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Decentralized Control Applied to Multi-DOF Tuned-Mass Damper Design Decentralized H2 Control Decentralized H  Control Decentralized Pole Shifting Decentralized

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Text of Decentralized Control Applied to Multi-DOF Tuned-Mass Damper Design Decentralized H2 Control...

  • Slide 1
  • Decentralized Control Applied to Multi-DOF Tuned-Mass Damper Design Decentralized H2 Control Decentralized H Control Decentralized Pole Shifting Decentralized H2 with Regional Pole Placement Lei Zuo and Samir Nayfeh
  • Slide 2
  • Control View of SDOF TMD Spring: feedback relative displacement with gain k 2 Damper: feedback relative velocity with gain c 2 k2k2 c2c2 u u = k 2 (x 2 - x 1 )+c 2 ( ) SDOF TMD MDOF TMD: ---- To make use of other degree of freedoms ---- Better vibration suppression ---- To damp multiple modes with one mass damper
  • Slide 3
  • Formulation for MDOF TMD Systems The mass-spring-damper systems can be cast as a Decentralized Static Output Feedback problem Cost Output Measurement Disturbance 0 0
  • Slide 4
  • #PerformanceDisturbanceApproach 1Decentralized H 2 /LQr.m.s. response (impulse energy) white noisegradient-based 2Decentralized H peak in frequency domain worst-case sinusoid LMI iteration/ gradient-based 3Pole shiftingmodal dampingunknown -subgradient 4Decentralized H 2 + pole constraint r.m.s. response +transient char. partially-known white noise Methods of multipliers decentralized control for different disturbances and performance requirements
  • Slide 5
  • k1k1 k2k2 c1c1 c2c2 2d Minimal ||H|| 2 of x 0 x s versus /d Minimal ||H|| 2 Radius of gyration / location ( /d) mass ratio m d /m s =5% 2DOF TMD for Single Mode Vibration /d=1: two separate SDOF TMDs /d= : traditional SDOF TMD /d=1/ : 2DOF TMDs (uniform) /d=0.780: 2DOF TMDs (optimal) k1k1 c2c2 k1k1 c2c2
  • Slide 6
  • 2DOF TMD: Decentralized H /d= Normalized Frequency Magnitude x s /x 0 /d=1 /d=1/sqrt(3) /d=0.751 k1k1 k2k2 c1c1 c2c2 2d mass ratio m d /m s =5% 2DOF TMD can be better than the traditional SDOF TMD and two separate TMDs
  • Slide 7
  • 2DOF TMD: Negative Damping mass ratio m d /m s =5%, /d=0.2 Much better performance if one of the damper can be negative. A new reaction mass actuator
  • Slide 8
  • Application: Beam Splitter of Lithography Machine flexures beam splitter (mockup) table (Acknowledgement: Thanks to Justin Verdirame for making this mockup)
  • Slide 9
  • 6DOF TMD for 6DOF Beam Splitter excitation accelerometer spring-dashpot connections mass damper
  • Slide 10
  • Measured T.F. of 6DOF TMD SIX modes are damped well just by using ONE secondary mass Phase (deg) Magnitude(dB)
  • Slide 11

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