SpinSatellite

SpinSatellite - min | det I M 0 1 1 1 min min | diag 1 , 2...

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                  12 1 min | det 0 1 min 1 min | , 1 min | , max min IM diag diag MU DMD           
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    1 max min 01 00 1 1 0 1 1 1 1 1 11 1 1 0 0 1 1 1 1 22 10 1 det 1 1 MU DMD x xy y                                       12 1 min | det 0 1 min 1 min | , 1 min | , max min IM diag diag MU DMD         
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                      12 1 2 1 2 1 min | det 0 1 min 1 min | , 1 min | , , 0 1 min | , max min IM diag diag diag MU DMD                
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01 0 1 1 10 1 det 1 0 1 x xy y                12 1 2 1 2 1 min | , 1 min | , , 0 diag diag           
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       11 1 01 2 2 det 2 2 2 24 2 22 xy x y xy      
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c c Gary J. Balas 2006 AEM 8421 – 1 / 37 AEM 8421: Robust Multivariable Control Systems Gary J. Balas Aerospace Engineering and Mechanics University of Minnesota Minneapolis, MN 55455 balas@umn.edu Spring Semester 2006
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Multivariable (Multi-Input/Multi-Output, MIMO) Robust Control MIMO Control Robust Control Nominal System Conclusion (Incorrect) But . .. Of-diagonals LFTs Matrix Norm Uncertainty Robust Per±ormance Analysis Test Perturbed LFTs Constant Matrix Diagonal Scalings Robust Per±ormance Summary Exercises c c Gary J. Balas 2006 AEM 8421 – 2 / 37
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Robust Feedback Control MIMO Control Robust Control Nominal System Conclusion (Incorrect) But . .. Of-diagonals LFTs Matrix Norm Uncertainty Robust Per±ormance Analysis Test Perturbed LFTs Constant Matrix Diagonal Scalings Robust Per±ormance Summary Exercises c c Gary J. Balas 2006 AEM 8421 – 3 / 37 1. What can go wrong in MIMO Feedback Systems? s Loop-at-a-time margins are not acceptable block diagram, plant and controller data nominal closed-loop information: decoupled command response, great margins nominal time responses terrible perturbed closed-loop behavior s Nominal Performance and Robust Stability do not imply Robust Performance 2. Are these intrinsically hard problems?
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SpinSatellite - min | det I M 0 1 1 1 min min | diag 1 , 2...

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