1 / 35

Magnetohydrodynamical element in the problems of RC and SC stabilization

Magnetohydrodynamical element in the problems of RC and SC stabilization. Boris I. Rabinovich Electronic version Victoria Prokhorenko and Aleksey Grishin. 2. Magnetohydrodynamical element in the problems of RC and SC stabilization.

lyle-beck
Download Presentation

Magnetohydrodynamical element in the problems of RC and SC stabilization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Magnetohydrodynamical element in the problemsof RC and SC stabilization Boris I. Rabinovich Electronic version Victoria Prokhorenko and Aleksey Grishin

  2. 2 Magnetohydrodynamical element in the problems of RC and SC stabilization • The use of the control system including the MHD elements for stabilization of the dynamically unstable objects has been considered. The mathematical model of MHD element is transformed to the model of equivalent oscillator. • The possibilities of the control system with MHD elements are presented: RC unstable in the longitudinal direction (POGO) and the unstable rotating SC with the flexible spike antenna located along the rotation axis (like Auroral probe of INTERBALL project).

  3. General view 3 MHD element • Reynolds, Strouhal, and Alfven`s numbers • The main constants • The criterion of applicability of the mathematical model

  4. Vortex Processes and Solid Body Dynamics Spacecraft and Magnetic Levitation Systems Dynamic Problems by Boris I. Rabinovich Moscow Institute for Control Devices Design, Russia Valeriy G. Lebedev Research and Design Institute, Moscow, Russia Alexander I. Mytarev Research and Design Institute, Moscow, Russia translated by A.S.. Leviant FLUID MECHANICS AND ITS APPLICATIONS 25 Translated from the Russian October 1994, 308 pp. The mathematical model of the MHD element 4 • General equations • Equivalent oscillator Kluwer Academic Publishers Group U – liquid velocity; I – external current; J – eddy current;

  5. 5 Methodical example • G - Gravity center • M – MHD element; • О0 –Accelerometer; • Y – Non conservative force

  6. Mathematical model Characteristic equation and stability condition 6 The maintenance of dynamical stability

  7. 7 POGO – problem • RC body strains during its longitudinal oscillations The eigen frequencies of the longitudinal oscillations of the RC body (f q j ) and of the LOX in the oxidizer line (f s 2 ) of Saturn 5 RC ( ___ AS-501, AS-502 ; __ . __ AS – 503)

  8. , q, s, r – the generalized coordinates of RC as a solid body, and as a elastic bar, of the liquid in the propellant line and inside the MHD element 8 The mathematical model of POGO for the RC with MHD element and accelerometer

  9. The non-dimensional parameters: , , . The subscripts: q -RC body; r - liquid in MHD element; s - liquid propellant in the line; 9 9 Approximate solution of the characteristic equation

  10. 10 The designation of the stability and instability regions 10 - - + - - + + +

  11. The initial propellant line (instability at the frequency~ q) The improved propellant line with hydro-accumulator (stability) 11 The stability and instability regions. LPM with the phase retarding α α - + - + + - - - 1 β < 0 β > 0 0 0 1 - - + - - +

  12. The initial propellant line ( instability at the frequency~ q) The propellant line with hydro-accumulator (instability at two frequencies: ~ sand ~ q ) 12 The stability and unstability regions. LPM with the phase outstripping α α - + - + + - - + + - - - 1 1 1 β < 0 0 0 + + β > 0 0 1 + + - - 0 + - - + + - - +

  13. The real parts of the characteristic equations roots The conjugate control law 13 The control law for the MHD element

  14. The propellant line with hydro-accumulator and damping device (instability at the frequency ~ q) The use of the additional control loop with MHD element and accelerometer (stability) 14 The stability and instability regions. LPM with the phase outstripping α α + - + - - + - + 1 - - 1 0 β >0 0 β > 0 - - + - - +

  15. 15 Auroral Probe (AP)spacecraft of the INTERBALL project • The flexible spike antenna located along the rotation axis

  16. а) 23.10.96, 17 : 38 MT; b) 24.10.96, 05 : 10 MT; c) 02. 08.97, 07 : 20 MT    8 6 4 2 0 - 2 - 4 - 6  - 8   - 8 - 6 - 4 - 2 0 2 4 6 8 16 The samples of unstable nutation of AP, 0 = 3/s,TMI from Sun sensor а) b) c)

  17. a) 23.10.96, 05 : 58 MT, 0= 3/s ; b) 24.10.96, 11 : 47 MT, 0= 3/s; c) 03.09.96, 12 : 04 MT, 0= 4/s  βо  αо   17 Evolutionary rife unstable nutation of the AP, the attitude control system is switched on (а, b), TMI from Sun sensor a)  b) c) 

  18. 18 The main designations • j (j = 2, 3) – the angles characterizing the attitude of SC relative to the inertial frame; • j(j = 2, 3) – the angular velocity components in the frame connected with SC; • p j, q j (j = 1, 2) – the transversal shifts of the attached masses of the flexible and MHD elements relative to the SC; • m, l – the attached mass and the length of the flexible element; • а – the distance from the connection point of the flexible element to the center of masses of SC; • 0 – the angular velocity of SC rotation around the longitudinal axis; • c – the eigen frequency of the flexible elements oscillations.

  19. The equations of disturbed motion The generalized coordinates 19 The mathematical model of SC of AP type with MHD elements and accelerometers (k=2) and non-controlled SC (k=1, a0=0, a1=0) • The main parameters

  20. 20 Stability and instability regions for the rotating SC of AP type - - stability + - instability, one root + + instability, two roots

  21. 21 Root locuses for variable parameter(solid line -exact, thin line _ approximate)

  22. 22 Root locuses for variable parameters and I 2root locus 3root locus

  23.  vector  vectors locus 23 The analytical solutionfor SC of AP type

  24. 24 The variable parameters of mathematical model of AP and the initial values of coordinates and velocities(c = const = 0.0465 s-1)

  25. a) See table 24 b) See table 24     The initial stage of the unstable nutation of the AP (0 = 3/ s and 0 = 4/s), mathematical simulation 25

  26. а), b), c) See table 24 a)       26 Unstable nutation of AP (0 = 3° / s), mathematical simulation b) c)

  27. 27 Stability and instability regions for variable parameters а0 , а1 (0 = 0.06 s-1)

  28. 28 Stability and instability regions for variable parameters а0 , а1 (0 = 0.03 s-1)

  29. 29 Root locuses for SC AP type with MHD elements and accelerometers in the control loop (а0=2, а1=3) for variable parameter (solid line - exact, thin line _ approximate) 2root locus 3root locus 4root locus

  30. 30 Mathematical simulation of the nutation of gyro stable SC of the AP type(c = 0.06 c -1) Svector locus corresponding to the massm displacement by the strains of the flexible element vector locus corresponding to the angular velocity of the rotating SC

  31. 31 Stabilization of the gyro stable SC of AP type with MHD elements and accelerometers, mathematical simulation(с = 0.06 s-1, a0 = 2, a1= 3) Svector locus corresponding to the massm displacement by the strains of the flexible element vector locus corresponding to the angular velocity of the rotating SC

  32. 32 Mathematical simulation of the nutation of gyro unstable SC of the AP type(c = 0.03 c-1) Svector locus corresponding to the massm displacement by the strains of the flexible element vector locus corresponding to the angular velocity of the rotating SC

  33. Stabilization of the gyro unstable SC of AP type with MHD elements and accelerometers, mathematical simulation(с = 0.03 s-1, а0 = 2, а1 = 3) 33 Svector locus corresponding to the massm displacement by the strains of the flexible element vector locus corresponding to the angular velocity of the rotating SC

  34. Stability regions Instability regions 34 Liquid hyroscope as MHD element Mathematical model r0 , h - mean radus and thickness of the liquid sheet The roots of the characteristic equation The stability borders

  35. 35 Magnetohydrodynamical element in the problems of RC and SC stabilizationSummary • The RPM of new generation having the open loop response from pump inlet pressure to the combustion chamber pressure with the phase outstripping on the low frequencies make the POGO probability much higher. • The use of the flexible elements with relative low eigen frequencies located along the rotation axis of the gyro-stabilized SC may lead to non-stability of the steady-state rotation around the axis with maximum moment of inertia. The logarithmic increment of nutation oscillations is proportional to the oscillations decrement of the flexible element and the difference between the SC angular velocity and the eigen frequency of the flexible element. • One of the possible approaches to solve the stability problems is the use of the additional control system with MHD elements, accelerometers, and (or) angular velocity sensors, accelerometers, and (or) angular velocity sensors.

More Related