins along he cable he models are analysed and compared by increasing he magniude of R (Resisor, Inducance and apaciance) componens for a fixed lengh versus increase in lengh by replicaing he same R componens of he cable along ransmission line by he same facor Analysis of responses from hese models is made subjec o sep and square inpu signals omparison was based on mos popular parameers ha are used in ransien signal responses Simulaion resuls confirmed he signal dumping effec of increasing he cable lengh Index erms umped parameers, Signal ransmission ables, ROV ables, Sae Space Model, Simulaion I INRODUION Modelling elecrical signal ransmission cable requires prior knowledge abou he frequency of he signal o be ransmied [3] and his dicaes he modelling mehod Unlike signals in high frequency bands such as radio frequency bands where ransmission sysems are modelled by disribued parameer approach using parial differenial equaions[],[], lower frequency ransmission cables such as conrol signal ransmission sysems can modelled by lumped parameer approach using Ordinary Differenials Equaion [],[] hese low frequency conrol signals are pracically applicable in Remoe Operaed Vehicles (ROV) deployed in subsea aciviies which can be moniored Manuscrip received Jan, 4 Firs Auhor name, Elecronic Engineering, Konkuk Universiy, Seoul, Korea, onshore In ROVs, conrol signal cables are aligned and shielded ogeher wih daa ransmission cables such as opical cables o ransmi signals such as row video daa required for real-ime subsea Monioring [5] In his paper, we base on well known behaviour of R circuiry subjec o signal source [] and model a low frequency elecrical based ransmission cable using Ordinary Differenial Equaions (ODEs) Our aim is no o propose a novel echnique bu o make a concepualised comparaive analysis We firs model arbirarily an lengh cable ( Model) wih specified magniude of R componens as depiced in (fig ) We furher model lengh cable ( model) by duplicaing he firs model along he ransmission lengh Based on he firs model in (fig), we also develop anoher model by using a cable of fixed lengh bu doubling he magniude of R componens (Va model) as depiced in secion IV hese models are simulaed subjec o boh sep and square inpu signals Oupu signals are analysed and he behaviour of he sysem models are compared based on rise ime, peak ampliude, seling ime and final sae value of he oupu signal II R OMPONENS SAE SPE (SSM) MODE he relaion beween he volage V R, across he resisor, R and he curren hrough i, I R caused by poenial difference across i, is ohmic in naure [6], [] and is described in () I V ; I V RI R R R R R R Unlike in resisors, he volage across he capacior changes wih respec o imehe rae a which he volage across he capacior changes wih respec o ime is proporional o he charging curren hrough i and inversely proporional o he magniude of is capaciance[6],[] as shown in () () All Righs Reserved 3 IJSER 5

2 dvc( ) dv ( ) ( ) ( ) c ic ic d c d For an inducor, he charging curren changes wih ime and is proporional he volage applied across i and inversely proporional o he magniude of is inducance [6], [] as shown from equaion (3) di( ) di( ) V( ) V( ) d d () (3) X ()= Ax()+ Bu() y()= x()= Du() R R /, R R /, / / / / / / R /, 5 F /, R, and, l H / () (8) Having already described he behavior of each R componen in ODE perspecive in secion II, we model enire cable in secions III and IV based on hese R fundamenals III INREASED ENGH ABE MODE Based on individual R componen sae space represenaion in (), () and (3), he circui in (figb) can be represened in sae space in expressions (4) For simpliciy, based on assumpions (8), respecive SSM marices are depiced in (9) / / A / R / / ( R R ) / B /, R, and, D (9) dvc () d V () _ i ( ) V ( ) c di () R i d i() di() R R ( ) d (4) Vc () Vo ( ) R i ( ) Vi ( ) i () ISSN: 8 98 I is a common pracice o express such models in a sandard sae space model in () and we do so by assumpions in (5) o ge expression (6) according our circui in figb V ()= x (),i ()= x (),i ()= x (), c 3 V ()= y(),andv ()= u() o x () i / - / x () = - / -R / x () + / u() x () 3 / -(R + R ) / x () 3 x () 3 y() = R x () + u() (4) (5) x () x () 3 (6) x () x () 3 y() = R x () + u() All Righs Reserved 4 IJSER A ENGH ABE MODE In his model, we duplicae he R componens in fig (b) along he ransmission line o make i double lengh of he firs model he double lengh model () is depiced in fig () By considering respecive loops, we ge expression in () dvc() d dvc () / / Vc( ) d / / Vc ( ) di () / R / i ( ) / Vi () d / / R / i ( ) di () / ( R R) / i( ) d di() d Vc() Vc () Vo ( ) R i() Vi ( ) i () i() () We again represen expressions () in form of () o ge () ha makes i easier for simulaions subjec o inpu signals X( ) / / x( ) X( ) / / x( ) X3( ) / R/ x3( ) / u () / / R / x4( ) X4( ) / ( R R) / x5( ) X5( ) x( ) y( ) x( ) Rx3( ) u( ) x4( ) x5( ) () 53

3 aking assumpions in (8) and (), SSM marices are depiced in (3) / / /, / / / / / R R R / R / R / ( R R ) / ( R R ) / () V IRUI MODE REPRESENAION is a Uni lengh of he cable in he model R is he resisance of he cable per uni lengh in Ω/ is inducance of he cable per uni lengh in H/ is capaciance of he cable per uni lengh in F/ R/ / / R/ R (a) / / / / A / R / / / R / / ( R R ) / A (3) B / ; R, and, D R R oop oop Figure an lengh cable represenaion Vi (b) R/ / / R/ (A) R/ / / R R R/ / / R/ R mere (B) mere R R R IV INREASED R VAUES MODE While in secion III, we duplicaed lumped parameers in model along ransmission lengh o make model, in his secion we concepualise he cable as if he R magniude were increased bu keeping is lengh o develop model Va model Ic() i() i(i) i() oop oop3 Ic() oop R Vi() mere () Figure a concepualised lengh cable model Vo() Based on expressions (6), () and (8), we double he values of R componens associaed wih circuiry depiced in fig (b) o obain model (4) / / A / R /, / ( R R ) / B /, R, D (4) VI SIMUAION RESUS For simulaions, he following assumpions were made o invesigae he model response subjec o boh sep and square inpu signals R = Ω/m, = H/m and = 5 μf/m and he load is aω resisor I is worh menioning ha for a square wave, he signal used in our simulaions was V, a 5 Hz All Righs Reserved 3 IJSER 54

4 Figure 3 Sep signal response for model Figure 6 Sep signal response for model Figure4 Square Signal response for model Figure Square inpu signal response for model Figure5 Daa saisics for figure 4 ISSN: 8 98 All Righs Reserved 4 IJSER 55

5 6 onclusion he aim was o model, simulae a concepualised a low-frequency-signal ransmission cable by increasing R values versus increasing lengh by duplicaing R componen along he same concepualised elecrical signal ransmission cable and make a comparaive analysis Boh sep and square signal inpu responses showed ha increasing lengh ( model ) had a poor response if quick seling sysem is required compared wih doubling magniude of R componen his delay in seling was due o high overshoo Figure8 Sep signal response for Va model oncepually, duplicaing R values along ransmission line increases oscillaions of an signal leading o under damped response hus, no suiable for quick response demanding conrols sysems REFERENES Figure9 Square inpu signal response for Va model able Verical (Volage) variable daa saisics for square signal response [] Sefan Bilbao and Julius O, Discree-ime umped Models Smih III, MUS4/EE36A ecure D, ener for ompuer Research in Music and Acousics (RMA), Deparmen of Music, Sanford Universiy Sanford, Jan, 3 [] Modeling a R ircui's urren wih Differenial Equaions, Kenny Harwood, May, [3] Rodriguez Valdez, Suden Member, R M allam, Senior Member, RJKerman, A New Frequency-Dependen-Model for ables Elecro/Informaion echnology, IEEE Inernaional onference, May, 8 [4] yco Elecronics, Umbilical and eher cables for Subsea ROV Applicaions, April, 8 [5] Horn, Gaylor Super Phanom S Remoely Operaed Vehicle User s Guide, NOAA ooperaive Insiue for Ocean Exploraion, Research, and echnology [6] John O Aia, Elecronics and ircui Analysis using MAAB, R Press, 999 [] Analyse R second order parallel circuis using dualiy [online] hp://wwwdummiescom/how-o/conen/analyze-an-rlc-secondorder-pa rallel-circui-using-hml M o d e l Min Max Mn Mdn Mod Sd Rng James Naganda holds An Msc Degree in ommunicaions Engineering from he Rober Gordon Universiy (RGU), Scoland He is now a PhD candidae in Elecronics Engineering a Konkuk Universiy, Souh Korea His research focuses bu no limied o DSP, Video and Image Processing, onrol Sysems Engineering He has worked also on Fiber Opic ommunicaion Sysems for subsea remoe sensing projecs He has co-auhored differen papers on Video coding using SIMD insrucions He someimes involves himself in simulaions of concepualised Sysems for Signal ransmissions like he one in his paper V a he parameer values presened here are Minimum (Min), Maximum (Max), Mean (Mn), Mode (mod), Sandard (Sd) and Range (Rng) All Righs Reserved 3 IJSER 56