19-10-2012, 04:22 PM
Linear Dynamic Model for Advanced LIGO Isolation System
[attachment=36723]
Aim of modeling
Help to understand the dynamics of the system.
Help to control the system.
Help to design future system.
What are we trying to model?
LIGO suspension system is a complicated nonlinear dynamic mass spring system.
We need to build a linear model of it in full degrees of freedom.
Elements of the systems.
Stages (Masses)
Springs
Sensors
Actuators
Stiffness Matrix K
The stiffness matrix is defined as the reaction forces and torques on stages due to small movement of the stages around equilibrium positions.
In small range of motion, the changes of reaction forces and torques are linear to the perturbations of the positions of stages.
3 Steps of making stiffness matrix K
Convert Stage motion into relative motion of two ends of springs around equilibrium positions.
Calculate each spring’s reaction force and torque.
Sum up forces and torques from all springs on stages.
Some features of the model
The principle is simply based on F=Kx and F=Ma.
To linearize each spring is simpler than to linearizie the whole system at ones.
Make use of Simulink and toolboxes in Matlab.
Model constructor
There are many systems to be modeled.
There are many different types of springs, actuators and sensors in the system.
Springs: Stretchable Wire, Blade, more general spring.
Sensors: Optical Sensor, Geophone.
Actuators: Voice coil.
For each system, we only need to feed its geometry and physical information to the model constructor.
The information should be in the form of defined data structures.
Stage, spring, actuator, sensor, control law.
Conclusion
A linear dynamic model of advanced LIGO isolation system directly based on very simple physics principles.
This model is used to analysis the dynamics of several prototype systems and to design control laws for them.
This model is also used to design future LIGO isolation systems. Based on our experience, we feel confident of the predictions which the model made.
[attachment=36723]
Aim of modeling
Help to understand the dynamics of the system.
Help to control the system.
Help to design future system.
What are we trying to model?
LIGO suspension system is a complicated nonlinear dynamic mass spring system.
We need to build a linear model of it in full degrees of freedom.
Elements of the systems.
Stages (Masses)
Springs
Sensors
Actuators
Stiffness Matrix K
The stiffness matrix is defined as the reaction forces and torques on stages due to small movement of the stages around equilibrium positions.
In small range of motion, the changes of reaction forces and torques are linear to the perturbations of the positions of stages.
3 Steps of making stiffness matrix K
Convert Stage motion into relative motion of two ends of springs around equilibrium positions.
Calculate each spring’s reaction force and torque.
Sum up forces and torques from all springs on stages.
Some features of the model
The principle is simply based on F=Kx and F=Ma.
To linearize each spring is simpler than to linearizie the whole system at ones.
Make use of Simulink and toolboxes in Matlab.
Model constructor
There are many systems to be modeled.
There are many different types of springs, actuators and sensors in the system.
Springs: Stretchable Wire, Blade, more general spring.
Sensors: Optical Sensor, Geophone.
Actuators: Voice coil.
For each system, we only need to feed its geometry and physical information to the model constructor.
The information should be in the form of defined data structures.
Stage, spring, actuator, sensor, control law.
Conclusion
A linear dynamic model of advanced LIGO isolation system directly based on very simple physics principles.
This model is used to analysis the dynamics of several prototype systems and to design control laws for them.
This model is also used to design future LIGO isolation systems. Based on our experience, we feel confident of the predictions which the model made.