# Three-Axis Gyroscope

Implement three-axis gyroscope

## Description

The Three-Axis Gyroscope block implements a gyroscope on each of the three axes. The measured body angular rates $\left({\overline{\omega }}_{meas}\right)$ include the body angular rates $\left({\overline{\omega }}_{b}\right)$, errors, and optionally discretizations and nonlinearizations of the signals.

`${\overline{\omega }}_{meas}={\overline{\omega }}_{b}×{\overline{\omega }}_{SFCC}+{\overline{\omega }}_{bias}+Gs×{\overline{\omega }}_{gsens}+noise$`

where ${\overline{\omega }}_{SFCC}$ is a 3-by-3 matrix of scaling factors on the diagonal and misalignment terms in the nondiagonal, ${\overline{\omega }}_{bias}$ are the biases, (Gs) are the Gs on the gyroscope, and ${\overline{\omega }}_{gsens}$ are the g-sensitive biases.

Optionally, discretizations can be applied to the block inputs and dynamics along with nonlinearizations of the measured body angular rates via a Saturation block.

## Parameters

Second order dynamics

Select to apply second-order dynamics to gyroscope readings.

The natural frequency of the gyroscope. The units of natural frequency are radians per second.

Damping ratio

The damping ratio of the gyroscope. A dimensionless parameter.

Scale factors and cross-coupling

The 3-by-3 matrix used to skew the gyroscope from body axes and to scale angular rates along body axes.

Measurement bias

The three-element vector containing long-term biases along the gyroscope axes. The units are in radians per second.

G-sensitive bias

The three-element vector contains the maximum change in rates due to linear acceleration. The units are in radians per second per g-unit.

Update rate (sec)

Specify the update rate of the gyroscope. An update rate of 0 will create a continuous gyroscope. If noise is selected and the update rate is 0, then the noise will be updated at the rate of 0.1. The units of update rate are seconds.

If you:

• Update this parameter value to 0 (continuous)

• Configure a fixed-step solver for the model

• Do not have a Control System Toolbox™ license

you must also select the Automatically handle rate transition for data transfer check box in the Solver pane. This check box enables the software to handle rate transitions correctly.

Noise on

Select to apply white noise to gyroscope readings.

Noise seeds

The scalar seeds for the Gaussian noise generator for each axis of the gyroscope.

Noise power

The height of the PSD of the white noise for each axis of the gyroscope. The units are (rad/s)2/Hz.

Lower and upper output limits

The six-element vector containing three minimum values and three maximum values of angular rates in each of the gyroscope axes. The units are in radians per second.

## Inputs and Outputs

InputDimension TypeDescription

First

Three-element vectorContains the angular rates in body-fixed axes, in radians per second.

Second

Three-element vectorContains the accelerations in body-fixed axes, in Gs.

OutputDimension TypeDescription

First

Three-element vectorContains the measured angular rates from the gyroscope, in radians per second.

## Assumptions and Limitations

Anisoelastic bias and anisoinertial bias effects are not accounted for in this block. Additionally, this block is not intended to model the internal dynamics of different forms of the instrument.

 Note:   This block requires the Control System Toolbox product for discrete operation (nonzero sample time).

## Reference

Rogers, R. M., Applied Mathematics in Integrated Navigation Systems, AIAA Education Series, 2000.