Three-axis Gyroscope

Implement three-axis gyroscope

• 

Libraries:
Aerospace Blockset / GNC / Navigation

Description

The Three-Axis Gyroscope block implements a gyroscope on each of the three axes. For more information on the measured body angular rates, see Algorithms.

Optionally, to apply discretizations to the block inputs and dynamics along with nonlinearizations of the measured body angular rates, use the Saturation block.

Limitations

• Anisoelastic bias and anisoinertial bias effects are not accounted for in this block.

• This block is not intended to model the internal dynamics of different forms of the instrument.

Ports

Input

ω — Angular rates

three-element vector

Angular rates in the body-fixed axes, specified as a three-element vector, in radians per second.

Data Types: double

G's — Accelerations

three-element vector

Accelerations in the body-fixed axes, specified as a three-element vector, in Gs.

Data Types: double

Output

ω_meas — Measured angular rates

three-element vector

Measured angular rates from the gyroscope, returned as a three-element vector, in radians per second.

Data Types: double

Parameters

Second order dynamics — Second-order dynamics

on (default) | off

To apply second-order dynamics to gyroscope readings, select this check box.

Programmatic Use

Block Parameter: dtype_g

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Natural frequency (rad/sec) — Natural frequency

190 (default) | scalar

Natural frequency of the gyroscope, specified as a double scalar, in radians per second.

Programmatic Use

Block Parameter: w_g

Type: character vector

Values: double scalar

Default: '190'

Damping ratio — Damping ratio

0.707 (default) | scalar

Damping ratio of the gyroscope, specified as a double scalar.

Programmatic Use

Block Parameter: z_g

Type: character vector

Values: double scalar

Default: '0.707'

Scale factors and cross-coupling — Scale factors and cross coupling

[1 0 0; 0 1 0; 0 0 1] (default) | 3-by-3 matrix

Scale factors and cross-coupling, specified as a 3-by-3 matrix, to skew the gyroscope from body axes and to scale accelerations along body axes.

Programmatic Use

Block Parameter: g_sf_cc

Type: character vector

Values: 3-by-3 matrix

Default: '[1 0 0; 0 1 0; 0 0 1]'

Measurement bias — Measurement bias

[0 0 0] (default) | three-element vector

Long-term biases along the gyroscope axes, specified as a three-element vector, in radians per second.

Programmatic Use

Block Parameter: g_bias

Type: character vector

Values: 3-by-3 matrix

Default: '[0 0 0]'

G-sensitive bias — Maximum change in rates

[0 0 0] (default) | three-element vector

Maximum change in rates due to linear acceleration, specified as a three-element vector, in radians per second per g-unit.

Programmatic Use

Block Parameter: g_sen

Type: character vector

Values: three-element vector

Default: '[0 0 0]'

Update rate (sec) — Update rate

0 (default) | scalar

Update rate of the gyroscope, specified as a double scalar, in seconds. An update rate of 0 creates a continuous gyroscope. If the Noise on check box is selected and the update rate is 0, the block updates the noise at a rate of 0.1.

Tip

If you:

• Update this parameter value to 0 (continuous)

• Configure a fixed-step solver for the model

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.

Programmatic Use

Block Parameter: g_Ts

Type: character vector

Values: double scalar

Default: '0'

Noise on — White noise

on (default) | off

To apply white noise to the gyroscope readings, select this check box.

Programmatic Use

Block Parameter: g_rand

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Noise seeds — Noise seeds

[23093 23094 23095] (default) | three-element vector

Scalar seeds for the Gaussian noise generator for each axis of the gyroscope, specified as a three-element vector.

Dependencies

To enable this parameter, select Noise on.

Programmatic Use

Block Parameter: g_seeds

Type: character vector

Values: three-element vector

Default: '[23093 23094 23095]'

Noise power — Noise power

[0.0001 0.0001 0.0001] (default) | three-element vector

Height of the power spectral density (PSD) of the white noise for each axis of the gyroscope, specified as a three-element vector, in (rad/s)²/Hz.

Dependencies

To enable this parameter, select Noise on.

Programmatic Use

Block Parameter: g_pow

Type: character vector

Values: three-element vector

Default: '[0.0001 0.0001 0.0001]'

Lower and upper output limits — Minimum and maximum values of angular rates

[-inf -inf -inf inf inf inf] (default) | six-element vector

Three minimum values and three maximum values of angular rates in each of gyroscope axes, specified as a six-element vector, in radians per second.

Programmatic Use

Block Parameter: g_sat

Type: character vector

Values: six-element vector

Default: '[-inf -inf -inf inf inf inf]'

Algorithms

The measured body angular rates $$({\overline{\omega }}_{meas})$$ include the body angular rates $$({\overline{\omega }}_b)$$, errors, and, optionally, the discretizations and nonlinearizations of the signals:

$${\overline{\omega }}_{meas}={\overline{\omega }}_b\times {\overline{\omega }}_{SFCC}+{\overline{\omega }}_{bias}+Gs\times {\overline{\omega }}_{gsens}+noise$$

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.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a