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E-raamat: Theory of Adaptive Structures: Incorporating Intelligence into Engineered Products

(Duke University)
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Theory of Adaptive Structures: Incorporating Intelligence into Engineered ProductsSuurem pilt
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On-board microprocessors have taken over from humans the function of evaluating telemetry data from spacecraft. Utku (civil engineering and computer science) addresses the new challenges in controlling the behavior of engineering systems created by advances in sensor, actuator, and microprocessor technologies, furnishing theoretical grounding for the structural engineer in the design and control of discrete parameter adaptive structures. Coverage spans such topics as: excitation-response relations and active control of response (in diverse cases). Annotation c. by Book News, Inc., Portland, Or.

Theory of Adaptive Structures provides the basic theory for controlling adaptive structures in static and dynamic environments. It synthesizes well-established theories on modern control as well as statics and dynamics of deformable bodies. Discussions concentrate on the discrete parameter adaptive structures dealing with actuator placement, actuator selection, and actuation computation problems - keeping these structures at close proximity of any chosen nominal state with the least energy consumption. An introduction to the distributed parameter adaptive structures is also provided.

The book follows that modern trend in research and industry striving to incorporate intelligence into engineered products through microprocessors that are becoming smaller, faster, and cheaper at astounding rates. Not using them in engineered products may become an enormous liability.

Resulting from the advances in materials technology on sensors and actuator technologies as well as the availability of very powerful and reliable microprocessors, there is an ever-increasing interest in actively controlling the behavior of engineering systems. Engineers and engineering scientists must revive and broaden their activities to maximize applications for predicting and controlling the behavior of deformable bodies.

Topics include:
  • An introduction to adaptive structures
  • Incremental excitation-response relations in static and dynamic cases
  • Active control of response in static case
  • Statically determinate adaptive structures
  • Statically indeterminate adaptive structures
  • Active vibration control for autonomous and non-autonomous cases
  • Active control against wind
  • Active control against seismic loads
  • Distributed parameter adaptive structures

    The technology of adaptive structures has created an environment where the analysis, not the computation, of structural response - due to actuator-inserted deformations - has become important. Problems related to the placement, the operation in real time, and the energy consumption of the actuators require the review and broadening of the theories long dormant due to the emphasis placed in the numerical simulations of structural behavior by the displacement finite element method.
    This book furnishes the basic theory needed by modern engineers in the design and control of discrete parameter adaptive structures .
    • Preface
    1 Introduction
    		1(18)
    1.1 History
    		1(2)
    1.2 Definitions
    		3(2)
    1.3 Types of Structures
    		5(2)
    1.4 Types of Problems
    		7(1)
    1.5 Qualitative Analysis in State Space
    		7(3)
    1.5.1 Example of Static Transient Loading
    		8(1)
    1.5.2 Example of Dynamic Transient Loading
    		9(1)
    1.6 Constituents of Adaptive Structures
    		10(7)
    1.6.1 Structure
    		10(4)
    1.6.2 Sensors
    		14(1)
    1.6.3 Actuators
    		15(1)
    1.6.4 Microprocessors and Their Software
    		16(1)
    1.7 Objectives, Scope, and Outline
    		17(2)
    2 Incremental Excitation-Response Relations, Static Case
    		19(28)
    2.1 Basic Definitions
    		19(6)
    2.1.1 Structure
    		19(2)
    2.1.2 Excitations
    		21(1)
    2.1.3 Incremental Response
    		22(3)
    2.1.4 Excitation-Response Relations
    		25(1)
    2.2 Equilibrium of Forces
    		25(11)
    2.2.1 Equilibrium of Structural Elements
    		26(2)
    2.2.2 Equilibrium of Nodes
    		28(3)
    2.2.3 Effect of Preexisting Internal Forces
    		31(5)
    2.3 Geometric Relations
    		36(3)
    2.3.1 Case When Delta v(0)=O
    		36(1)
    2.3.2 Case When Delta Xi=O
    		37(2)
    2.3.3 Final Form
    		39(1)
    2.4 Stiffness Relations of Elements
    		39(6)
    2.4.1 Element Stiffness Matrices
    		40(1)
    2.4.2 Element Flexibility Matrices
    		41(2)
    2.4.3 Obtaining K(k) from F(k)
    		43(2)
    2.5 Incremental Excitation-Response Relations
    		45(2)
    3 Active Control of Response, Static Case
    		47(20)
    3.1 Inverse Relations
    		48(6)
    3.1.1 By Displacement Method
    		48(2)
    3.1.2 By Force Method
    		50(3)
    3.1.3 Statically Determinate Case
    		53(1)
    3.2 Actuators of Adaptive Structures
    		54(1)
    3.3 Basic Equations for Adaptive Structures
    		55(1)
    3.4 Actuator Locations and Controls
    		56(1)
    3.5 Observed Response Components and Output
    		57(1)
    3.6 Determination of Controls
    		58(2)
    3.7 Fate of Unobserved Response Components
    		60(2)
    3.8 Control Energy
    		62(2)
    3.9 Compatibility of Controls in Adaptive Structures
    		64(1)
    3.10 Recapitulation
    		65(2)
    4 Statically Determinate Adaptive Structures
    		67(20)
    4.1 Excitation-Response Relations
    		67(2)
    4.2 Observed Response Components and Disturbances
    		69(1)
    4.3 Actuators and Controls
    		70(1)
    4.4 Actuator Placement and Control Problems
    		71(2)
    4.5 Actuator Placement and Control Computation When q=p less than n
    		73(2)
    4.5.1 Actuator Placement Problem
    		73(1)
    4.5.2 Computation of Controls
    		74(1)
    4.6 Actuator Selection and Control Computation When p less than q=n
    		75(1)
    4.6.1 Actuator Selection Problem
    		75(1)
    4.6.2 Computation of Controls in Selected Actuators
    		76(1)
    4.7 Actuator Placement and Control When p less than q less than n
    		76(2)
    4.7.1 Actuator Placement Problem
    		77(1)
    4.7.2 Selection of Actuators and Computation of Controls
    		78(1)
    4.8 Precision Control
    		78(1)
    4.9 Adaptive Trusses as Slow Moving Mechanical Manipulators
    		79(4)
    4.9.1 Actuator Placement When p=q less than n
    		82(1)
    4.9.2 Actuator Selection When p less than q=n
    		82(1)
    4.9.3 Actuator Placement When p less than q less than n
    		82(1)
    4.9.4 Computation of Controls
    		83(1)
    4.10 Generation of Output-Control Matrix
    		83(3)
    4.11 Recapitulation
    		86(1)
    5 Statically Indeterminate Adaptive Structures
    		87(22)
    5.1 Excitation-Response Relations
    		87(5)
    5.1.1 Relations for Adaptive Structures
    		88(1)
    5.1.2 Inverse Relations
    		88(1)
    5.1.3 Computation of Matrices C and C'
    		89(1)
    5.1.4 Response due to Delta v(0)
    		90(2)
    5.2 Observed Response Components and Disturbances
    		92(1)
    5.3 Actuators and Controls
    		93(1)
    5.4 Prevention of Stress Build-up
    		94(3)
    5.5 Secondary Actuators
    		97(3)
    5.5.1 Transformation of Compatibility Equation
    		97(2)
    5.5.2 Placement and Control of Secondary Actuators
    		99(1)
    5.6 Primary Actuators
    		100(7)
    5.6.1 Number of Primary Actuators q
    		101(2)
    5.6.2 Placement and Control of Primary Actuators
    		103(4)
    5.6.3 Generation of Matrix I(T)(Alpha)B(-T)(1)
    		107(1)
    5.7 Recapitulation of Actuator Placement
    		107(1)
    5.8 Recapitulation
    		108(1)
    6 Excitation-Response Relations, Dynamic Case
    		109(12)
    6.1 Equilibrium Equations
    		109(6)
    6.1.1 Restoring Forces
    		110(1)
    6.1.2 Inertial Forces
    		111(2)
    6.1.3 Frictional Forces
    		113(1)
    6.1.4 External Forces
    		114(1)
    6.1.5 Dynamic Equilibrium Equations of Nodes
    		114(1)
    6.2 Geometric Relations
    		115(2)
    6.2.1 Uncontrolled Part of Prescribed Element Deformations
    		115(1)
    6.2.2 Controlled Part of Prescribed Element Deformations
    		116(1)
    6.3 Stiffness Relations of Elements
    		117(1)
    6.4 Excitation-Response Relations
    		117(4)
    6.4.1 Dynamic Equilibrium Equations in terms of Xi
    		118(1)
    6.4.2 Equations of Motion of Nodes
    		119(1)
    6.4.3 Initial Conditions
    		120(1)
    7 Inverse Relations, Dynamic Case
    		121(28)
    7.1 Method for Obtaining the Inverse Relations
    		121(3)
    7.2 Undamped Free Vibrations of Nodes
    		124(4)
    7.3 Damped Free Vibrations of Nodes
    		128(2)
    7.4 Nodal Motion due to Nodal Forces
    		130(2)
    7.5 Nodal Motion due to Prescribed Element Deformations
    		132(1)
    7.6 Nodal Vibrations due to Support Movements
    		133(1)
    7.7 Nodal Motion due to Actuator Induced Deformations
    		134(1)
    7.8 Trajectory of Nodes in State Space
    		135(10)
    7.8.1 Uncontrolled Autonomous System
    		136(4)
    7.8.2 Uncontrolled Non-Autonomous System
    		140(3)
    7.8.3 Controlled Autonomous System
    		143(1)
    7.8.4 Controlled Non-Autonomous System
    		144(1)
    7.9 Steady State of Nodal Deflections
    		145(3)
    7.9.1 Time Function of Loads Becomes Constant
    		146(1)
    7.9.2 Time Function of Loads is Cyclic
    		146(2)
    7.10 Recapitulation of Inverse Relations
    		148(1)
    8 Active Control of Response, Autonomous Case
    		149(34)
    8.1 Response to Actuator Induced Element Deformations
    		149(2)
    8.2 Energy Cost of Inducing Element Deformations
    		151(3)
    8.2.1 Element Forces by the Displacement Method
    		152(1)
    8.2.2 Element Forces by the Force Method
    		152(2)
    8.3 Response Control
    		154(1)
    8.4 Open-Loop Control
    		155(2)
    8.5 Optimal State Feedback Control
    		157(6)
    8.5.1 Identification of Optimal Trajectory
    		158(2)
    8.5.2 Identification of the Optimal Control Law
    		160(2)
    8.5.3 Practical Difficulties with Optimal State Control
    		162(1)
    8.6 Optimal Output Feedback Control
    		163(2)
    8.7 Optimal Direct Output Feedback Control
    		165(4)
    8.8 Alternatives to Optimal Control
    		169(7)
    8.8.1 Choosing Gain Matrix by Trial and Error
    		169(3)
    8.8.2 Choosing Gain Matrix by Eigenvalue Assignment
    		172(4)
    8.9 Actuator Placement
    		176(4)
    8.9.1 Placement Criteria to Minimize Control Time
    		177(1)
    8.9.2 Placement Criteria to Minimize Spill-Over
    		178(2)
    8.10 Time Lag in Feedback Control
    		180(1)
    8.11 Recapitulation, Autonomous Case
    		181(2)
    9 Active Control of Response, Non-Autonomous Case
    		183(14)
    9.1 Total Response Including Control Excitations
    		183(4)
    9.1.1 Treatment in n-Space
    		183(3)
    9.1.2 Treatment in State Space
    		186(1)
    9.2 Response Control
    		187(1)
    9.3 Energy Considerations
    		188(2)
    9.4 Optimal State Feedback Control
    		190(3)
    9.4.1 Case When Excitation is Known a Priori
    		190(2)
    9.4.2 Case When Tracked Trajectory is Known a Priori
    		192(1)
    9.4.3 Case When Excitation is not Known a Priori
    		193(1)
    9.5 Non-Optimal Control Possibilities
    		193(1)
    9.6 Actuator Placement
    		194(2)
    9.7 Recapitulation, Non-Autonomous Case
    		196(1)
    10 Active Control Against Wind
    		197(12)
    10.1 State Equations for Wind Type Excitations
    		198(1)
    10.2 Control Possibilities of Nodal Motion
    		199(2)
    10.2.1 Insulate Structure Against Wind Forces
    		199(1)
    10.2.2 Determine Controls by Measuring Nodal Wind Forces
    		199(1)
    10.2.3 Determine Controls by Measuring the State
    		200(1)
    10.3 Excitation Power
    		201(1)
    10.4 What to Control
    		202(2)
    10.5 Actuator Placement
    		204(2)
    10.6 Control Law
    		206(1)
    10.7 Recapitulation of Active Control Against Wind
    		207(2)
    11 Active Control Against Seismic Loads
    		209(18)
    11.1 State Equations for Seismic Excitations
    		209(1)
    11.2 Control Possibilities of Nodal Motion
    		210(3)
    11.2.1 Insulate Structure Against Support Motions
    		211(1)
    11.2.2 Determine Controls by Sensing Support Motion
    		211(1)
    11.2.3 Determine Controls by Sensing the State
    		212(1)
    11.3 Managing Excitation Power
    		213(1)
    11.4 Passive Base Isolation Systems
    		214(5)
    11.4.1 Justification
    		215(2)
    11.4.2 Analysis
    		217(2)
    11.5 Actuator Placement for Active Base Isolation
    		219(3)
    11.5.1 Planar Frames under Horizontal Ground Motion
    		219(1)
    11.5.2 Planar Frames under Vertical Ground Motion
    		220(1)
    11.5.3 Space Frames under Horizontal Ground Motion
    		221(1)
    11.6 Control of Active Base Isolation Systems
    		222(3)
    11.6.1 Control Energy
    		222(1)
    11.6.2 Control System
    		223(1)
    11.6.3 Control Law
    		223(2)
    11.7 Recapitulation of Active Control Against Seismic Excitations
    		225(2)
    12 Distributed Parameter Adaptive Structures
    		227(28)
    12.1 Incorporating Intelligence
    		227(2)
    12.2 Composite Materials
    		229(4)
    12.2.1 Piezo-Electric Composite Materials as Actuators
    		229(1)
    12.2.2 Piezo-Electric Composite Materials as Sensors
    		230(1)
    12.2.3 Distributed Parameter Adaptive Structures
    		230(3)
    12.3 Static Case
    		233(17)
    12.3.1 Incremental Linear Excitation-Response Relations
    		233(9)
    12.3.2 Inverse Relations
    		242(6)
    12.3.3 Compatibility of Induced Strains
    		248(1)
    12.3.4 Control
    		249(1)
    12.4 Dynamic Case
    		250(4)
    12.4.1 Excitation-Response Relations
    		250(2)
    12.4.2 Inverse Relations
    		252(1)
    12.4.3 Control
    		253(1)
    12.5 Recapitulation
    		254(1)
    References 255
    Utku, Senol
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