Three-axis Inertial Measurement Unit

blockType: SubSystem

Path in the library:

/Aerospace/GNC/Navigation/Three-axis Inertial Measurement Unit

Description

Block Three-axis Inertial Measurement Unit It is a combination of an accelerometer and a gyroscope. For a description of the equations, see the blocks Three-axis Gyroscope and Three-axis Accelerometer.

Ports

Input

# A_b (m/s²) — actual accelerations
`vector 1 to 3

Details

Actual accelerations in the coupled axes in m/s²^ given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# ω (rad/s) — angular velocities
`vector 1 to 3

Details

Angular velocities in the coupled axes in rad/s, given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# dω/dt — angular accelerations
`vector 1 to 3

Details

Angular accelerations in the coupled axes in rad/s²^ given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# CG (m) — centre of gravity location
`vector 1 to 3

Details

The position of the centre of gravity in m given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# g (m/s²) — free-fall acceleration
`vector 1 to 3

Details

Free-fall acceleration in coupled axes in m/c²^, given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

Output

# A_meas (m/s²) — measured accelerations
`vector 1 to 3

Details

Measured accelerations from the accelerometer in m/c², returned as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# ω_meas (rad/s) — measured angular velocities
`vector 1 to 3

Details

Measured angular velocities in rad/s, returned as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main group

# IMU location: — location of the inertial measuring unit

Details

The location of the inertial measuring unit, the reference frame coincides with the one used to enter the center of mass.

Default value	`[0.0 0.0 0.0]`
Program usage name	`imu`
Tunable	No
Evaluatable	Yes

# Update rate: — refresh rate

Details

The refresh rate of the inertial measurement unit.

Default value	`0.0`
Program usage name	`i_Ts`
Tunable	No
Evaluatable	Yes

Accelerometer

# Second-order dynamics for accelerometer — second-order dynamics for the accelerometer

Details

Select this option to account for second-order dynamic effects when processing accelerometer data.

Default value	`true (switched on)`
Program usage name	`dtype_a`
Tunable	No
Evaluatable	Yes

# Accelerometer natural frequency (rad/sec): — the natural frequency of the accelerometer

Details

The natural frequency of the accelerometer, set by a scalar, in rad/s.

Default value	`190.0`
Program usage name	`w_a`
Tunable	No
Evaluatable	Yes

# Accelerometer damping ratio: — accelerometer damping coefficient

Details

The damping coefficient of the accelerometer, set by a dimensionless scalar value.

Dependencies

To use this option, check the box Second-order dynamics for accelerometer

Default value	`0.707`
Program usage name	`z_a`
Tunable	No
Evaluatable	Yes

# Accelerometer scale factor and cross-coupling: — scale factors and accelerometer cross-links

Details

Scale coefficients and cross-links of the accelerometer, specified by the matrix 3 on 3, to introduce distortions between the axes of the accelerometer and the associated axes of the object, as well as to scale accelerations along the axes.

Default value	`[1 0 0; 0 1 0; 0 0 1]`
Program usage name	`a_sf_cc`
Tunable	No
Evaluatable	Yes

# Accelerometer measurement bias: — systematic error of the accelerometer

Details

Systematic errors of the accelerometer along the axes, specified as a three-element vector.

Default value	`[0 0 0]`
Program usage name	`a_bias`
Tunable	No
Evaluatable	Yes

# Accelerometer upper limit: — maximum accelerometer acceleration value

Details

The maximum acceleration value of the accelerometer, set by a scalar.

Default value	`Inf`
Program usage name	`a_sat1`
Tunable	No
Evaluatable	Yes

# Accelerometer lower limit: — minimum accelerometer acceleration value

Details

The minimum acceleration value of the accelerometer, set by a scalar.

Default value	`-Inf`
Program usage name	`a_sat2`
Tunable	No
Evaluatable	Yes

Gyroscope

# Second-order dynamics for gyroscope — second-order dynamics for a gyroscope

Details

Select this option to take into account second-order dynamic effects when processing gyroscope data.

Default value	`true (switched on)`
Program usage name	`dtype_g`
Tunable	No
Evaluatable	Yes

# Gyro natural frequency (rad/sec): — gyroscope natural frequency

Details

The natural frequency of the gyroscope.

Dependencies

To use this option, check the box Second-order dynamics for gyroscope

Default value	`190.0`
Program usage name	`w_g`
Tunable	No
Evaluatable	Yes

# Gyro damping ratio: — gyroscope damping coefficient

Details

The damping coefficient of the gyroscope.

Dependencies

To use this option, check the box Second-order dynamics for gyroscope

Default value	`0.707`
Program usage name	`z_g`
Tunable	No
Evaluatable	Yes

# Gyro scale factors and cross-coupling: — scale factors and gyroscope cross-links

Details

Scale coefficients and cross-links of the gyroscope, specified as a matrix 3 on 3, allow you to deflect the gyroscope from the axes of the body and scale accelerations along the axes of the body.

Default value	`[1 0 0; 0 1 0; 0 0 1]`
Program usage name	`g_sf_cc`
Tunable	No
Evaluatable	Yes

# Gyro measurement bias: — measurement error of the gyroscope

Details

Systematic measurement errors along the gyroscope axes.

Default value	`[0 0 0]`
Program usage name	`g_bias`
Tunable	No
Evaluatable	Yes

# G-sensitive bias: — sensitivity to accelerations

Details

The maximum change in angular velocity caused by linear acceleration is given as a three-element vector in rad/s per unit acceleration of gravity .

Default value	`0.0`
Program usage name	`g_sen`
Tunable	No
Evaluatable	Yes

# Gyro upper limit: — the maximum value of the angular velocities of the gyroscope

Details

The maximum value of angular velocities set by a scalar.

Default value	`Inf`
Program usage name	`g_sat1`
Tunable	No
Evaluatable	Yes

# Gyro lower limit: — minimum value of gyroscope angular velocities

Details

The minimum value of angular velocities set by a scalar.

Default value	`-Inf`
Program usage name	`g_sat2`
Tunable	No
Evaluatable	Yes

Noise

# Noise on — white noise

Details

To add white noise to the gyroscope and accelerometer readings, select this option.

Default value	`false (switched off)`
Program usage name	`i_rand`
Tunable	No
Evaluatable	Yes

Literature

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