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Developrnent of 2DOF Actuation Slosh Rig: A Novel Mechatronic Systern Prasanna S. Gandhi, Member, IEEE, Jatinder Mohan, Keyur B. Joshi, N. Ananthkrishnan Indian Institute of Technology, Bombay, Mumbai MH, India gandhi@me.iitb.ac.in URL: www.me.iitb.ac.in/ gandhi Abstract Sloshing of liquid in a tank is important in sev- pitching excitation for a tank held by means of a torsion eral areas including launch vehicles carrying liquid fuel in bar. Several researchers [3], [4], [6], [5] have reported ex- space application, ships, and liquid cargo carriages. Hence modeling and characterization of nonlinear slosh dynamics perimental study of slosh using linear excitation and re- is critical for study of dynamics of these systems. Addition- sults are compared with that obtained from analytical and ally control of sloshing liquid offers a challenging problem of FEM models. More recently Gangadharan et al. [8] have control of underactuated systems. To study slosh dynamics, reported Spinning Slosh Test Rig (SSTR). develop useful identification schemes, and design and verify slosh control algorithms, a new 2DOF actuation slosh rig Thus to the best of our knowledge, a two simultaneous is reported in this paper considering the fact that most of DOF excitations have not been reported thus far. How- the times the liquid tanks are subjected to linear as well as pitching excitation. The paper discusses mechatronic de- ever, the actual motion of vehicle carrying the tank (may sign and several advantages offered by the new design. Fur- be rocket or satellite or aircraft) may involve both linear thermore, a mathematical model of the rig is developed us- part and rotational part simultaneously also not neces- ing Lagrange formulation assuming two-pendulum model for sarily in the same plane. So the motion of liquid with slosh. Slosh parameter identification with the rig is demon- strated in pitching and linear excitation cases. Nonlinear both these excitations being a nonlinear phenomenon can parameter identification schemes developed using simplified be quite complex than that with a single DOF excitation. version of rig model are used for the purpose. Further re- Thus, for more realistic study, it is important to provide sults on compensation of slosh and rotary slosh phenomena are presented. Thus the proposed rig is ideal tool for study, motion to the tank, which is closer to the actual motion identification, and control of slosh phenomena. experienced by the tank in launch vehicles. Even other- wise, study of nonlinear slosh dynamics, identification and I. INTRODUCTION control with two DOF actuation would be quite interesting and challenging academically. With this motivation, this Detrimental effects of liquid sloshing are experienced in ape propoes acnewitetlri With 2- Dotuation. a number of areas, including the transportation of liquid . . . tanks, aircraft, and launch ve- aner importantwpoint with th pOp designi ~~~~~~~Another important point with the proposed design is cargo, storage of liquid in hil fetak.Ilanhvhcsor spcerat fr e e-improvement in theidea of measurement scheme. The proposed ample,fueltanksmotIons gdancecran, resulting from s cotrol design uses a novelbase of mounting a six axis forcewill see trans- system commandmotionsorest theafu eidncle ancceraion andte canminduce from ge ca aneletiq- ducer right at the liquid tank. This, as we and can induce sloshing. As the fuel is consumed and liq- later avoids need for expensive pressurized oil film suspen- sloshing. As iS consmed uid level changes with time, slosh dynamics can be fur- sion to reduce friction noise in the measurement of forces ther complicated and make the system unstable. A slosh- and moments. This design will bring down drastically the induced instability may lead to structural failure, drift from cost of scaled versions for actual space vehicle tanks. Sev- desired trajectories, higher fuel consumption, premature eral experiments carried out with the rig verifies its effec- engine shutdown or inability of the spacecraft to achieve tiveness at accurate measurement of slosh forces and mo- upper-stage engine start. A recent article by Vreeburg [1] ments in all the directions. presents some examples of failures caused by sloshing. From academic perspective, the rig offers a platform to It is important to study and characterize the phe- study, characterize, and further develop control algorithms nomenon of sloshing, to develop, identify, and experimen- for complex fluid motions with simultaneous excitations tally verify simple mathematical models of slosh that can of both the DOFs. Such studies are currently underway. be used for mission simulation and control development. Slosh control problem approximated to the first mode of For reliable mission simulation, these models must capture slosh vibration is similar to inverted pendulum. However the true dynamic behavior of the liquid as will be seen by as higher modes get excited it becomes more complex and the vehicle carrying the tank. challenging to develop nonlinear control strategies. Literature on slosh characterization [2], [3], [4], [5], [6], This paper is organized as follows. Section II presents [7], [8], shows that either linear or pitching or spinning mechatronics system of the proposed rig. Sensors, actu- excitation has been provided to the tank to capture the ators, controller and plant are discussed in this section. motion dynamics of interest. Widmayer et al. [2] used Several advantages offered by this new mechatronics de- 1-4244-0726-5/06/$20.OO '2006 IEEE 1810 sign are presented. Section III presents Lagrange formu- lation of nonlinear system dynamics of the rig. Results of experiments carried out to successfully identify slosh pa- rameters with linear and pitching excitation are presented in Section IV. Some interesting experimental results of ro- tary slosh effects and both excitation effects are presented. Finally, Section V concludes research findings. II. PROPOSED MECHATRONIC DESIGN The proposed mechatronic system has a plant consist- ing of mechanisms to drive tank in linear as well as pitch- ing direction. The linear stage motion is realized using a ball screw mechanism. It carries the entire system for / . _ Linear ! _ w ; | ; 3 ; _ e~ x5jAation ! Axisofthetank Tank attached T to the crank ionto ireassembly usingballscrewmechanism i Ballscrew pitching motion. Ball screw arrangement also provides F speed reduction and increase in the linear force necessary to drive the liquid tank. This arrangement is less expensive than electrodynamic shaker [5], [6] or hydraulic actuator [4] used previously for linear DOF excitation but gives the same positioning accuracy for excitation waveform. An- other ball screw arrangement is used to drive the pitching stage through slider crank mechanism where the driver is slider realized using ball screw mechanism. The schematic of the mechanisms is shown in Figure 1. The CG of the tank is matched with the hinge location for the pitching joint. This arrangement helps to get pure pitching motion of liquid. With different fill fractions of liquid in the tank the CG will move off the hinge location by small amount. This can be compensated by adjusting height of the tank on the base. The setup can be converted Fig. 2. Photograph of slosh rig interfaced with PC into 1-DOF actuation by holding linear or pitching actu- ation. Mechanical locking arrangements are provided for both the degrees of freedom for this purpose. lOAD Moreover, arrangement is provided to rotate the axis of the pitching DOF (with respect to direction of linear mo- TANK SULPIDR S LO CElL ACTUATOR tion) in the horizontal plane by 150 degrees. Using this (a)Previous arrangement various possible cases of excitation can be studied. For example, linear motion in one direction and pitching motion of the tank giving excitation in the per- TANK CELL SUPPORT pendicular direction can be possible. The six axis load cell UI OI would measure the slosh forces and moments coming on the tank with this excitation. The photograph of the rig (b)Proposed depicted in Figure 2 shows the assembly of mechanisms for linear and pitching motion along with the respective Fig. 3. Schematic diagram illustrating placement of load cell motors. Sensors: Another novel part in the design of the pro- posed rig is use of six-axis force transducer. To measure tage. Previous rigs used pressurized oil film to support forces, the previous designs [3], [4], [6], [5] used a single the tank to minimize the friction which corrupt their slosh axis force transducer or two force sensors for moment mea- data with frictional force. The location of load cell below surement. With this instrumentation, forces and moments the tank in the proposed design naturally overcomes this generated due to sloshing in all other directions could not problem. Figure 3 shows schematically the previous and be measured. Thus, for example, the effect of linear excita- the proposed way to clarify the point. Thus in the pro- tion in other directions could not be measured. Hence it is posed design, efforts and expenses of putting pressurized proposed to incorporate a six-axis load cell directly below oil film or any such other means to reduce friction can be the tank in our new design. This will capture forces and avoided and at the same time accuracy of measurement of moments due to sloshing in all directions and several cases forces and moments is improved. Of slosh excitation (including rotary slosh) can be charac- Other sensors in the system include encoders used to terized. measure both the motor positions. These are mounted in- This location of six axis load cell gives another advan- tegral with the brushless DC servomotors. The encoder 1811 Tank nPC with mass in the first and second pendulum. The kinetic energy DAQ card (KE) and potential energy (PE) of system as sum of those of individual elements are obtained as /~~~~~~~~ I Tl.2 ITn~2+122 Six-axis stage += KE=m1c9 p2+ l(Ip +mpk2)2 loadcell X S /, , in Linear olinarstary cotole 2\ actuation -m.nk5 ±cosO Tmn5iz2 + 1 (Is, + msTlse)(O1 + 1)2 + )( e t 3 =i MotorH | ~controller 1 l~ + 2mTsir T + s±pel cos(O + 0b1)(O + ~b1) n 1;1 :m:o:to cont C-mOSrOc - Tmslrllpel CoSq5(02 + i) r -Tns 1 T Linear stage for linear excitations IXl + I2 + m 2pe2( ) Motor S c2 -Tms2 i2 + 1 (Is2 + mns2l12e2)(O + 4b2)2 +2ms2r222 + ms2xlpe2 COS(O + 4b2)(O + 4b2) Fig. 4. Schematic diagram of slosh rig interfaced with PC -mns2r'2-' s2,r21pe_2 cos ¢(02 + 0¢)2), cos 0- 1 PE =-mpgk cos 0 + mnsgh, + mslgrl cos 0 -mslglpel cos(O + 0) + mpgh, + ms2gh, output is quadrature; hence position resolution of 1.25 ,um +ms2gr2 cos 0 -ms2glpe2 cos(O + 0b2) (2) is obtained considering reduction in the ballscrew assem- bly. Thus relatively low resolution positioning sensors (en- coders) can be used without sacrificing resolution of tank linear and pitching motion. lp1 Actuators: The design of actuators (in terms of the power) is carried out to drive the rig at least with first three 0 modal frequencies of sloshing. The actuation is carried out \ \1 using brushless DC servomotors from Jayashree Electrode- vices Pvt Ltd. The motion control drives are configured to run these motors in torque control mode based on analog |pe2 input. The required analog control signal is provided by Pendulum Hinges using analog channels of dSPACE [9] 1104 card. 2 Interface: Sensor signals are captured and actuators m2 are controlled using SIMULINK and dSPACE DAQ card 2 interface. Six ADCs capture signals from six axes of the \ \ load cell (3 moments about x,y,z axes and 3 forces in x,y,z Axis of Pitching direction). These sensor signals are filtered using second order filter to remove unwanted noise. Two quadrature encoder interfaces capture motor position data. Based on 0 feedback from encoders, a control torque signal is generated k for each motor. The torque control signal is implemented m, + mT on motors through two DACs of the dSPACE. Figure 4 shows the schematic of the rig interfaced with PC. Control: For the proposed rig any linear or nonlinear control strategies for either slosh analysis, identification, or control purpose can be programmed in SIMULINK and implemented using dSPACE. For preliminary experiments PID controllers were programmed for both motors using encoder position feedback to give sinusoidal and other exci- x h tation of desired amplitude and frequency to the rig. Gains were tuned to minimize the error between the actual and Ground Reference Line the desired position. Thus a variety of excitations and cor- responding slosh dynamic studies can be performed based Fig. 5. Model of rig under co-planar pitching and translation exci- tation considering two pendulum slosh on the force and moment data. III. MODEL OF THE RIG Using these expressions we form Lagrangian as L This section develops mathematical model of the pro- KE - PE. Using standard Lagrange equation with x, 0, posed slosh rig using Lagrange method and assuming two and .5 as generalized coordinates we obtain the equations pendl model of the slosh. Figure 5 shows the schematic of motion of the entire system as follows: diagram defining all the variables and parameters used. To- &&AL AL tal mass of liquid is divided into rigid mass and the slosh Nc -C = - ___ 9 __ 1812 &&0L &L4 To C° - /d-:ol6l0 T0-C00 &&OL &L ;| ll;!' ,an g: Cf2¢2 ( at + (902 =at-Cxz 0¢' ms2)S + [mpk cos23 =ml+mp+msl 0 -2 ° 0 1 2 5 3 &&OL &L 02 Co,(l) ()-4 _ -Ttl5llpel ¢1) + flls20 5 1o 5 20 25 30 at&q52 '902' Quick stop Time (sec) Working out the partial derivatives and simplifying further F .6 E we obtain the following four second order differential equa- tions of system dynamics: Fx- Cx (mnl +Tmp +Tmsl + Ms2)>% + [m pk cos 0 _________________ +mnsllpel cos(O + 00i + mns2lpe2 COS(O + 0b2) Tm sc -mslrl CoOS mns2r2 CoOS ]O + mnsllpel cos(O + 0ik~1 - Fig. 6. Forces and moments on the tank for 5kg liquid mass +Ms2lpe-2 COS(O + 0b2>)2 + [-mrnk sin 0 + mslrl sin 0 -mnsllpel sin(O + 00i + ms2,r2 sin 0the proposed rig. First set of experiments are carried out -ms2lpe2 sin(O + 4b2)]O + [msilpei sin(O + i)lii52 to identify various slosh parameters for pendulum model +[-ms2lpe2 sin(O + 52)] 52 + [-2ms1lpei sin(O + q)]&Xi using classical linear DOF excitation [7,3] for cylindrical 4 tank with several fill fractions. Sinusoidal excitation close +[-2ms2lpe2 sin(O + ¢k'2}J0¢'2, (4) to the first mode of vibration and then a quick stop is used to allow liquid to follow its natural first mode of vibra- To- Co0= [mpkcosO + msllpel cos(O + q$) tion. From recorded force (Fx) and moment (My) data -mTsrl COS0 +ms2lpe2 COS(O + 02) - ms2r2 COS 0]o (see Figure 6) various parameters including natural fre- quency, slosh mass, damping, and pendulum hinge location +mT1rs2 k2 +[Ip + mpk + Isl + 12 msltpel-2pel cos + Is2 + mn2 12 + ms2r2 -2ms2r2lpe2 COS2]O are identified and compared with the analytical and exper- imental data in [3]. A simplified version (considering only +[I[s, + -s12,1 mslrllpe COS 1]4 linear DOF) of model presented in the previous section and 21 recently developed identification schemes [10] are used for +[1s2 + ms2lpe2 - ms2r2lpe2 cos 02] 02 estimating various parameters. Figure 7 shows the compar- +[mTsrilpei sin 51]q2 + [ms2r2lpe2 sin 02] 2 ison of identified slosh parameters with analytical results .. .. of [3]. We observe that the values match well within 6 % +[2mTnsrlIpei sin ¢b1]O¢b1 + [2ms2r2lpe2 sin 4b2]04b2 for frequencies and within 12 % for hinge location and bet- + [mpgk sin 0 -mslgrl sin 0 + mslglpel sin(O + 01) ter than similar results in [3]. This confirms the successful -ms2gr2 sin 0 + ms2glpe2 sin(O + X2)], (5) implementation and working of the proposed rig. [mTs1lpe1 coS(O + ¢b1)]. + [isi + mste12 2- 9 _CO01¢ = -Tn COSJU] + Sl cosIPe }71slrlpel CS)]+ [Is, + Tsl21 StlS1pelJ)1' xperimental result + ,,15 o NASA-SP-106 results +[-mnsirlrpei sin ]02 + mnsiglpel sin(O + 00i), (6)(6) 3 4 5 6 7 8 9 -C202 = [[ms2lpe2 cos(O + 02)]x + [1s2 + ms2lpe2 E E 400 - -mns2r2lpe2 COS )2]0 + [5s2 + Tns2Ipe2]12 300 +[-ns2r2lpe2 sin 02]02 + ns2glpe2 sin(0 + 02). (7) ° 200 - i, 100 - Fx is the force on the liner motion x stage, To is torque in I _ the direction of pitching excitation, Cx, and Co are damp- 3 oa5 m w ( 7 w ing in x and 0 direction respectively. These equations which 4 5 s6 8k9 are fairly general can be used to simulate the motion of rig Fig. 7. Experimental and analytical values of frequencies and hinge and sloshing liquid for various cases. We use them in the locations next section for identification of slosh pendulum model pa- rameters and slosh compensation. Similarly by giving excitation in pitching degree of free- dom and using recently developed identification schemes, IV. RESULTS we obtained liquid moment of inertia. A simplified version This section presents simulation and experimental re- (considering only pitching DOF) of the model presented sults of various cases that demonstrate the effectiveness of in the previous section is used for this purpose. Figure 8 1813 shows comparison of the values identified from experimen- 6 Mkg 1 Slosh Cancellation Experiment tal data and those from [3]. The experimental estimates 10L Pitching amp 3 deg Fo at pitching only Fx slosh cancellation = Freq=1.8Hz in are higher than theoretical values. The discrepancy can be 0 ra m 458mm Phasedif=0deg attributed to surface wiping effects and viscosity of water. -, -5 -to -tS 0 1 2 3 4 5 6 7 8 9 10 0.1 x NASA SP-106 0.09 Pitching Freq 1.8 hz o Experimental 3 0.08 2- My in pitching only E 0.07 0.06 E 0.05 0 -2- 1 2 10~~~~~~~~~~~~~~~~ 76 9 3 8 4 5 Z 00.04 o~~~~~~~~ --3 E 0 2 3 4 5 6 7 8 9 to0 700 Time(s) 0.7 0.8 0.9 t.t t.2 0~~~~~~~~~~~~~ .3 .5 .4 Liquid Depth Ratio(h/d) Rotary Slosh Fig. 8. Experimenltal and analytical values of liquid inuick Stopate M1 =7kgiaeciaonrq29H 2~~~~ inertia estimates s Initaial ectratinamreq = 24 Hz Investigation has also been carried out in excitation in 0 Inta trnlml=4m pitching and implementing control compensation in linear tl DOF such that there is no slosh. Model developed in the -2( 5 10 15 210 25 30 previous section is used to determine the amplitude and t(sec) phase of excitation. Figure 9 and Figure 10 show simu-3 lation and experimental results respectively. We observe e 2_ thaththdue.d copenation pimplemented In linear DOF cancels S s Additional experiments were carried out to observe ro- - l tary slosh by giving sinusoidal excitation just beyond the -2 l l l lel natural frequency. Figure 11 shows the experimental mo- -3( t5 t15 20 25 30 ments in two perpendicular directions on the tank. We clearly see (in the steady state after quick stop) the ex- Fig. 11. Rotary slosh captured in two moments MX and My pected variation out of phase with each other in x and y moments. This data can be used to determine the parame- ters of the rotary slosh model. Several such slosh phenom- ena can be studied and characterized using both linear and rotary excitation facility in the proposed rig. latin l 30 rV. CONCLUSION = 3 ideg resp lnAfteraplying control e po t n c m 6ekg an= Before applying control pitching amp =4.58deg transampl Deeper h cof eslosh- phenomenon, 20 phase diff - 0 deg ing, can be pursued more effectively with support of appro- Additional exp s we c d o to oe r-priate experimental results and techniques. The proposed 1o0_X } 1 || i |||] | / 2 DOF design is capable of providing several cases of ex- tary slosh b givis sinusoidta lexcitati ist1\ ]1 1citationofsloshbyusingeitherofthemorbothofthem ments two perpendicular directions on dv in n ot of p e wh e theC- itank.a We with controlled phase lag, or with axis of pitching excita- o x ltion tilted with respect to the direction of linear motion 10mt \ 1 1 / \ 1 l 1 \ l W \ } \ 1 z } \ 1 / \ / } l \ 1 0an d so on. For the first time a six-axis load cell is used to mleasure slosh forces and moments in all direction; hence -20 U U 1l U U U U U V U U W 0 rthe proposed rig facilitates study of wide variety of slosh simulation ~ ~ ~ ~ ~ ~ phenomena. ih epctt results of identification of slosh to ile Experimental h drcin flnarmto 30 l p d gparameters in traditional way match well with theoretical 90 92 94 Time(s) 96 98 100 results confirming the successful operation of the proposed rig. Sample set of experimental results are presented to Fig. 9. Excitation in pitching and compensation in linear DOF: further demonstrate some of the capabilities of the rig. sl20 ion The new proposed rig opens up several avenues of analy- 1814 sis, identification, and control of slosh both from academic as well as industrial application perspective. For example the actual mission trajectory data can be fed to the rig and estimation of slosh force and moments in actual launch ve- hicle can be done, new nonlinear slosh control strategies could be developed and verified experimentally, and slosh with various damping structures (baffles) can be character- ized for forces and moments in all directions. Thus the pro- posed rig has immense potential for both teaching and re- search in the identification, modeling, and control of slosh. ACKNOWLEDGMENT This work is supported by Indian Space Research Orga- nization (ISRO) under Project Code 031S001 through STC program at IIT Bombay. REFERENCES [1] J. P. Vreeburg, "Spacecraft maneuvers and slosh control," IEEE Control Systems Magazine, vol. 25, no. 3, pp. 1216, June 2005. [2] E. Widmayer and J. Reese, "Moment of inertia and damping of fluid in tanks undergoing pitching oscillations," NACA National Advisory Committee on Aeronautics, Washington, Research Mem- orandum RM L53EOla, 1953. [3] H. Abramson, "The dynamic behavior of liquids in moving con- tainers," NASA (National Aeronautics and Space Administra- tion), no. NASA SP-106,, 1966. [4] J. Unruh, D. Kana, F. Dodge, and T. Fey, "Digital data analy- sis techniques for extraction of fuel slosh parameters," Journal of Spacecraft, vol. 23, no. 2, pp. 171177, March-April 1986. [5] N. Pal and S. Bhattacharya, "Experimental investigation of slosh dynamics of liquid-filled containers," Experiment Mechanics,, vol. 41, no. 1, pp. 6369, 2001. [6] J. Anderson, 0. Turan, and S. Semercigil, "Experiments to con- trol sloshing in cylindrical containers," Journal of Sound and Vi- bration, vol. 240, no. 2, pp. 398404, June 2001. [7] R. Ibrahim and V. Pilipchuk, "Recent advances in liquid sloshing dynamics," Applied Mechanics Review, vol. 54, no. 2, pp. 133197, March 2001. [8] S. Gangadharan, J. Sudermann, A. Marlowe, and C. Njenga, "Parameter estimation of spacecraft fuel slosh model," 45th AIAAIASMEIASCEIAHSIASC Structures, Structural Dynamics and Materials Conference, vol. AIAA Paper 2004-1965, 19-22 April 2004. [9] dSPACE, DS1104 R & D Controller Board: Installation and Configuration Guide, Release 3.5, dSPACE GmbH, Paderborn, Germany, March 2003. [10] Odhekar, D.D, Gandhi P.S., and Joshi K.B, "Novel methods for slosh parameter estimation using pendulum analogy" AIAA Atmo- spheric Flight Mechanics Conference, San Francisco, California, August 2005. 1815

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