Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback

1. Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback B. F. Spencer, Jr. University of Illinois Brian M. Phillips University of Maryland

2. Introduction and Motivation

3. m2 x2(t) c2 k2 m1 x1(t) k2 c1 k1 k1 x xi xi+1 ti ti+1 t Hybrid Simulation (pseudodynamic testing) Schematic procedure: Numerical substructure R2 Numerical integration Ri+1 xi+1 R1 Numerical component Experimental component Displacements imposed at slow rates Physical substructure Time scale extension factor = 100 - 1000

4. Real-Time Hybrid Simulation • 1:1 time scaling • Accurately test rate dependent structural components (i.e. dampers, friction devices, and base isolation) • Cycles must be performed very quickly • System dynamics become important • Time delays – due to data communication and computation • Time lags – due to actuator dynamics Numerical Calculations Apply Displacement Measure Restoring Forces Base Isolation MR Damper

5. Effects of Time Delays and Time Lags • Systematic errors that propagate throughout experiment • Introduces energy  negative damping • Problems arise with • structures with low damping • experiments with large hydraulic actuators f x Actual Response Measured xm t x Desired xd Measured Response

6. Multi-Metric Feedback • Rate-dependent specimens are sensitive to velocity and acceleration trajectories • Sensors measuring higher-order derivatives can be incorporated into model-based actuator control for RTHS • Better estimate of model states • Improved tracking of higher-order derivatives • Improved frequency bandwidth Base Isolation MR Damper

7. Actuator Dynamics and Compensation

8. Model of Actuator Dynamics Gyu(s) am QL ic fp xv e pL u A Kprop + + - - xm Servovalve Dynamics Servovalve flow Controller Actuator Specimen A s Natural velocity feedback Because of the “natural” velocity feedback, the dynamics of the experimental component directly affect the response of the actuator (Dyke et al., 1995).

9. Actuator Dynamics Compensation • Actuator dynamics produce effects on both magnitude and phase lag • Actuator transfer function dependents on the attached specimen (i.e., actuator-specimen interaction) • Models of actuator dynamics are used to develop model-based compensation strategies

10. Framework for Actuator Dynamics Compensation Outer-loop control Gyu(s)Inner-loop control am xd QL fp ic u e Control algorithm PID ad + + xm - - Compensator for actuator dynamics Servo-controller Actuator Specimen Servovalve Natural vel. feedback • Goal: to make measured displacement xm and acceleration am as close as possible to the desired displacement xd and acceleration ad(minimizing phase lag and amplitude changes)

11. Tracking Control through Regulator Redesign • Express servo-hydraulic system model in state space: • Assume ideal system with perfect tracking: • Create deviation system: • Define tracking control as combination of feedforward and feedback terms:

12. Feedforward Component • Open-loop control, processes the reference signal directly to produce the ideal response • Allows combining knowledge of the command/plant to improve the system response • Design of a feedforward compensator is in essence a calculation of the inverse of a dynamic system (Åström and Wittenmark, 1984) uFF xm xd GFF(s) Gxu(s) FeedforwardController Servo-HydraulicSystem

13. FeedforwardComponent • Linearized poles-only model • Implement improper inverse by adding a low-pass filter (Carrion and Spencer, 2007) • Higher order derivatives can be pulled from numerical integration of structure Identified System Model Inverse Inverse in Time Domain

14. Model-Based Feedforward-Feedback Control • Use LQG regulator design • Reduces effect of • Innacuracies in the modeling or identification of the plant • Variations of the plant dynamics during the experiment (e.g., specimen yielding or MR damper changes) uFF GFF(s) Feedforward Controller + + e uFB u Gxu(s) LQG + ‒ Feedback Controller Servo-Hydraulic Dynamics

15. Multi-Metric Feedback • Include acceleration measurements • Better state estimates • Add LQG weighting to acceleration uFF FeedforwardController + uFB + LQG ‒ u + Servo-Hydraulic Dynamics Feedback Controller + ‒

16. Large-Scale Experimental Setup@ the University of Illinois 556 kN Actuator ±152 mm Stroke Accelerometers 445 kN Load Cell Reaction Angle Tie Down Reaction Angle Block and Wedge Shear Key Tie Down Shear Key Block and Wedge Internal AC LVDT

17. Tracking Performance:Frequency Domain, Passive-Off

18. Tracking Performance:Frequency Domain, Passive-On

19. RTHS Study ofSDOF Structure • Numerical substructure • 20,000 kg mass • 2% damping • 0.5, 1, 5, 10, 20, and 30 Hz models • Experimental substructure • Passive-off (0.0 Amps) 200kN MR damper • Input • 0 to 50 Hz BLWN ground acceleration • Numerical Integration • CDM at 2000 Hz

20. RMS Tracking Error Norm During RTHS Model-based compensator performs very well, providing accurate compensation for actuator dynamics Zoom

21. Multi-Actuator Systems

22. 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

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

24. MIMOSystem Model Servo-Hydraulic System Gxu(s) + + − − Actuator Servo-Controllerand Servo-Valve Specimen Natural Velocity Feedback Servo-hydraulic system model:

25. Model-Based Multi-Actuator Control Total control law is a combination of feedforward and feedback: uFF GFF(s) FeedforwardController + + e uFB u Gxu(s) LQG + - Feedback Controller Servo-Hydraulic Dynamics

26. Prototype Structure Actuator 3 Actuator 2 Actuator 1 Total Structure Experimental Substructure

27. MIMO Transfer FunctionMagnitude Input 1 Input 2 Input 3 Output 1 Output 2 Output 3

28. MIMO Transfer FunctionPhase Input 1 Input 2 Input 3 Output 1 Output 2 Output 3

29. 5 Hz BLWN Tracking 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 %

30. RTHS Parameters • 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)

31. Semi-Active RTHS Results0.12x Northridge Model-based compensator performs well for multi-actuator systems as well as under changing specimen conditions

32. Conclusions

33. Conclusions • A state-of-the-art experimental setup has been assembled for RTHS • The source of actuator dynamics including control-structure interaction and actuator coupling has been demonstrated and modeled • A framework for model-based actuator control has been developed • Model-based control has proven successful for RTHS • Robust to changes in specimen conditions • Robust to nonlinearities • Naturally can be used for MIMO systems • Flexible to include multi-metric feedback

34. Thank you for your attention