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A simplified LPF system identification experiment

In this section we give an overview of the main elements we will use in the following to simulate some experiments in the LTP and estimate system parameters from them. In order to capture the main concepts of the analysis we perform a limited analysis based on the following constraints:

Model used

Fig. Scheme of the LTP as a closed loop system. The triangles represent cross-couplings and rhombus the injections to the system.

The scheme above show the main elements in the model: D stands for the dynamics of the test mass; S is the sensor (interferometer in our case); the control is split in the controller transfer functions (H), the decoupling matrix (C) and the actuators (H). DELAY and D3 are delay boxes that we will not use in our exercise. In the exercise we will use two ssm models implementing the previous scheme: one to generate the data (which) include noise sources and a second used for parameter estimation (where we do not need the noise inputs). These are the following:

Model name Comment

LTP

noise sources not included (type: help ssm_model_LTP)

LPF

noise sources included (type: help ssm_model_LPF)

Parameters used

The parameters relevant for our analysis are described in the table below. The names are according to the notation in the ssm models

Parameter Description

FEEPS_XX

FEEPs actuation gain in X direction

CAPACT_TM2_XX

Capacitive actuation in TM2 in X direction

IFO_X12X1

Interferometer cross-coupling X1 -> X12

EOM_TM1_STIFF_XX

TM1 stifness in X direction (squared)

EOM_TM2_STIFF_XX

TM2 stifness in X direction (squared)

Injections signals

We will apply two signals to the system. These follow the prescription described in the technical note S2-UTN-TN-3045. Since these are quite used, the LTPDA contains two built-in models to create them in a single line. The first experiment will inject a sinusoid sequence to the x1 channel and the second experiment will inject a different sinusoid sequence to the x12 channel. Hence, the experiments we will study can be summarized in the following table:

Experiment name Signal applied Injection port

Inv0001

built-in model: 'signals_3045_1_1'

GUIDANCE.IFO_x1

Inv0002

built-in model: 'signals_3045_1_2'

GUIDANCE.IFO_x12

Measured quantities

In this simplified analysis, our analysis of the displacement (or acceleration) measured on the test masses will only come from the X component of optical read-out for the two channels, x1 and x12. Hence, discarding the remaining degrees of freedom. We will add two quantities that will, as described in Topic 3, will be useful when translating displacement into acceleration noise. The summary of measured quantities (for each experiment) used in the analysis is the following:

Output port Description

DELAY_IFO.x1

Interferometer x1 measurement

DELAY_IFO.x12

Interferometer x12 measurement

DFACS.sc_x

Commanded force on spacecraft

DFACS.tm2_x

commanded force on test mass #2


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