Structural Control: Introduction and Fruitful Research Areas

Transcription

1 Structural Control: Introduction and Fruitful Research Areas T.T. Soong State University of New York at Buffalo Buffalo, New York 14260, USA Active (Responsive) Structures Under Normal Load Load Under Extreme Load Structure m x + c x + k x = f ( t) Response Load Structure Response m x + c x + k x + Γ( x) = F ( t) Structural Protective Systems Passive Systems Active and Semi-active Systems Seismic Isolation Dampers Electro-hydraulic Systems Smart Materials Elastomeric Bearings Lead Rubber Bearings Sliding Friction Pendulum Metallic Friction Viscoelastic Viscous Fluid TMD TLD Active Bracing Active Mass Damper Variable Stiffness and Damping Shape Memory Alloy Piezoelectric Layer ER Fluid MR Fluid Research Areas 1

2 Research Areas 2

3 Research Areas 3

4 Passive Systems Semi-active and Active Systems Hybrid Systems Structure with various control schemes PED: Passive Energy Dissipation Excitation Structure CONVENTIONAL STRUCTURE Response Excitation PED Structure Response STRUCTURE WITH PASSIVE ENERGY DISSIPATION (PED) Research Areas 4

5 Structure with various control schemes PED: Passive Energy Dissipation Sensors Computer Controller Sensors Control Actuators Excitation Structure Response STRUCTURE WITH ACTIVE CONTROL Structure with various control schemes PED: Passive Energy Dissipation Sensors Computer Controller Sensors Control Actuators Excitation PED Structure Response STRUCTURE WITH HYBRID CONTROL Structure with various control schemes PED: Passive Energy Dissipation Sensors Computer Controller Sensors Control Actuators PED Excitation Structure Response STRUCTURE WITH SEMI-ACTIVE CONTROL Research Areas 5

6 Basic Principles x Structure m x + c x + k x = m x g x g x Structure with Passive Systems m x + c x + k x + Γ x = m x g u x g x g Structure with Active, Semi-active x and Hybrid Control m x + c x + k x = m u m x g Γ x with: u = we m have m x + c x + k x + Γ x = m x g Advantages over Passive Systems Adaptability to Load Variability Enhanced Effectiveness in Response Modification Applicability to Multi-hazard Situations Selectivity of Control Objectives Research Areas 6

7 Research Areas 7

8 Research Areas 8

9 Research Areas 9

10 Research Areas 10

11 Research Areas 11

12 Research Areas 12

13 Applicability of Newer Technologies Base Isolation Passive Energy Dissipation Semi-active and Active Control Impact 1. Structural Response Control Structural Safety and Reliability Natural Hazard Mitigation Creative Engineering 2. Education Interdisciplinary Approach Innovation Research Areas 13

14 Assessment Fundamentally Sound and Innovative Natural Evolution from Passivity to Adaptability Insensitivity to Load Variables Application to Other Extreme Loads Open to New Possibilities Multi-purpose, Multi-functional Longer, Taller, more open Fruitful Research Areas Implementation of Structural Control Technology Critical Facilities and Contents Integrated Design Theory: Algorithm Development Device Development Experiment Benchmark Studies Research Areas 14

15 Theory: Algorithm Development Device Development Experiment Benchmark Studies Practice: Algorithm Development Device Development Experiment Benchmark Studies Implementation- Related Issues Frequently Asked Questions Reliability Verification of Control Performance Cost Research Areas 15

16 Contents Chapter 1. Chapter 2. Chapter 3. Chapter 4. Chapter 5. Chapter 6. Introduction Hardware Description Control Software Implementation Theoretical and practical Control Techniques Control Performance Verification Summary Computer-aided Control Performance Verification (CPV) Sampling Period of RTSS (T s ) Sampling Period of DSP Controller (T u ) Total Delay Time (t d ) Scaling Factors CPV Research Areas 16

17 Critical Facilities and Contents Examples of Nonstructural Components Architectural Partitions Piping Systems Ceilings Mechanical and Electrical Equipment Exterior Cladding Contents Investments in Building Construction (Miranda) 100% 80% 60% 40% 20% 0% 20.0% 17.0% 44.0% 62.0% 70.0% 48.0% 18.0% 13.0% 8.0% Office Hotel Hospital Contents Nonstructural Structural Research Areas 17

18 Direct Economic Loss due to Building Damage 1994 Northridge Earthquake (Kircher, 2003) Total: $18.5 Billion Nonstructural Related: ~ 50% 1994 Northridge Earthquake (Kircher, 2003) (Non-residential Buildings) Total: $6.29 Billion Nonstructural Related: $5.20 Billion (83%) Improved Nonstructural Performance Better Engineered Conventional Anchors Improved Nonstructural Performance Better Engineered Conventional Anchors (continued) Research Areas 18

19 Improved Structural Performance Economic Loss (in millions) Nonstructural System As Constructed With Damping System % Benefit With Isolation System % Benefit Drift--related related $1,086 $ $ Acceleration--related related 1,952 1, Contents/Inventory 2,162 1, Total $5,200 $2, $1, Reduction in direct economic loss through improved building performance of non-residential buildings (adapted from Kircher, 2003) Improved Nonstructural Performance Newer Technologies (continued) Semi-active device (Rana and Soong, 2004) Configuration of a Hybrid platform (Xu and Li, 2005) Research Areas 19

20 Integrated Control/Structural System w(t) Base Structure Pre-controlled Structure x(t) w(t) Base Structure x(t) Actuator Sensors Controller Controlled Structure A. Variational approach Equation of motion: ( t) = ( ) ( t) ( ) ( ) + ( ) ( t) + ( t, ) z A ξ z B ξ f z B ξ u e ξ s Problem: Determine ξ and u(t) such that performance objective is achieved by, for example, minimizing t f T T J ( z, ξ, u ) = z Qz + u Ru + γw( ξ, u ) dt 0 Subjected to constraints such as: ξ ξ s Research Areas 20

21 A. Variational approach Variational Calculus leads to: Az + Bu Bf + e z = 0, z ( 0) = 0 s T 2 Qz + A λ+ λ = 0, λ ( t f ) = 0 T 2Ru + B λ = 0 ( ) T λ ξaz ξbu ξbf + ξe + ξw = 0 s Over t = ( 0, t f ) with ξ ξ 0 B. Redesign approach Equation of motion: ( t) = ( ) ( t) ( ) ( ) + ( ) ( t) + ( t, ) z A ξ z B ξ f z B ξ u e ξ s Step 1: Based on desired ξ, determine u(t) such that some structural performance is achieved; Step 2: Determine optimal ξ and u(t) to achieve same structural performance by, for example, minimizing t f T uru dt 0 Subjected to constraints on ξ B. Redesign approach S a 1 (T 0, b 0 ) 4 (T 2, b 2 ) 3 (T 1, b 1 ) 2 T1>T0 Performance S d S d Research Areas 21

22 Consider B. Redesign approach () t = () t + () t + () t z Az Bu e Step 1: Control design based on desired ξ, giving u () t = Gz() t Step 2: Consider ( M + ΔM) x( t) + ( C+ ΔC) x ( t) + ( K+ ΔK) x( t) = HGaz( t) + ηw( t) where u ( t) = G z( t) a To achieve same performance objective, we have ( ) () a ( ) () ( ) () x t x t x t HG = HGa [ ΔK ΔC] ΔMx x t x t x t = H G + G z ( active passive ) () t () t where active B. Redesign approach G = HG = T Gpassive -I B G B L with K+ΔK =K+BG k kb G = diag (, Δki, ) T k k C+ΔC=C+BG c cb Gc = diag (, Δci, ) T c M+ΔM =M+BmGmB G = diag (, Δmi, ) T m m Bk 0 0 Gk 0 0 B = 0 Bc 0 p G 0 G 0 p = c I 0 = [ I I I] 0 0 B m 0 0 G m and a I L = 1 M ( HG [ K C] ) 0 p p p B. Redesign approach Under mild conditions G G T I0BpGp( ΔM,ΔC,ΔK) BpL = + a G p and G a are determined by minimizing, for example, t f T dt uru 0 Subjected to constraints on ΔM, ΔC, ΔK Solution can be found by using, for example, Exterior Penalty Function Method Research Areas 22

23 Numerical Example (3) W (W33 118) (4) W (W14 257) W (W14 311) (1) (2) (a) L=9150mm h=3960mm Figure 1. SDOF steel frame under white noise excitation Numerical Example Objective: a lighter structure maintaining drift equal to 0.5% x MAX /xlim U MAX (kn) K s /K= K s /K= K a /K (a) K a /K (b) x MAX /xlim U MAX (kn) C a /C C a /C (c) (d) Figure 2. normalized maximum displacement (a) and maximum control force (b) versus normalized structural stiffness and damping (c-d) Numerical Example Step 1: Select a reduction of k of 60% Table 1. Maximum response for white noise with pga of 0.25g Uncontrolled Umax=94.86kN (1) (2) (3) (4) (5) (6) Drift xi [%] W (W14 99) x a [m/sec 2 ] MS0 (kg) Drift xi [%] W (3) (W33 118) (4) Umax=94.86kN x a [m/sec 2 ] (1) (2) W (W14 99) (a) L=9150mm Figure 3. Steel frame under white noise excitation MS (kg) h=3960mm Research Areas 23

24 Numerical Example Step 2: Redesign subject to ΔM M 0.25, K K = 0.18K Table 2. Optimal structural parameters after redesign for white noise with pga of 0.25g s M K C Mopt Kopt Copt Uopt kg kn/m kn sec/m kg kn/m kn sec/m kn Table 3. Percentage increment or reduction of structural parameters ΔM ΔK ΔC (%) (%) (%) A substantially lighter structure can be designed to achieve a specific performance objective when an active brace is integrated into the structure in an optimal fashion Advantages Easier quadratic mathematical format Rapid convergence Guarantees optimal control Applicable to nonlinear as well as multi-degree-offreedom structures Conclusions Integrated control/structural systems can lead to: New Structural Forms and Configurations; Lighter, longer, taller, more open structures; Multi-purpose and multi-functional Research Areas 24

25 Sears Tower, Chicago Integrated design Weight of Steel, LBS/SQ.FT. FLOOR AREA Designed for drift index (Δ/H)=0.25% Designed for drift index (Δ/H)=0.25%with integrated control/structural systems Sears Tower, Designed for 110 stories gravity load Number of stories Acknowledgments Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, USA U.S. National Science Foundation G.P. Cimellaro Research Areas 25