Three-axis Accelerometer | Engee Documentation

Description

Unit Three-axis Accelerometer is designed to measure accelerations along three mutually perpendicular axes . It is used in navigation, stabilisation, vibration monitoring and motion control systems.

Algorithms

Ideally measured accelerations ( ) include the linear acceleration of the centre of mass in the linked coordinate system ( ), additional accelerations caused by the lever arm effect due to the offset of the accelerometer relative to the centre of mass. If necessary, the gravity component can be excluded from the resulting signal.

This is described by Eq:

where

- are angular velocities in the coupled axes;
- angular accelerations in the coupled axes;
- leverage (displacement of the accelerometer relative to the centre of mass).

Leverage is defined as the distances by which a group of accelerometers is displaced relative to the centre of gravity:

The orientation of the axes used to locate the accelerometer group ( ) and the centre of gravity ( ) is set from the zero reference point (usually the nose) to the tail, to the right of the vertical centreline and above the horizontal centreline. The axis and the axis of this measurement system are opposite to the hull-related axes, resulting in negative signs in the lever arms for the axis and the axis . The measured accelerations ( ) produced by this unit contain error sources and are defined as:

where

- is a 3 by 3 matrix containing scaling coefficients along the diagonal and cross terms (mutual orientation errors) off-diagonal;
- offsets.

Limitations

This block does not take into account errors introduced due to vibration and hysteresis effects.

Ports

Input

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

Details

Actual accelerations in the coupled axes 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, given as a three-element vector, in radians per second.

Data types	`Float64`.
Complex numbers support	No

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

Details

Angular accelerations in the coupled axes, given as a three-element vector, in radians per second squared.

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 given by 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 the coupled axes given by a three-component 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, returned as a three-component vector.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# Accelerometer location: — accelerometer location

Details

The position of a group of accelerometers, specified as a three-component vector. The coordinates are read from the zero point (usually the nose) in the direction towards the tail, to the right of the vertical centreline and upwards from the horizontal centreline. The reference frame is the same as that used for the centre of mass input.

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

# Second-order dynamics — second-order dynamics

Details

Select this check box to take second-order dynamic effects into account when processing accelerometer data.

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

# Natural frequency (rad/sec): — accelerometer natural frequency

Details

The natural frequency of the accelerometer, given by a scalar, in radians per second.

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

# Damping ratio: — damping factor

Details

The damping factor of an accelerometer given as a dimensionless scalar quantity.

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

# Scale factors and cross-coupling: — scaling factors and cross-correlations

Details

Scaling factors and cross-correlations, specified by a 3 by 3 matrix, to introduce distortions between the accelerometer axes and the related axes of the object, and to scale the 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

# Measurement bias: — systematic error

Details

Systematic errors of the accelerometer in the axes given by a three-component vector.

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

# Update rate (sec): — refresh rate

Details

Accelerometer data refresh rate, specified as a scalar value in seconds. When 0 is set, the accelerometer operates in continuous mode. If the checkbox Noise on is set and the update frequency is 0, the unit generates noise with frequency 0.1.

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

Noise

# Noise on — white noise

Details

To add white noise to the acceleration readings, select this checkbox.

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

# Noise seeds: — seed values of the random noise generator

Details

Seed-values of the white noise generator given by a vector of three scalar quantities.

Dependencies

To use this parameters, set the checkbox Noise on.

Default value	`[23093 23094 23095]`
Program usage name	`a_seeds`
Tunable	No
Evaluatable	Yes

# Noise power: — noise power

Details

The height of the power spectral density (PSD) of white noise for each axis of the accelerometer, given as a three-element vector.

Dependencies

To use this parameter, select the Noise on checkbox.

Default value	`[0.001 0.001 0.001]`
Program usage name	`a_pow`
Tunable	No
Evaluatable	Yes

# Upper output limit: — maximum value of accelerations

Details

The maximum value of accelerations specified by a scalar.

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

# Lower output limit: — minimum value of accelerations

Details

The minimum value of accelerations specified by a scalar.

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

Literature

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