Model-based Real-Time Hybrid Simulation for Large-Scale Experimental Evaluation Brian M. Phillips University of Illinois B. F. Spencer, Jr. University of Illinois Yunbyeong Chae Lehigh University Karim Kazemibidokhti Lehigh University Shirley J. Dyke Purdue University Tony A. Friedman Purdue University James M. Ricles Lehigh University Quake Summit 2012 Boston, Massachusetts June, 2012

INTRODUCTION 2

Large-Scale RTHS Project Performance-based design and real-time, large-scale testing to enable implementation of advanced damping systems Joint project between Illinois, Purdue, Lehigh, UConn, and CCNY 3

Hybrid Simulation Loop Servo-hydraulic system introduces dynamics into the hybrid simulation loop Actuator dynamics are coupled to the specimen through natural velocity feedback When multiple actuators are connected to the same specimen, the actuator dynamics become coupled 4 Numerical Substructure u Experimental Substructure Sensors ff meas x Loading System Servo-Hydraulic System

SERVO-HYDRAULIC SYSTEM MODEL 5

MIMO System Model 6 + Servo-Hydraulic System G xu (s) Natural Velocity Feedback Actuator SpecimenServo-Controller and Servo-Valve +

Multi-Actuator Setup Equations of motion: 7 Actuator 3 Actuator 1 Actuator 2 Servo-Controller 1 Servo-Controller 2 Servo-Controller 3 Computer Interface

MIMO System Model Component models: Servo-hydraulic system model: + Servo-Hydraulic System G xu (s) Natural Velocity Feedback Actuator Specimen ufx Servo-Controller and Servo-Valve + 8

MODEL-BASED ACTUATOR CONTROL 9

Regulator Redesign 10 Servo-hydraulic system transfer function in state space: Tracking error: Ideal system with perfect tracking: Deviation system:

Model-Based Control Feedforward Feedback Links 11 Total control law is a combination of feedforward and feedback: G FF (s) LQG G xu (s) eu FB u FF u Feedforward Controller Feedback ControllerServo-Hydraulic Dynamics

LARGE-SCALE EXPERIMENTAL STUDY 12

Prototype Structure 13 Actuator 3 Actuator 1 Actuator 2 Experimental Substructure

MIMO Transfer Function Magnitude 14 Input 1Input 2Input 3 Output 1 Output 2 Output 3

MIMO Transfer Function Phase 15 Input 1Input 2Input 3 Output 1 Output 2 Output 3

5 Hz BLWN Tracking 16 RMS Error Norm No Comp: 44.8% FF + FB: 3.75 % No Comp: 47.8% FF + FB: 4.43 % No Comp: 50.8% FF + FB: 4.39 %

15 Hz BLWN Tracking 17 No Comp: 97.8% FF + FB: 10.7 % No Comp: 96.6% FF + FB: 13.5 % No Comp: 98.1% FF + FB: 11.5 % RMS Error Norm

Prototype Structure 18 Actuator 3 Actuator 1 Actuator 2 Modef n (Hz) % % % Total Structure Experimental Substructure

Ground acceleration 0.12x NS component 1994 Northridge earthquake Numerical integration CDM at 1024 Hz Actuator control FF + FB control w/ coupling Structural control Clipped-optimal control algorithm (Dyke et al., 1996) RTHS Parameters 19

Semi-Active RTHS Results 0.12x Northridge 20

CONCLUSIONS 21

Conclusions The source of actuator dynamics including actuator coupling has been demonstrated and modeled A framework for model-based actuator control has been developed addressing Actuator dynamics Control-structure interaction Model-based control has proven successful for RTHS Robust to changes in specimen conditions Robust to nonlinearities Naturally can be used for MIMO systems 22

Thank you for your attention 23 The authors would like to acknowledge the support of the National Science Foundation under award CMMI