Control of Structures

1 — Introduction to Structural Control.- 1.1 Introduction.- 1.2 Structural Control.- 1.3 Classification of Structural Control.- 1.4 Elaboration of Vibration Control.- 1.4.1 Response to a Constant Force with Finite Rise Time.- 1.4.2 Effect of Damping.- 1.5 Active Control of ODOF Systems.- 1.5.1 Control Using an Auxiliary Mass.- 1.5.2 Control Using Auxiliary Tendons (Springs).- 1.5.3 Control Using an Auxiliary Damper.- 1.6 The Control Devices.- 1.6.1 Electro-Hydraulic Servomechanism.- 1.6.2 Proportional Gain Controller.- 1.6.3 Automatic Gain Controller.- 1.7 References.- Appendix A — Classical Control Theory.- A. 1 Introduction.- A. 2 Feedback Control Systems.- A. 3 Design of a Control System.- A. 3.1 Stability.- A.3.1.1 Routh’s Criterion.- A. 3.1.2 Root Locus.- A.3.1.3 Bode Plots.- A.3.1.4 Polar Plots and Nyquist’s Stability Criterion.- A.3.1.5 Nichols’ Charts.- A.3.2 Steady-State Accuracy.- A.3.3 Satisfactory Transient Response.- A.3.4 Satisfactory Frequency Response.- A. 4 References.- 2 — Morphology Of Structural Control.- 2.1 Preliminary Remarks.- 2.2 On the Basics and the Actual Nature of Structural Control Problems.- 2.3 Examples.- 2.4 The Modal Approach.- 2.5 References.- 3 — Automatic Active Control of Simple Span Bridges.- 3.1 Mathematical Models of Simple Span Bridges.- 3.2 Active Control Mechanisms in Bridges.- 3.2.1 Control through Auxiliary Masses.- 3.2.2 Control through Auxiliary Tendons.- 3.2.3 Control through Auxiliary Dampers.- 3.2.4 Control using Aerodynamic Appendages.- 3.3 Active Control by Classical Control Methods.- 3.3.1 Equation of Motion of the System.- 3.3.2 Control of the Fundamental Mode of Vibration.- 3.3.2.1 Stability Requirement.- 3.3.2.2 Damping Requirement.- 3.3.2.3 Steady State Error Requirement.- 3.3.2.4 Sensitivity Requirement.- 3.3.2.5 Controlled System’s Response.- 3.3.2.6 Summary and Conclusion.- 3.3.3 Control of Three Modes of Vibration.- 3.3.3.1 Controlled Systems’ Response.- 3.3.3.2 Design of the Control System using a Servomechanism.- 3.3.3.3 Design of the Control System using a Proportional Controller.- 3.3.3.4 Summary and Conclusions.- 3.4 Active Structural Control by Pole Assignment Method.- 3.4.1 The Pole Assignment Method.- 3.4.1.1 Controllability.- 3.4.1.2 Observability.- 3.4.1.3 Design Procedure.- 3.4.1.4 Design of State Feedback.- 3.4.1.5 Design of Output Feedback.- 3.4.1.6 Design of the Observer.- 3.4.2 Application of the Pole Assignement Method.- 3.4.2.1 Example 1.- 3.4.2.2 Example 2.- 3.4.2.3 Example 3.- 3.4.3 Summary and Conclusion.- 3.5 Active Structural Control by Optimal Control Methods.- 3.5.1 The Optimal Control Problem.- 3.5.2 Solution of the Optimal Control Problem.- 3.5.3 Numerical Applications.- 3.5.3.1 Application of the Regulator Problem.- 3.5.3.2 Application of the Tracking Problem.- 3.5.4 Summary and Conclusions.- 3.6 Study of Secondary Effects.- 3.6.1 Inertia Effect of the Moving Load.- 3.6.1.1 Uncontrolled Response.- 3.6.1.2 Controlled Response using a Regulator Control System.- 3.6.1.3 Controlled Response using a Tracking Control System.- 3.6.2 Normal Force Effect.- 3.6.2.1 Passive Control Response.- 3.6.2.2 Active Control Response using a Regulator Control System.- 3.6.2.3 Active Control Response using a Tracking Control System.- 3.6.3 Effect of Uneveness of the Bridge Deck.- 3.6.3.1 Uncontrolled Response.- 3.6.3.2 Active Control Response using a Regulator Control System.- 3.6.3.3 Active Control Response using a Tracking Control System.- 3.6.4 Stochastic Control Against Uneveness.- 3.6.4.1 Stochastic Control Problem.- 3.6.4.2 Numerical Application.- 3.6.4.3 Summary and Conclusions.- 3.6.5 Effect of Various Moving Loads.- 3.6.5.1 Pulsating Force Moving with Constant Speed.- 3.6.5.2 Uniform Load Moving with Constant Speed.- 3.6.5.3 Concentrated Load Moving with Decelerated Speed.- 3.6.5.4 Concentrated Load Moving with Accelerated Speed.- 3.6.6 Summary and Conclusions.- 3.7. Optimal Control and Sensors Locations.- 3.7.1 The Optimal Observer.- 3.7.2 The Design Method.- 3.7.3 Numerical Examples.- 3.7.3.1 Example.- 3.7.3.2 Example.- 3.7.4 Conclusions.- 3.8 References.- 4 — Automatic Active Control of Tall Buildings.- 4.1 Introduction.- 4.2 Building Response due to Wind Forces.- 4.2.1 Wind Forces.- 4.2.2 Stochastic Response.- 4.2.3 Deterministic Analysis in the Time Domain.- 4.2.4 Stochastic Analysis.- 4.3 Active Control of Tall Buildings.- 4.3.1 Movable Appendages.- 4.3.2 Tuned Mass Dampers.- 4.3.3 Active Tendons.- 4.3.4 Practical Control Mechanisms.- 4.4 Control Using Active Tendons.- 4.4.1 Design of the Control Force.- 4.4.2 Response Analysis.- 4.5. Control Using Tuned Mass Dampers.- 4.5.1 Design of the Active Control Law.- 4.5.2 Controlled Response.- 4.5.3 Effectiveness of Active TMD.- 4.5.4 Concluding Remarks.- 4.5.5 Design of an Active TMD.- 4.5.5.1 Stochastic Analysis.- 4.5.5.2 The Design Process for an Active TMD.- 4.5.5.3 Numerical Investigation.- 4.5.5.4 Conclusions.- 4.6 Active Control By Means of Appendages.- 4.6.1 Design of Optimal Appendage Movement.- 4.6.2 Contributions.- 4.6.3 Example.- 4.6.3.1 Klein’s Method.- 4.6.3.2 Soong’s Method.- 4.6.3.3 The Authors’ Method.- 4.6.4 Extension.- 4.6.5 Example.- 4.7 Stochastic Control of Tall Buildings.- 4.7.1 Introduction.- 4.7.2 Equations of Motion.- 4.7.3 Spectrum of Wind Forces.- 4.7.4 Design of Filters.- 4.7.5 Design of a Stochastic Control Law.- 4.7.6 Numerical Investigations for Tendon Control.- 4.7.7 Numerical Investigation of Tuned Mass Damper Control Application.- 4.7.8 Control by Appendages.- 4.7.9 Conclusions.- 4.8 Control of Tall Buildings Taking Time Delay into Account.- 4.8.1 Equations of Motion.- 4.8.2 Design of Control Laws.- 4.8.3 Numerical Applications to Tendon Control.- 4.8.4 Numerical Application to TMD Control.- 4.9 Feasibility of Active Control of Tall Buildings.- 4.9.1 Introduction.- 4.9.2 Feasibility of Active Tendon Control.- 4.9.3 Feasibility of Active Tuned Mass Damper Control.- 4.9.4 Feasibility of Active Control by Appendages.- 4.10 Finding a Practical Control Mechanism for Tall Buildings.- 4.10.1 Introduction.- 4.10.2 The Uncontrolled Building Response.- 4.10.3 Combined Passive Tendon and PTMD.- 4.10.4 Combined Active Tendon and Passiv Passive TMD.- 4.10.5 Combined Passive Tendon and Active TMD.- 4.10.6 Combined Active Tendon and Active TMD.- 4.10.7 Combined Appendages, Passive Tendon and PTMD.- 4.10.8 Combined Appendage, Active Tendon and PTMD.- 4.10.9 Combined Appendage, Active Tendon and ATMD.- 4.10.10 Conclusions.- 4.11 References.- 5 — A Review of Methods in the Control of Continuous Systems.- 5.1 Introduction.- 5.2 Considerations of Existence and Performance of a Control.- 5.3 A Closed Form Solution to the Control Problem.- 5.4 A Liapunov-Like Assessment of a Spillover-Safe Design.- 5.5 References.