A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis. Martin Altenburg Johannes Burkhardt (EADS Astrium, Germany)

Transcription

1 119 Appendix H A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis Martin Altenburg Johannes Burkhardt (EADS Astrium, Germany)

2 120 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis Abstract The presentation discusses the development of the software tool TransFAST, which firstly transfers the classical thermal network to a standard linear control system, and subsequently solves this system in the frequency domain. Application of this type of analysis becomes more and more important for missions, where extremely demanding requirements on geometrical and thus thermo-elastic stability are involved. In such cases the deviations from a certain steady-state are small enough for performing thermal analysis on linearized systems. As a major advantage, thermal stability analyses can be performed without running extensive transient thermal analysis, delivering reasonable and even more accurate results, compared to the classical approach, and in general with significantly less effort. For solving one key issue, the inversion of the system matrix, the presentation discusses two different numerical approaches, the direct inversion of the transformed system matrix (DIT) and the conditioned evaluation of the frequency response (CEF). A comparison of the different methods is provided for the application example LISA. For this mission, requirements imposed on the satellite system design and/or on the scientific payload design are defined in the frequency domain because these requirements have to be met for a certain measurement bandwidth only. Mission specific requirements are typically expressed in terms of quantity/ Hz, the so-called linear spectral density, in analogy to the power spectral density, i.e. quantity 2 /Hz. TransFAST also comprises powerful post-processing features for graphical output, which allows checking the analysis results directly after the calculation is performed. As a further feature of this software the user can import also results from external sources like ESATAN for further post- processing.

3 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis 121 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis Martin Altenburg // martin.altenburg@astrium.eads.net Motivation Current & future science missions require ultra-stable S/C structures, with extremely demanding thermo-elastic stability requirements Thermal analysis accuracy has to be significantly improved Application Examples: LISA aims to detect gravitational waves GAIA aims to create a precision 3-d star map of the galaxy Perform thermal disturbance analysis for small deviations from the nominal state (i.e. thermal analysis steady-state solution) Linearization of the radiative terms of the heat balance equation subsequent solution of the equation (linear control system now) 28/10/2008 Page 2

4 122 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis Linearization Approach (1) 1) Heat transport equation (conduction & radiation) dt n A n i i, j i, j CP i T j T i i A i T j T i Q dt i i j l i j 4 4, 1 i j,, 1 2) Re-arrangement of thermal network matrices dt diag C K T F T 4 Q dt 3) Linearization of radiative terms around equilibrium state 4 4 e 3 e T T T 1T 4T T e T diag C K diag C F diagt T diag C Q e 28/10/2008 Page 3 Linearization Approach (2) Node Properties Node Links Node Property Node number (N) External & internal heat sources (Q) Steady-State temperature (T) Heat capacity (CP) Heat conductance coefficient (GL) Heat radiation coefficient (GR) Heat capacity (CP) [A] [B] [A] [B] [C] [D] [u] [x] [y] system matrix input matrix measurement matrix input/output coupling matrix input/control vector state vector output vector Distinguish node types: boundaries are no state variables T D A DD T A BD B A DB T D Q D B T B Q A B BB x A x B u Linear Control System ycxdu 28/10/2008 Page 4

5 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis 123 Linear Control Methods for Thermal Systems Frequency domain analysis (Transfer Function Approach): Apply Laplace Transform on the Linear Control System Y ( s) U ( s) 1 G ( s) C si A B D G(s) includes gain and phase shift information G(s) provides the complete thermal system characterization Two different numerical approaches: direct inversion of the transformed system matrix (DIT) conditioned evaluation of the frequency response (CEF) Post processing possibility 28/10/2008 Page 5 Frequency Domain Analysis Inputs (from external and internal noise sources), e.g. solar, S/C equipment: Power Dissipation Input Temperature Fluctuation Input Evaluation of these inputs at all or selected thermal nodes (system characterization) In terms of linear control system: SISO MIMO Many options for visualization of the results: Gain vs. frequency for all nodes, 3d-plot Gain vs. frequency (for selected nodes), 2d-plot Gain for all nodes for one selected frequency, gain vs. nodes, 2d-plot Tool capabilities are presented exemplary for LISA S/C (payload), see next slides 28/10/2008 Page 6

6 124 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis TransFAST GUI Build-up Linear System 1) Import ESATAN Output Files 2) Generate State Space Model 3) System Definition Report Area 28/10/2008 Page 7 TransFAST GUI Gain vs. Frequency (1) 1) Source Definition 2) Input Definition 3) Sampling Point 4) Output Definition 5) Plot Options 28/10/2008 Page 8

7 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis 125 Gain vs. Frequency (2) Results Non-perfect final equilibrium state Unit Step (FFT) Approach Transfer Function Approach Input: all boundary nodes 10-2 Gain [K/K] 10-4 Numerical noise induced error Comparison with classical method, time domain analysis & subsequent Fourier Transform Results consistent for both methods Frequency [Hz] Output: electrode housing 28/10/2008 Page 9 TransFAST GUI Gain vs. Nodes (1) 1) Input Definition 2) Frequency Selection 3) Plot Options 28/10/2008 Page 10

8 126 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis Gain vs. Nodes (2) Results Optical Bench Optical Bench Diode Radiative and conductive coupling between diodes Gain [K/W] Nodes Nodes Telescopes Diode Input: diode power dissipation Proof Mass f = Hz interne Node Knotennummern number system characterization 28/10/2008 Page 11 TransFAST GUI Gain vs. Freq. & Nodes (1) 1) Input Definition 2) Frequency Selection 3) Plot Options 28/10/2008 Page 12

9 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis 127 Gain vs. Frequency & Nodes (2) Results Input: all boundary nodes Frequency [Hz] Output: telescope 1 28/10/2008 Page 13 Node number TransFAST GUI Post Processing, Plot Tool 1) Input Definition 2) System Selection 3) Grouping by label Report Area 28/10/2008 Page 14

10 128 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis Summary Methods for Application of Linear Control Methods established & verified in a standard S/W environment, MATLAB Linearization, Laplace Transform, Post-processing Powerful S/W tool available for system characterization derivation of stability requirements for (sub)systems requirement verification by analysis Significant advantages compared to standard methods: Promises higher accuracy Reduced computational & memory effort Application on present and future missions whenever high thermal (thermoelastic) stability is required (not necessarily limited to LISA pathfinder & LISA missions!) 28/10/2008 Page 15 Outlook Extend S/W tool by implementation of linear system solver in the time domain (ODE) Implementation of project-specific post processing options (frequency domain) Improve user friendliness (GUI) 28/10/2008 Page 16

11 A Software Tool Applying Linear Control Methods to Satellite Thermal Analysis 129 Contact Dipl.-Ing. Martin Altenburg Dr.-Ing. Johannes Burkhardt EADS Astrium GmbH EADS Astrium GmbH Friedrichshafen Friedrichshafen Germany Germany Phone: Phone: Fax: Fax: astrium.eads.net astrium.eads.net 28/10/2008 Page 17

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