Three-axis Inertial Measurement Unit

Implement three-axis inertial measurement unit (IMU)

• Library:

• Aerospace Blockset / GNC / Navigation

• 

Description

The Three-Axis Inertial Measurement Unit block implements an inertial measurement unit (IMU) containing a three-axis accelerometer and a three-axis gyroscope.

For a description of the equations and application of errors, see Three-axis Accelerometer and Three-axis Gyroscope.

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

Limitations

• Vibropendulous error, hysteresis affects, anisoelastic bias, and anisoinertial bias 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

Ab — 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

Ameas — 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

ωmeas — 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

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)'

IMU location — IMU location

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

The location of the IMU, which is also the accelerometer group location, is 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 in the units specified in the Units parameter.

Programmatic Use

Block Parameter: imu

Type: character vector

Values: three-element vector

Default: '[0 0 0]'

Update rate (sec) — Update rate

0 (default) | scalar

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

Type: character vector

Values: double scalar

Default: '0'

Second order dynamics for accelerometer — 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'

Accelerometer natural frequency (rad/sec) — Accelerometer natural frequency

190 (default) | scalar

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

Dependencies

To enable this parameter, select Second order dynamics for accelerometer.

Programmatic Use

Block Parameter: w_a

Type: character vector

Values: double scalar

Default: '190'

Accelerometer damping ratio — Accelerometer damping ratio

0.707 (default) | scalar

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

Dependencies

To enable this parameter, select Second order dynamics for accelerometer.

Programmatic Use

Block Parameter: z_a

Type: character vector

Values: double scalar

Default: '0.707'

Accelerometer scale factor 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]'

Accelerometer measurement bias — Accelerometer 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: three-element vector

Default: '[0 0 0]'

Accelerometer upper and lower 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 accelerometer axes, specified as a six-element vector, in 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]'

Second-order dynamics for gyro — Gyroscope 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'

Gyro natural frequency (rad/sec) — Gyroscope natural frequency

190 (default) | scalar

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

Dependencies

To enable this parameter, select Second-order dynamics for gyro.

Programmatic Use

Block Parameter: w_g

Type: character vector

Values: double scalar

Default: '190'

Gyro damping ratio — Gyroscope damping ratio

0.707 (default) | scalar

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

Dependencies

To enable this parameter, select Second-order dynamics for gyro.

Programmatic Use

Block Parameter: z_g

Type: character vector

Values: double scalar

Default: '0.707'

Gyro scale factors and cross-coupling — Gyroscope scale factors and cross-coupling

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

Gyroscope scale factors and cross-coupling, specified as a 3-by-3 matrix, to skew the gyroscope from body axes and to scale angular rates 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]'

Gyro measurement bias — Gyroscope measurement bias

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

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

Programmatic Use

Block Parameter: g_bias

Type: character vector

Values: three-element vector

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_sens

Type: character vector

Values: three-element vector

Default: '[0 0 0]'

Gyro upper and lower 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 the 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]'

Noise on — White noise

on (default) | off

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

Programmatic Use

Block Parameter: i_rand

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Noise seeds — Noise seeds

[23093 23094 23095 23096 23097 23098] (default) | six-element vector

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

Dependencies

To enable this parameter, select Noise on.

Programmatic Use

Block Parameter: i_seeds

Type: character vector

Values: six-element vector

Default: '[23093 23094 23095 23096 23097 23098]'

Noise power — Noise power

[0.001 0.001 0.001 0.0001 0.0001 0.0001] (default) | six-element vector

Height of the power spectral density (PSD) of the white noise for each axis of the accelerometer and gyroscope, specified as a six-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: i_pow

Type: character vector

Values: six-element vector

Default: '[0.001 0.001 0.001 0.0001 0.0001 0.0001]'

Model Examples

Lightweight Airplane Design

How to use MathWorks® products to address the technical and process challenges of aircraft design using the design of a lightweight aircraft.

Open Model

References

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

Extended Capabilities

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