Read the research attached here, mainly the first three pages (Abstract, Introduction, Definition of the Problem), to formulate a one-page abstract paper. The abstract paper should include and answer:1- Why is this research important?2- What are the research questions associated with it?3- What is the state of art of this research in 2021?4- Find five references to use, and at least two of them must be peer-reviewed (They can be the same as the references from the last page of the research)
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/293098755 In-orbit identification of drag-free satellite dynamics Article · January 2006 CITATIONS 0 READS 38 3 authors, including: Some of the authors of this publication are also working on these related projects: Satellite Launch Vehicle (VLS-1) View project Inertial Systems for Aerospace Applications View project Waldemar de Castro Leite Filho Castro Leite Consultoria 75 PUBLICATIONS 260 CITATIONS SEE PROFILE Michel Guilherme National Institute for Space Research, Brazil 9 PUBLICATIONS 13 CITATIONS SEE PROFILE All content following this page was uploaded by Waldemar de Castro Leite Filho on 06 March 2017. 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This new key technology allows to reduce the resid- ual accelerations on experiments on board satellites significantly. In or- der to achieve this very low disturbance environment (for some missions < 10−14m/s2) the drag-free control system has to be optimized. this optimization process is required because of uncertainties in system param- eters which demand a robustness of the control system. the paper will present an approach for the in-orbit identification of a drag-free control system. the discussion includes the modeling, possible excitation signals as well as simulation results. introduction drag-free control (dfc) is an enabling technology for current and future scientific space missions. its concept follows the approach to create a real free-fall environment by com- pensating the external non-gravitational (non-conservative) forces on the satellite. this can be achieved either by forcing the satellite to follow a free-flying proof mass or by using the test mass as an accelerometer. in the latter case the motion of the test mass with respect to the satellite is driven to zero. the acceleration needed to keep the test mass at zero position is then used as a measurement for compensating the external forces. achieving this, accelerations on the test mass as well as on the satellite can be reduced to a very low level which allows the execution of high sensitive experiments, e.g. fundamen- tal physics experiments like the test of the equivalence principle. this experiment is the goal of the two future missions micro-satellite à traînée compensée pour l’observation 1iae - instituto de aeronáutica e espaço, 12228-904 - são josé dos campos (sp), brazil, phone: +55 12 39474654 fax: +55 12 39474621, e-mail:
[email protected] 2zarm, center of applied space technology and microgravity, university of bremen, germany, phone: ++49 (0) 421 218-3551, fax: ++49 (0) 421 218-4356, e-mail:
[email protected] 3zarm, center of applied space technology and microgravity, university of bremen, germany, phone: ++49 (0) 421 218-4786, fax: ++49 (0) 421 218-4356, e-mail:
[email protected] 2 du principe d’equivalence (microscope) by onera and cnes and the satellite test of the equivalence principle (step) by stanford university. for that purpose both mis- sion will carry differential accelerometers in order to measure the differential acceleration between two test masses of different materials. the classical drag-free satellite can be seen as two satellites in one. a small inner satellite (proof mass) is located in a cavity inside of a larger (normal) satellite. the cavity contains sensors (capacitive, magnetic or optical) which determine the position of the proof mass with respect to the outer satellite. the main satellite has small thrusters which are providing a fine tuned thrust in order to chase the proof mass which then always remains centered in the cavity. definition of the problem the goal of the drag-free control system is the creation of a low disturbance environment. its quality is determined by the quality of the drag-free control system. in case that the test masses are used as an accelerometer the control of the test mass is also influencing the overall drag-free performance. since the measurement of the test mass position can not be obtained without applying a force on the test mass, a dynamic coupling exists between the satellite and the proof mass. this coupling can be modeled as a spring and a damper between the two corresponding bodies (see figure 1). these coupling coefficients need to be known for an optimal design of the control system. therefore they need to be estimated with a proper process. so, the main goal of this work is to propose a strategy to identify parameters of a drag-free satellite. for simplicity, in this work only one direction of the translational motion of a drag-free satellite is considered. the satellite is controlled by using measurements of two differential accelerometers. each accelerometer has two test masses (tm) or inertial sensors as it is proposed for microscope and step [11]. important parameters for the control are the damping and elastic coupling (stiffness) co- efficients that exist between the test masses and between the satellite and test masses. as shown in figure 1, there are 12 coefficients (6 elastic and 6 damping) to be determined. in addition, each test mass is controlled by an electrostatic actuator [3, 11]. the satellite is controlled by small proportional thrusters for example field emission electric propulsion (feep) thrusters [8]. the dynamics of all these actuators can be also determined by the identification process. modeling the derivation of the models is presented in detail in [2]. it is based on the work published in [5, 13]. if we consider the model shown in figure 1 the equations of motion for the satellite can be written for the satellite as: 3 figure 1: pictorial representation of a drag-free satellite with two differential accelerome- ters m · ẍs = ffeep − fdrag − fact11 + k11 · (x11 − xs) + β11 (ẋ11 − ẋs) − fact12 + k12 · (x12 − xs) + β12 (ẋ12 − ẋs) − fact21 + k21 · (x21 − ẋs) + β21 (ẋ21 − xs) − fact22 + k22 · (x22 − xs) + β22 (ẋ22 − ẋs) (1) where ffeep is the specific force of the actuation system, fdrag is the drag force, factij is the actuation force on test mass j in accelerometer i, xij is the absolute position of test mass j in accelerometer i, kij and βij are the corresponding stiffness and damping coefficients of the coupling. for the test mass 1 of accelerometers 1 we can write: m11 · ẍ11 = fact11 − k11 · (x11 − xs)− β11 (ẋ11 − ẋs) + k13 · (x12 − x11) + β13 (ẋ12 − ẋ11) + β13 (ẋ12 − ẋ11) . (2) if we substitute the relative positions of the test masses with respect to the satellite: x11 = x11 − xs; x12 = x12 − xs; x21 = x21 − xs; x22 = x22 − xs. (3) then the acceleration of the satellite or the second derivative of the satellite position be- comes: 4 ẍs = ffeep m − fdrag m − fact11 m + k11 m · x11 + β11 m · ẋ11 − fact12 m + k12 m · x12 + β12 m · ẋ12 − fact21 m + k21 m · x21 + β21 m · ẋ21 − fact22 m + k22 m · x22 + β22 m · ẋ22. (4) in the following, what will be done for the equation of motion of one test mass, it’s ana- log for the other test masses of the two accelerometers considered. then, for the local displacements we get: ẍ11 + ẍs = fact11 m11 − k11 m11 · x11 − β11 m11 · ẋ11 − k13 m11 · (x12 − x11)− β13 m11 · (ẋ12 − ẋ11) (5) then the laplace transform for test mass 1 of accelerometer 1 is: ( s2 + β11 + β13 m11 s + k11 + k13 m11 ) · x11(s) = ( β13 m11 s + k13 m11 ) · x12(s) + fact11 m11 (s)− as(s) (6) where as(s) denotes the satellite acceleration xs. we consider that the control loop feeds back the test mass position. then the controller is called c1(s) for test mass 1 and c2(s) for test mass 2. in addition, it is assumed that the controllers are identical for both accelerometers. for identification we have test signals. the test signals (ts) can be placed as a reference for the control system (tsijref ) or as a command signal to the actuators (tsijcom) which is added to the output of the controller. so, the actuation for each test mass is given by: factij mij (s) =kmij(s) · uij(s) =kmij(s) · [tsijcom + cj(s) · (tsijref − xij(s))] (7) where kmij(s) is the gain of the test mass actuator. figure 2 shows the block diagram of one differential accelerometer with all the possible excitation inputs. if we substitute equation 7 in equation 6 we get after some manipulations equation 8 for test mass 1 on the accelerometer 1: ( s2 + β11 + β13 m11 s + k11 + k13 m11 ) · x11(s) = ( β13 m11 s + k13 m11 ) · x12(s) + km11(s) · u11(s)− as(s) (8) 5 figure 2: accelerometer block diagram the controller of the drag-free satellite is denoted as cdf (s). it is considered that the control loop feeds back information from the two accelerometers [11, 14] in a weighted form. where η1 and η2 are the balance coefficients (η1 + η2 = 1). the output of each accelerometer is the mean of its test masses position. the block diagram of a satellite with two differential accelerometers is shown in figure 3. as for the test mass control, possible test signals (ts) for the satellite control can be placed as reference of control system tsref or commanded as an addition tscom to the command signal. so, the actuation for the satellite is given by ffeep m (s) = kdf (s) · udf (s) = kdf (s)·[ tsdfcom + cdf (s) · ( tsdfref − η1 · x11(s) + x12(s) 2 − η2 · x21(s) + x22(s) 2 )] . (9) the laplace transform of equation 4 with equations 7 and 9 results in 6 figure 3: complete block diagram of the satellite with one accelerometer 7 as(s) = kdf (s) · udf (s)− fdrag m (s) −km11(s) · u11(s) + β11 · s + k11 m · x11(s)−km12(s) · u12(s) + β12 · s + k12 m · x12(s) −km21(s) · u21(s) + β21 · s + k21 m · x21(s)−km22(s) · u22(s) + β22 · s + k22 m · x22(s)· (10) identification approach for the accelerometers if we consider the controller structures (c1(s) in equation 7 (similar for the others test masses), and consequently in equation 8, and (cdf (s) in equation 9, and consequently in equation 10 (for the satellite), it will increase the complexity of the parameter estimation process. then, it comes the question on how to estimate the parameters of a controlled sys- tem without to consider the controller structure. this problem can be overcome because it is possible to identify the plant like it is in open-loop, regardless whether the data have been collected under 10−14m/s2)="" the="" drag-free="" control="" system="" has="" to="" be="" optimized.="" this="" optimization="" process="" is="" required="" because="" of="" uncertainties="" in="" system="" param-="" eters="" which="" demand="" a="" robustness="" of="" the="" control="" system.="" the="" paper="" will="" present="" an="" approach="" for="" the="" in-orbit="" identification="" of="" a="" drag-free="" control="" system.="" the="" discussion="" includes="" the="" modeling,="" possible="" excitation="" signals="" as="" well="" as="" simulation="" results.="" introduction="" drag-free="" control="" (dfc)="" is="" an="" enabling="" technology="" for="" current="" and="" future="" scientific="" space="" missions.="" its="" concept="" follows="" the="" approach="" to="" create="" a="" real="" free-fall="" environment="" by="" com-="" pensating="" the="" external="" non-gravitational="" (non-conservative)="" forces="" on="" the="" satellite.="" this="" can="" be="" achieved="" either="" by="" forcing="" the="" satellite="" to="" follow="" a="" free-flying="" proof="" mass="" or="" by="" using="" the="" test="" mass="" as="" an="" accelerometer.="" in="" the="" latter="" case="" the="" motion="" of="" the="" test="" mass="" with="" respect="" to="" the="" satellite="" is="" driven="" to="" zero.="" the="" acceleration="" needed="" to="" keep="" the="" test="" mass="" at="" zero="" position="" is="" then="" used="" as="" a="" measurement="" for="" compensating="" the="" external="" forces.="" achieving="" this,="" accelerations="" on="" the="" test="" mass="" as="" well="" as="" on="" the="" satellite="" can="" be="" reduced="" to="" a="" very="" low="" level="" which="" allows="" the="" execution="" of="" high="" sensitive="" experiments,="" e.g.="" fundamen-="" tal="" physics="" experiments="" like="" the="" test="" of="" the="" equivalence="" principle.="" this="" experiment="" is="" the="" goal="" of="" the="" two="" future="" missions="" micro-satellite="" à="" traînée="" compensée="" pour="" l’observation="" 1iae="" -="" instituto="" de="" aeronáutica="" e="" espaço,="" 12228-904="" -="" são="" josé="" dos="" campos="" (sp),="" brazil,="" phone:="" +55="" 12="" 39474654="" fax:="" +55="" 12="" 39474621,="" e-mail:=""
[email protected]="" 2zarm,="" center="" of="" applied="" space="" technology="" and="" microgravity,="" university="" of="" bremen,="" germany,="" phone:="" ++49="" (0)="" 421="" 218-3551,="" fax:="" ++49="" (0)="" 421="" 218-4356,="" e-mail:=""
[email protected]="" 3zarm,="" center="" of="" applied="" space="" technology="" and="" microgravity,="" university="" of="" bremen,="" germany,="" phone:="" ++49="" (0)="" 421="" 218-4786,="" fax:="" ++49="" (0)="" 421="" 218-4356,="" e-mail:=""
[email protected]="" 2="" du="" principe="" d’equivalence="" (microscope)="" by="" onera="" and="" cnes="" and="" the="" satellite="" test="" of="" the="" equivalence="" principle="" (step)="" by="" stanford="" university.="" for="" that="" purpose="" both="" mis-="" sion="" will="" carry="" differential="" accelerometers="" in="" order="" to="" measure="" the="" differential="" acceleration="" between="" two="" test="" masses="" of="" different="" materials.="" the="" classical="" drag-free="" satellite="" can="" be="" seen="" as="" two="" satellites="" in="" one.="" a="" small="" inner="" satellite="" (proof="" mass)="" is="" located="" in="" a="" cavity="" inside="" of="" a="" larger="" (normal)="" satellite.="" the="" cavity="" contains="" sensors="" (capacitive,="" magnetic="" or="" optical)="" which="" determine="" the="" position="" of="" the="" proof="" mass="" with="" respect="" to="" the="" outer="" satellite.="" the="" main="" satellite="" has="" small="" thrusters="" which="" are="" providing="" a="" fine="" tuned="" thrust="" in="" order="" to="" chase="" the="" proof="" mass="" which="" then="" always="" remains="" centered="" in="" the="" cavity.="" definition="" of="" the="" problem="" the="" goal="" of="" the="" drag-free="" control="" system="" is="" the="" creation="" of="" a="" low="" disturbance="" environment.="" its="" quality="" is="" determined="" by="" the="" quality="" of="" the="" drag-free="" control="" system.="" in="" case="" that="" the="" test="" masses="" are="" used="" as="" an="" accelerometer="" the="" control="" of="" the="" test="" mass="" is="" also="" influencing="" the="" overall="" drag-free="" performance.="" since="" the="" measurement="" of="" the="" test="" mass="" position="" can="" not="" be="" obtained="" without="" applying="" a="" force="" on="" the="" test="" mass,="" a="" dynamic="" coupling="" exists="" between="" the="" satellite="" and="" the="" proof="" mass.="" this="" coupling="" can="" be="" modeled="" as="" a="" spring="" and="" a="" damper="" between="" the="" two="" corresponding="" bodies="" (see="" figure="" 1).="" these="" coupling="" coefficients="" need="" to="" be="" known="" for="" an="" optimal="" design="" of="" the="" control="" system.="" therefore="" they="" need="" to="" be="" estimated="" with="" a="" proper="" process.="" so,="" the="" main="" goal="" of="" this="" work="" is="" to="" propose="" a="" strategy="" to="" identify="" parameters="" of="" a="" drag-free="" satellite.="" for="" simplicity,="" in="" this="" work="" only="" one="" direction="" of="" the="" translational="" motion="" of="" a="" drag-free="" satellite="" is="" considered.="" the="" satellite="" is="" controlled="" by="" using="" measurements="" of="" two="" differential="" accelerometers.="" each="" accelerometer="" has="" two="" test="" masses="" (tm)="" or="" inertial="" sensors="" as="" it="" is="" proposed="" for="" microscope="" and="" step="" [11].="" important="" parameters="" for="" the="" control="" are="" the="" damping="" and="" elastic="" coupling="" (stiffness)="" co-="" efficients="" that="" exist="" between="" the="" test="" masses="" and="" between="" the="" satellite="" and="" test="" masses.="" as="" shown="" in="" figure="" 1,="" there="" are="" 12="" coefficients="" (6="" elastic="" and="" 6="" damping)="" to="" be="" determined.="" in="" addition,="" each="" test="" mass="" is="" controlled="" by="" an="" electrostatic="" actuator="" [3,="" 11].="" the="" satellite="" is="" controlled="" by="" small="" proportional="" thrusters="" for="" example="" field="" emission="" electric="" propulsion="" (feep)="" thrusters="" [8].="" the="" dynamics="" of="" all="" these="" actuators="" can="" be="" also="" determined="" by="" the="" identification="" process.="" modeling="" the="" derivation="" of="" the="" models="" is="" presented="" in="" detail="" in="" [2].="" it="" is="" based="" on="" the="" work="" published="" in="" [5,="" 13].="" if="" we="" consider="" the="" model="" shown="" in="" figure="" 1="" the="" equations="" of="" motion="" for="" the="" satellite="" can="" be="" written="" for="" the="" satellite="" as:="" 3="" figure="" 1:="" pictorial="" representation="" of="" a="" drag-free="" satellite="" with="" two="" differential="" accelerome-="" ters="" m="" ·="" ẍs="fFEEP" −="" fdrag="" −="" fact11="" +="" k11="" ·="" (x11="" −="" xs)="" +="" β11="" (ẋ11="" −="" ẋs)="" −="" fact12="" +="" k12="" ·="" (x12="" −="" xs)="" +="" β12="" (ẋ12="" −="" ẋs)="" −="" fact21="" +="" k21="" ·="" (x21="" −="" ẋs)="" +="" β21="" (ẋ21="" −="" xs)="" −="" fact22="" +="" k22="" ·="" (x22="" −="" xs)="" +="" β22="" (ẋ22="" −="" ẋs)="" (1)="" where="" ffeep="" is="" the="" specific="" force="" of="" the="" actuation="" system,="" fdrag="" is="" the="" drag="" force,="" factij="" is="" the="" actuation="" force="" on="" test="" mass="" j="" in="" accelerometer="" i,="" xij="" is="" the="" absolute="" position="" of="" test="" mass="" j="" in="" accelerometer="" i,="" kij="" and="" βij="" are="" the="" corresponding="" stiffness="" and="" damping="" coefficients="" of="" the="" coupling.="" for="" the="" test="" mass="" 1="" of="" accelerometers="" 1="" we="" can="" write:="" m11="" ·="" ẍ11="fact11" −="" k11="" ·="" (x11="" −="" xs)−="" β11="" (ẋ11="" −="" ẋs)="" +="" k13="" ·="" (x12="" −="" x11)="" +="" β13="" (ẋ12="" −="" ẋ11)="" +="" β13="" (ẋ12="" −="" ẋ11)="" .="" (2)="" if="" we="" substitute="" the="" relative="" positions="" of="" the="" test="" masses="" with="" respect="" to="" the="" satellite:="" x11="x11" −="" xs;="" x12="x12" −="" xs;="" x21="x21" −="" xs;="" x22="x22" −="" xs.="" (3)="" then="" the="" acceleration="" of="" the="" satellite="" or="" the="" second="" derivative="" of="" the="" satellite="" position="" be-="" comes:="" 4="" ẍs="fFEEP" m="" −="" fdrag="" m="" −="" fact11="" m="" +="" k11="" m="" ·="" x11="" +="" β11="" m="" ·="" ẋ11="" −="" fact12="" m="" +="" k12="" m="" ·="" x12="" +="" β12="" m="" ·="" ẋ12="" −="" fact21="" m="" +="" k21="" m="" ·="" x21="" +="" β21="" m="" ·="" ẋ21="" −="" fact22="" m="" +="" k22="" m="" ·="" x22="" +="" β22="" m="" ·="" ẋ22.="" (4)="" in="" the="" following,="" what="" will="" be="" done="" for="" the="" equation="" of="" motion="" of="" one="" test="" mass,="" it’s="" ana-="" log="" for="" the="" other="" test="" masses="" of="" the="" two="" accelerometers="" considered.="" then,="" for="" the="" local="" displacements="" we="" get:="" ẍ11="" +="" ẍs="fact11" m11="" −="" k11="" m11="" ·="" x11="" −="" β11="" m11="" ·="" ẋ11="" −="" k13="" m11="" ·="" (x12="" −="" x11)−="" β13="" m11="" ·="" (ẋ12="" −="" ẋ11)="" (5)="" then="" the="" laplace="" transform="" for="" test="" mass="" 1="" of="" accelerometer="" 1="" is:="" (="" s2="" +="" β11="" +="" β13="" m11="" s="" +="" k11="" +="" k13="" m11="" )="" ·="" x11(s)="(" β13="" m11="" s="" +="" k13="" m11="" )="" ·="" x12(s)="" +="" fact11="" m11="" (s)−="" as(s)="" (6)="" where="" as(s)="" denotes="" the="" satellite="" acceleration="" xs.="" we="" consider="" that="" the="" control="" loop="" feeds="" back="" the="" test="" mass="" position.="" then="" the="" controller="" is="" called="" c1(s)="" for="" test="" mass="" 1="" and="" c2(s)="" for="" test="" mass="" 2.="" in="" addition,="" it="" is="" assumed="" that="" the="" controllers="" are="" identical="" for="" both="" accelerometers.="" for="" identification="" we="" have="" test="" signals.="" the="" test="" signals="" (ts)="" can="" be="" placed="" as="" a="" reference="" for="" the="" control="" system="" (tsijref="" )="" or="" as="" a="" command="" signal="" to="" the="" actuators="" (tsijcom)="" which="" is="" added="" to="" the="" output="" of="" the="" controller.="" so,="" the="" actuation="" for="" each="" test="" mass="" is="" given="" by:="" factij="" mij="" (s)="Kmij(s)" ·="" uij(s)="Kmij(s)" ·="" [tsijcom="" +="" cj(s)="" ·="" (tsijref="" −="" xij(s))]="" (7)="" where="" kmij(s)="" is="" the="" gain="" of="" the="" test="" mass="" actuator.="" figure="" 2="" shows="" the="" block="" diagram="" of="" one="" differential="" accelerometer="" with="" all="" the="" possible="" excitation="" inputs.="" if="" we="" substitute="" equation="" 7="" in="" equation="" 6="" we="" get="" after="" some="" manipulations="" equation="" 8="" for="" test="" mass="" 1="" on="" the="" accelerometer="" 1:="" (="" s2="" +="" β11="" +="" β13="" m11="" s="" +="" k11="" +="" k13="" m11="" )="" ·="" x11(s)="(" β13="" m11="" s="" +="" k13="" m11="" )="" ·="" x12(s)="" +="" km11(s)="" ·="" u11(s)−="" as(s)="" (8)="" 5="" figure="" 2:="" accelerometer="" block="" diagram="" the="" controller="" of="" the="" drag-free="" satellite="" is="" denoted="" as="" cdf="" (s).="" it="" is="" considered="" that="" the="" control="" loop="" feeds="" back="" information="" from="" the="" two="" accelerometers="" [11,="" 14]="" in="" a="" weighted="" form.="" where="" η1="" and="" η2="" are="" the="" balance="" coefficients="" (η1="" +="" η2="1)." the="" output="" of="" each="" accelerometer="" is="" the="" mean="" of="" its="" test="" masses="" position.="" the="" block="" diagram="" of="" a="" satellite="" with="" two="" differential="" accelerometers="" is="" shown="" in="" figure="" 3.="" as="" for="" the="" test="" mass="" control,="" possible="" test="" signals="" (ts)="" for="" the="" satellite="" control="" can="" be="" placed="" as="" reference="" of="" control="" system="" tsref="" or="" commanded="" as="" an="" addition="" tscom="" to="" the="" command="" signal.="" so,="" the="" actuation="" for="" the="" satellite="" is="" given="" by="" ffeep="" m="" (s)="KDF" (s)="" ·="" udf="" (s)="KDF" (s)·[="" tsdfcom="" +="" cdf="" (s)="" ·="" (="" tsdfref="" −="" η1="" ·="" x11(s)="" +="" x12(s)="" 2="" −="" η2="" ·="" x21(s)="" +="" x22(s)="" 2="" )]="" .="" (9)="" the="" laplace="" transform="" of="" equation="" 4="" with="" equations="" 7="" and="" 9="" results="" in="" 6="" figure="" 3:="" complete="" block="" diagram="" of="" the="" satellite="" with="" one="" accelerometer="" 7="" as(s)="KDF" (s)="" ·="" udf="" (s)−="" fdrag="" m="" (s)="" −km11(s)="" ·="" u11(s)="" +="" β11="" ·="" s="" +="" k11="" m="" ·="" x11(s)−km12(s)="" ·="" u12(s)="" +="" β12="" ·="" s="" +="" k12="" m="" ·="" x12(s)="" −km21(s)="" ·="" u21(s)="" +="" β21="" ·="" s="" +="" k21="" m="" ·="" x21(s)−km22(s)="" ·="" u22(s)="" +="" β22="" ·="" s="" +="" k22="" m="" ·="" x22(s)·="" (10)="" identification="" approach="" for="" the="" accelerometers="" if="" we="" consider="" the="" controller="" structures="" (c1(s)="" in="" equation="" 7="" (similar="" for="" the="" others="" test="" masses),="" and="" consequently="" in="" equation="" 8,="" and="" (cdf="" (s)="" in="" equation="" 9,="" and="" consequently="" in="" equation="" 10="" (for="" the="" satellite),="" it="" will="" increase="" the="" complexity="" of="" the="" parameter="" estimation="" process.="" then,="" it="" comes="" the="" question="" on="" how="" to="" estimate="" the="" parameters="" of="" a="" controlled="" sys-="" tem="" without="" to="" consider="" the="" controller="" structure.="" this="" problem="" can="" be="" overcome="" because="" it="" is="" possible="" to="" identify="" the="" plant="" like="" it="" is="" in="" open-loop,="" regardless="" whether="" the="" data="" have="" been="" collected="">