Three-axis Accelerometer

Implement three-axis accelerometer

Libraries:
Aerospace Blockset / GNC / Navigation

Description

The Three-Axis Accelerometer block implements an accelerometer on each of the three axes. For more information on the ideal measured accelerations, see Algorithms.

Optionally, to apply discretizations to the Three-Axis Accelerometer block inputs and dynamics along with nonlinearizations of the measured accelerations, use the Saturation block.

The Three-axis Accelerometer block icon displays the input and output units selected from the Units parameter.

Limitations

Vibropendulous error and hysteresis 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

expand all

A_b — Actual accelerations
three-element vector

Actual accelerations in body-fixed axes, specified as a three-element vector, in the units specified in the Units parameter.

Data Types: double

ω — Angular rates
three-element vector

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

Data Types: double

dω/dt — Angular accelerations
three-element vector

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

Data Types: double

CG — Location of center of gravity
three-element vector

Location of the center of gravity, specified as a three-element vector, in the units specified in the Units parameter.

Data Types: double

g — Gravity
three-element vector

Gravity in body axis, specified as a three-element vector, in the units specified in the Units parameter.

Data Types: double

Output

expand all

A_meas — Measured accelerations
three-element vector

Measured accelerations from the accelerometer, returned as a three-element vector, in the units specified in the Units parameter.

Data Types: double

Parameters

expand all

Units — Units
`Metric (MKS)` (default) | `English`

Input and output units, specified as:

Units	Acceleration	Length
`Metric (MKS)`	Meters per second squared	Meters
`English` (British Imperial)	Feet per second squared	Feet

Programmatic Use

Block Parameter: units

Type: character vector

Values:

'Metric
									(MKS)'

| 'English'

Default:

'Metric
									(MKS)'

Accelerometer location — Accelerometer location
`[0 0 0]` (default) | three-element vector

Location of the accelerometer group, specified as a three-element vector, measured from the zero datum (typically the nose) to aft, to the right of the vertical centerline, and above the horizontal centerline. This measurement reference is the same for the center of gravity input. The units are the units specified in the Units parameter.

Programmatic Use

Block Parameter: acc

Type: character vector

Values: three-element vector

Default:

'[0 0
									0]'

Subtract gravity — Subtract gravity
`on` (default) | `off`

To subtract gravity from acceleration readings, select this check box.

Programmatic Use

Block Parameter: gtype

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Second order dynamics — Second-order dynamics
`on` (default) | `off`

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

Programmatic Use

Block Parameter: dtype_a

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Natural frequency (rad/sec) — Natural frequency
`190` (default) | scalar

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

Programmatic Use

Block Parameter: w_a

Type: character vector

Values: double scalar

Default: '190'

Damping ratio — Damping ratio
`0.707` (default) | scalar

Damping ratio of the accelerometer, specified as a double scalar, with no dimensions.

Programmatic Use

Block Parameter: z_a

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 accelerometer from body axes and to scale accelerations along body axes.

Programmatic Use

Block Parameter: a_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 accelerometer axes, specified as a three-element vector, in the units specified in the Units parameter.

Programmatic Use

Block Parameter: a_bias

Type: character vector

Values: 3-by-3 matrix

Default:

'[0 0
									0]'

Update rate (sec) — Update rate
`0` (default) | scalar

Update rate of the accelerometer, specified as a double scalar, in seconds. An update rate of 0 creates a continuous accelerometer. 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: a_Ts

Type: character vector

Values: double scalar

Default: '0'

Noise on — White noise
`on` (default) | `off`

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

Programmatic Use

Block Parameter: a_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 accelerometer, specified as a three-element vector.

Dependencies

To enable this parameter, select Noise on.

Programmatic Use

Block Parameter: a_seeds

Type: character vector

Values: three-element vector

Default:

'[23093 23094
									23095]'

Noise power — Noise power
`[0.001 0.001 0.001]` (default) | three-element vector

Height of the power spectral density (PSD) of the white noise for each axis of the accelerometer, specified as a three-element vector, in:

(m/s²)/Hz when Units is set to Metric (MKS)
(ft/s²)/Hz when Units is set to English

Dependencies

To enable this parameter, select Noise on.

Programmatic Use

Block Parameter: a_pow

Type: character vector

Values: three-element vector

Default:

'[0.001 0.001
									0.001]'

Lower and upper output limits — Minimum and maximum values of acceleration
`[-inf -inf -inf inf inf inf]` (default) | six-element vector

Three minimum values and three maximum values of acceleration in each of the accelerometer axes, specified as a six-element vector, in the units specified in the Units parameter.

Programmatic Use

Block Parameter: a_sat

Type: character vector

Values: six-element vector

Default:

'[-inf -inf
									-inf inf inf inf]'

Algorithms

The ideal measured accelerations ( ${\bar{A}}_{i m e a s}$ ) include the acceleration in body axes at the center of gravity ( ${\bar{A}}_{b}$ ) and lever arm effects due to the accelerometer not being at the center of gravity. Optionally, gravity in body axes can be removed. This is represented by the equation:

${\bar{A}}_{i m e a s} = {\bar{A}}_{b} + {\bar{ω}}_{b} \times ({\bar{ω}}_{b} \times \bar{d}) + {\dot{\bar{ω}}}_{b} \times \bar{d} - \bar{g}$

where ${\bar{ω}}_{b}$ are body-fixed angular rates, ${\dot{\bar{ω}}}_{b}$ are body-fixed angular accelerations, and $\bar{d}$ is the lever arm. The lever arm ( $\bar{d}$ ) is defined as the distances that the accelerometer group is forward, right, and below the center of gravity:

$\bar{d} = [\begin{array}{l} d_{x} \\ d_{y} \\ d_{z} \end{array}] = [\begin{matrix} - (x_{a c c} - x_{C G}) \\ y_{a c c} - y_{C G} \\ - (z_{a c c} - z_{C G}) \end{matrix}]$

The orientation of the axes used to determine the location of the accelerometer group (x_acc, y_acc, z_acc) and center of gravity (x_CG, y_CG, z_CG) is from the zero datum (typically the nose) to aft, to the right of the vertical centerline and above the horizontal centerline. The x-axis and z-axis of these measurement axes are opposite the body-fixed axes that produce the negative signs in the lever arms for the x-axis and z-axis.

Measured accelerations ( ${\bar{A}}_{m e a s}$ ) output by this block contain error sources and are defined as

${\bar{A}}_{m e a s} = {\bar{A}}_{i m e a s} \times {\bar{A}}_{S F C C} + {\bar{A}}_{b i a s} + n o i s e,$

where ${\bar{A}}_{S F C C}$ is a 3-by-3 matrix of scaling factors on the diagonal and misalignment terms in the nondiagonal, and ${\bar{A}}_{b i a s}$ are the 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

Three-axis Accelerometer

Description

Limitations

Ports

Input

Ab — Actual accelerations three-element vector

ω — Angular rates three-element vector

dω/dt — Angular accelerations three-element vector

CG — Location of center of gravity three-element vector

g — Gravity three-element vector

Output

Ameas — Measured accelerations three-element vector

Parameters

Units — Units Metric (MKS) (default) | English

Programmatic Use

Accelerometer location — Accelerometer location [0 0 0] (default) | three-element vector

Programmatic Use

Subtract gravity — Subtract gravity on (default) | off

Programmatic Use

Second order dynamics — Second-order dynamics on (default) | off

Programmatic Use

Natural frequency (rad/sec) — Natural frequency 190 (default) | scalar

Programmatic Use

Damping ratio — Damping ratio 0.707 (default) | scalar

Programmatic Use

Scale factors and cross-coupling — Scale factors and cross coupling [1 0 0; 0 1 0; 0 0 1] (default) | 3-by-3 matrix

Programmatic Use

Measurement bias — Measurement bias [0 0 0] (default) | three-element vector

Programmatic Use

Update rate (sec) — Update rate 0 (default) | scalar

Programmatic Use

Noise on — White noise on (default) | off

Programmatic Use

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

Dependencies

Programmatic Use

Noise power — Noise power [0.001 0.001 0.001] (default) | three-element vector

Dependencies

Programmatic Use

Lower and upper output limits — Minimum and maximum values of acceleration [-inf -inf -inf inf inf inf] (default) | six-element vector

Programmatic Use

Algorithms

References

Extended Capabilities

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

Version History

See Also

A_b — Actual accelerations
three-element vector

ω — Angular rates
three-element vector

dω/dt — Angular accelerations
three-element vector

CG — Location of center of gravity
three-element vector

g — Gravity
three-element vector

A_meas — Measured accelerations
three-element vector

Units — Units
`Metric (MKS)` (default) | `English`

Accelerometer location — Accelerometer location
`[0 0 0]` (default) | three-element vector

Subtract gravity — Subtract gravity
`on` (default) | `off`

Second order dynamics — Second-order dynamics
`on` (default) | `off`

Natural frequency (rad/sec) — Natural frequency
`190` (default) | scalar

Damping ratio — Damping ratio
`0.707` (default) | scalar

Scale factors and cross-coupling — Scale factors and cross coupling
`[1 0 0; 0 1 0; 0 0 1]` (default) | 3-by-3 matrix

Measurement bias — Measurement bias
`[0 0 0]` (default) | three-element vector

Update rate (sec) — Update rate
`0` (default) | scalar

Noise on — White noise
`on` (default) | `off`

Noise seeds — Noise seeds
`[23093 23094 23095]` (default) | three-element vector

Noise power — Noise power
`[0.001 0.001 0.001]` (default) | three-element vector

Lower and upper output limits — Minimum and maximum values of acceleration
`[-inf -inf -inf inf inf inf]` (default) | six-element vector

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