Multidisciplinary Analysis of the NEXUS Precursor Space Telescope

Transcription

1 Multidisciplinary Analysis of the NEXUS Precursor Space Telescope Olivier L. de Weck David W. Miller Gary E. Mosier mit.edu SPIE Highly Innovative Space Telescopes Session 6: Detectors, Modeling and Testbeds SPIE Astronomical Telescopes and Instrumentation -8 8 August, Waikoloa, Hawaii, USA Chart: 1

2 Problem Setting White Noise Input d Disturbances Appended LTI System Dynamics w Science Target Observation Mode [A zd, B zd, C zd, D zd ] Opto-Structural Plant [A p,b p,c p,d p ] z Phasing J z,1 =RMMS WFE Performances z=c zd q zd (RWA, Cryo) [A d,b d,c d,d d ] Actuator Σ Noise Parameters: p j u Control (ACS, FSM) [A c,b c,c c,d c ] Σ y Sensor Noise Pointing J z, = RSS LOS Traditionally: Define System Parameters p j = p o Isoperformance: Find Locus of Solutions p LB < p j < p UB Predict H performances J z,i Constrain performances J z,i = J z,req Chart:

3 Nexus Case Study Purpose of this case study: Nexus Spacecraft Concept Demonstrate the usefulness of Isoperformance on a realistic conceptual design model of a high-performance spacecraft Pro/E models NASA GSFC OTA launch configuration The following results are shown: Sunshield Integrated Modeling Nexus Block Diagram Baseline Performance Assessment Sensitivity Analysis Isoperformance Analysis () Deployable Multiobjective Optimization PM petal Error Budgeting Delta II Fairing Chart: 3 on-orbit configuration Instrument Module 1 meters NGST Precursor Mission.8 m diameter aperture Mass: 75.5 kg Cost: M$ (FY) Target Orbit: L Sun/Earth Projected Launch: 4

4 Nexus Integrated Model Legend: Design Parameters (I/O Nodes) Spacecraft bus (84) m_bus 8 m solar panel Cassegrain Telescope: PM (.8 m) PM f/# 1.5 SM (.7 m) f/4 OTA sunshield I_ss Instrument (7) X Z Y deployable PM petal (19) RWA and hex isolator (79-83) K_rISO fixed PM petals (149,169) K_yPM K_zpet Structural Model (FEM) (Nastran, IMOS) Ω, Φ SM spider t_sp SM () m_sm Chart: 4

5 Nexus Block Diagram Number of performances: n z = Number of design parameters: n p =5 Number of states n s = 3 Number of disturbance sources: n d =4 RWA Noise Out1 Out1 4 [N,Nm] Cryo Noise 3 [Nm] Control Torques x' = Ax+Bu 3 Mux Demux y = Cx+Du [N] x' = Ax+Bu y = Cx+Du Inputs ACS Controller 8 NEXUS Plant Dynamics Attitude Mux 3 [rad/sec] 3 [rad] [rad] Angles Outputs rates Out1 desaturation signal physical 3 dofs [m,rad] 3 ACS Noise K K WFE Sensitivity [m] K [m] Centroid Sensitivity Centroid FSM Coupling gimbal angles RMMS In1 Out1 LOS [microns] -Kmmic Measured Centroid [m] [nm] Performance Demux K [m] FSM Plant WFE Performance 1 Out1 WFE x' = Ax+Bu y = Cx+Du FSM Controller GS Noise [rad] Chart: 5

6 Initial Performance Assessment J z (p o ) RSS [ µm] 1 requirement Cumulative RSS for LOS Results J z,1 (RMMS WFE) J z, (RSS LOS) Lyap/Freq Time [nm] [µm] Frequency [Hz] Critical Mode 3.1 Hz Video Clip 6 Centroid Jitter on Focal Plane [RSS LOS] PSD [µm /Hz] Cent x Signal [µm] Frequency [Hz] 5 Freq Domain Time Domain Time [sec] Centroid Y [µm] 4 1 pixel T=5 sec µm - -4 Requirement: J z, =5 µm Centroid X [µm] Chart: 6

7 Nexus Sensitivity Analysis Design Parameters Norm Sensitivities: RMMS WFE Ru Us Ud fc Qc Tst Srg Sst Tgs m_sm K_yPM K_rISO m_bus K_zpet t_sp I_ss I_propt zeta lambda Ro QE Mgs fca Kc Kcf p /J * J / p o analytical finite difference z,1,o z,1 Norm Sensitivities: RSS LOS Ru Us Ud fc Qc Tst Srg Sst Tgs m_sm K_yPM K_rISO m_bus K_zpet t_sp I_ss I_propt zeta lambda Ro QE Mgs fca Kc Kcf p o /J z,,o * J z, / p disturbance parameters plant parameters optics params control params Graphical Representation of Jacobian evaluated at design p o, normalized for comparison. J = z p J o zo, J R L J K z,1 z, u u z,1 z, cf J R L J K RMMS WFE most sensitive to: Ru - upper op wheel speed [RPM] Sst - star track noise 1σ [asec] K_rISO - isolator joint stiffness [Nm/rad] K_zpet - deploy petal stiffness [N/m] RSS LOS most sensitive to: Ud - dynamic wheel imbalance [gcm ] K_rISO - isolator joint stiffness [Nm/rad] zeta - proportional damping ratio [-] Mgs - guide star magnitude [mag] Kcf - FSM controller gain [-] cf Chart: 7

8 D-Isoperformance Analysis isolator strut CAD Model Ud=mrd [gcm ] m K_rISO [Nm/rad] ω joint E-wheel K_rISO RWA isolator joint stiffness [Nm/rad] Isoperformance contour for RSS LOS : Jz,req = 5 µm HST 5 test Parameter Bounding Box 6 6 Initial design p o spec d m Ud dynamic wheel imbalance [gcm ] r Chart: 8

9 Nexus Multivariable Isoperformance n p =1 Tgs.4 [sec] Qc.5 [-] Ud 9 [gcm ] Us.7 [gcm] Pareto-Optimal Designs p * iso Design A Best mid-range compromise RMS [µm] 6 4 Cumulative RSS for LOS K r ISO 5 [Nm/rad] K z pet 18E+8 [N/m] t s p.5 [m] A: min(j c1 ) B: min(j c ) C: min(j r1 ) Mgs [mag] Kcf 1E+6 [-] Ru 385 [RPM] Performance Design B Smallest FSM control gain Design C Smallest performance uncertainty PSD [µm /Hz] Cost and Risk Objectives Jz,1 Jz, Jc,1 Jc, Jr,1 1 Frequency [Hz] 1 Frequency [Hz] Design A / % Design B / % Design C / % 1 1 Chart: 9

10 Error Source Contributions Chart: 1 n d Allocated Budget i i, j z, req, i j= 1 Nexus Error Budgeting LTI System, J z,req, p_bounds, p_nom (Design A) Isoperformance Toolbox p iso Ψ = Ψ = J FGS Error Source VAR % Allocation VAR% Capability RWA Cryocooler Attitude Noise E-6 GStar Noise Total var_contr.6 Plot Error Contribution Sphere B.6 Cryo.8 A C Budget RWA. Ψ ** Capability Budget Note: ACS sensor noise contributions not shown LOS Budget Capability

11 secondary hub SM Nexus Initial p o vs. Final Design p** iso +Z +Y +X SM Spider Support t sp Spider wall thickness D sp Deployable segment K zpet Improvements are achieved by a well balanced mix of changes in the disturbance parameters, structural redesign and increase in control gain of the FSM fine pointing loop. Parameters Initial Final Ru [RPM] Us [gcm] Ud [gcm ] Qc.5.14 [-] Tgs [sec] KrISO [Nm/rad] Kzpet.9E+8 8.9E+8 [N/m] tsp.3.3 [m] Mgs [Mag] Kcf E+3 4.7E+5 [-] Centroid Y µm T=5 sec Centroid Jitter on Focal Plane [RSS LOS] Initial: Final: Centroid X Chart: 11

12 Paper Conclusions For new generation of lightweight, deployable telescopes such as NGST and NEXUS the disciplines of structures, optics and controls are coupled and must be considered together during early design stages Performance predictions can be made for engineering metrics such as WFE, LOS jitter etc that flow down from science requirements. These predictions are based on integrated models, but are uncertain and depend on many assumptions. Nevertheless one can gain valuable insights from sensitivity analysis to identify key driving system parameters. Isoperformance seeks not the best achievable performance, but acceptable performance, while balancing the burden among subsystems. Error budgeting and Integrated Modeling can be linked. Chart: 1