Simulation and Control Aspects of FHT

Feb. 19, 2008 CU-NEES 2008 FHT WorkshopNEES at CU Boulder

The George E Brown, Jr. Network for Earthquake Engineering Simulation

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Simulation and Control Aspects of FHT

M. V. Sivaselvan

CO-PI CU-NEES

Assistant Professor

Dept. of Civil, Environmental and Architectural Eng.

University of Colorado at Boulder

[email protected]



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Outline• What is hybrid simulation?

• Why do it?

• Challenges in implementing a hybrid simulation system

• Types of hybrid simulation

• Hybrid simulation algorithms – architecture and equivalence

• Hybrid testing with shaking tables

• Current and planned work, Conclusions



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• Why do it?








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Multi-story Building

Earthquake

Most damage happens here – need better understanding by experimentation

Rest of the structure is undamaged – does not have to be physically build in the laboratory



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Wall Specimen

Actuators

Physical Experiment

Computer Model`

Interact during the experiment to mimic testing the whole building



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• Why do it?








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Use of hybrid simulationLaboratory Testing

For QualificationFor Discovery

Develop or calibrate Material/system models

• Examine the performance of a

component in its host

environment

• Proof of concept tests

• Interaction with surroundings

may significantly modify input

• Hybrid simulation is useful

• Hybrid simulation not very

useful for this purpose

• Some kind of computation-in-

the-loop with geometric

reasoning about state-space

may be possible

Hybrid Simulation is useful for qualification/proof-of-concept testing

when the interaction of a component with its surroundings

needs to be accurately represented



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• Why do it?








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Feedback interaction in reality

Substructure 1

Computational

Substructure 2

Physical

External Input

(Eg. Ground Motion) Boundary Condition

Work Conjugate

Boundary Condition



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In hybrid simulation however …

Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition

Actuator / Transfer Device



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Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition


Sensor



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Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition


Sensor Natural Physical

Feedback



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Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition



Feedback

Actuator

Feedback



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Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition



Feedback

Actuator

Feedback

NEW DYNAMICS



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Challenges• These additional dynamics create significant problems

• When the structure to be simulated is lightly damped, almost always

renders the system unstable

• Need to develop control algorithms to make hybrid simulation possible

• Causality → Design of such algorithms requires knowledge about physical

substructure (predictive model, implicit integration etc.) → This is a conflict

→ Robustness of algorithm with respect to modeling of the physical

substructure

• A numerical algorithm need not be causal, a hybrid simulation algorithm

does



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• Why do it?








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Hybrid Simulation

Pseudo-dynamic Dynamic

Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition

Has no inertia effects of interest

• Born from the displacement-based finite element –

one of the elements is now physical !

• Algorithms also reflect this

• If in addition, there are no frequency-dependent

behavior is the physical substructure – can be done

as slowly as we want to

Substructure 1

Computational

Substructure 2

Physical

External Input


Work Conjugate

Boundary Condition

Has significant inertia effects

• More practical applications necessitate

this form of hybrid simulation

• My research is in this area



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Hybrid Simulation

Pseudo-dynamic Dynamic

Real-time Slow

CU NEES Site

Hybrid simulation with Shaking Tables

CU NEES Site



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• Why do it?








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Recall

Substructure 1

Computational

Substructure 2

Physical

External Input

Boundary Condition

Work Conjugate

Boundary Condition


SensorNatural Physical

Feedback

Actuator

Feedback

Motivation: Want actuator to behave the same way as Substructure 1



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Introduce a controller

Substructure 1

Computational

Substructure 2

Physical

External Input

Boundary Condition

Work Conjugate

Boundary Condition


Natural Physical

Feedback

Actuator

Feedback

Controller



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Introduce a controller

Substructure 1

Computational

Substructure 2

Physical

External Input

Work Conjugate

Boundary Condition


Natural Physical

Feedback

Actuator

Feedback

ControllerTakes the same input as Substructure 1

Boundary Condition

+

-

Tries to do the same Thing as Substructure 1

Error



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Model Reference Control• Controller designed so that

does the same thing as

• Part implemented in the computer

Substructure 1

Computational

Substructure 2

Physical

External Input

Work Conjugate

Boundary Condition


Natural Physical

Feedback

Actuator

Feedback

ControllerTakes the same input as Substructure 1Takes the same input as Substructure 1

Boundary Condition

+

-


+

-


ErrorError

Substructure 1

Computational

Substructure 2

Physical

External Input

Work Conjugate

Boundary Condition


Natural Physical

Feedback

Actuator

Feedback

ControllerTakes the same input as Substructure 1Takes the same input as Substructure 1

Boundary Condition

+

-


+

-


ErrorError



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Computational Substructure

Physical Substructure

Actuator

External ExcitationInterface

Force

Interface Displacement


Model

ActuatorModel -

+Modeling

Error

+

+

Another Approach

Internal Model Control - IMCPart implemented in the computer



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Equivalence of different approaches

• The two approaches can be shown to be shown to be different

parametrizations of a 2 DOF controller

• Each offers a different perspective

– MRC useful in design

– IMC useful in robustness analysis



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CU FHT Algorithm

A R(u)+

-P

u

A +-

R u K

2

1

ms cs K F

Numerical Integration

Modeling Error Computation

• Computer implementation of IMC

Discretize at 10 ms Discretize at 1 ms

CU FHT Algorithm !!(Shing et. al., 2005)



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• Why do it?








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Hybrid Simulation with a Shaking Table

• Necessary when physical substructure has distributed mass

`Masses simulated

Physical substructure has no masses of significance, hence no inertia effects(Hence pseudo-dynamic)

• In many cases of practical interest for hybrid simulation, mass is distributed and there is no such natural way of lumping the mass for substructuring.

• Examples:

– Nonstructural components in civil structures

– Payloads in aerospace structures

– Machine components

– Dams, chimneys and other continuum civil structures

– Soil / fluid-structure interaction

• The interface device must be able to dynamically excited a system with distributed mass – shaking table



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• Why do it?








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Hybrid Testing with Shaking Tables• 1.5 m x 1.5 m working area• +/- 200 mm dynamic stroke• Frequency range – 0-50 Hz• Maximum payload – 2000 kg• Maximum Acceleration – 1.0-2.9 g• Maximum Velocity – 1 m/s• Will give CU structures lab capability to perform such hybrid

simulations as listed in the previous slide• Collaboration with MTS Systems



Shaking Table

External Actuator



Response Feedback `

Reaction Wall

Shaking Table


Response Feedback `

Hybrid Simulation ConfigurationsCombination of Shaking Table and

External Actuator Shaking Table Only



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Conclusions• Hybrid simulation – online combination of computation and physical experimentation

• Useful for qualification/proof-of-concept testing when the interaction of a component

with its surroundings needs to be accurately represented

• Challenge – added dynamics and feedback paths created by the transfer

system/actuator applying that applied interface conditions between the two

substructures.

• More difficult in dynamic hybrid simulation where physical substructure has

significant inertia (as opposed to pseudo-dynamic)

• Algorithms based on a control-systems perspective offer more promise than those

motivated by the finite element method

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Simulation and Control Aspects of FHT

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