Control Augmented Structural SynthesisNational Aeronautics and Space Administration, Scientific and Technical Information Branch, 1988 - Structural design - 174 pages |
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Page 48
... dual function ( Ã ) is defined as ( 5-2 ) 1 ( X ) = min L ( Y , λ ) YEYF where the Lagrangian function is given by L ... dual variables will yield the optimal values for the primal variables Y if the dual maximization problem has a ...
... dual function ( Ã ) is defined as ( 5-2 ) 1 ( X ) = min L ( Y , λ ) YEYF where the Lagrangian function is given by L ... dual variables will yield the optimal values for the primal variables Y if the dual maximization problem has a ...
Page 49
... dual function . While the dual method described above is clearly applicable to the solution of Eq . ( 5-1 ) , the efficiency of such a solution scheme is an important consideration . In general , maximization of the dual function is ...
... dual function . While the dual method described above is clearly applicable to the solution of Eq . ( 5-1 ) , the efficiency of such a solution scheme is an important consideration . In general , maximization of the dual function is ...
Page 54
... dual function is immediately available from the pri- mal constraint values ( Ref . 75 ) , i.e .: = = ñq ; qEQ ( 5-23 ) However , if l ( ) does not possess continuous first derivatives these methods may exhibit slow or nonconvergent ...
... dual function is immediately available from the pri- mal constraint values ( Ref . 75 ) , i.e .: = = ñq ; qEQ ( 5-23 ) However , if l ( ) does not possess continuous first derivatives these methods may exhibit slow or nonconvergent ...
Contents
The Control Augmented Structural Synthesis | 12 |
Structural Analysis | 20 |
Approximate Problem Generation | 34 |
8 other sections not shown
Common terms and phrases
1.0 indicates active control system actuator 2 actuators actuator Controlled Actuator Force approximate problem augmented structural synthesis bound value Table Cantilevered Beam constraint is critical control augmented structural control elements Control Force Minimization Control Theory Controlled 1 actuator critical Table Data for Problem denotes lower bound design problem Design Response Ratios design variables Designs for Problem displacement constraints dual dynamic displacements dynamic loading conditions eigenvalue equations Əxij Əxij Final Design cm Final Design Response Grillage Histories for Problem Independent Actuator Gains Iteration History Data linear load vectors lower bound value Lumped Mass Design Mass Minimization Maximum Constraint Violation Minimization Final Design move limits natural frequencies Nt-sec/cm Nt/cm objective function optimal control Problem 5 Cantilevered Ratios for Problem Response Minimization shown in Fig side constraints space frame static stiffness matrix straint structural mass techniques Tip Displacement total control force truss elements upper bound Пр