# Mapped Steering

Mapped steering with speed-dependent option

Libraries:
Vehicle Dynamics Blockset / Steering

## Description

The Mapped Steering block implements lookup tables to calculate the right and left wheel angles. Use the Speed dependent parameter to implement a speed-dependent table for the steering angle calculations. The block uses the vehicle coordinate system.

### Steering Wheel Angle

If you set Steering type to ```Steering wheel angle```, the block implements these tables.

Speed DependentImplementationCalculations
`on` (default)

Block uses three tables:

• fs — Function of vehicle speed

• fL — Function of superimposed steering wheel angle

• fR — Function of superimposed steering wheel angle

`$\begin{array}{l}{\delta }_{SpdF}={f}_{s}\left(v\right)\\ {\delta }_{SuprImp}={\delta }_{SpdF}\cdot {\delta }_{in}\\ \\ {\delta }_{L}={f}_{L}\left({\delta }_{SuprImp}\right)\\ {\delta }_{R}={f}_{R}\left({\delta }_{SuprImp}\right)\end{array}$`

`off`

Block uses two tables:

• fL — Function of steering wheel angle

• fR — Function of steering wheel angle

`$\begin{array}{l}{\delta }_{L}={f}_{L}\left({\delta }_{in}\right)\\ {\delta }_{R}={f}_{R}\left({\delta }_{in}\right)\end{array}$`

### Rack Travel Displacement

If you set Steering type to ```Rack travel displacement```, the block implements these tables.

Speed DependentImplementationCalculations
`on` (default)

Block uses three tables:

• fs — Function of vehicle speed

• fL — Function of rack travel displacement

• fR — Function of rack travel displacement

`$\begin{array}{l}{\delta }_{SpdF}={f}_{s}\left(v\right)\\ {\delta }_{SuprImp}={\delta }_{SpdF}\cdot {\delta }_{in}\\ {\Delta }_{Rack}={\delta }_{SuprImp}\cdot Gr\\ {\delta }_{L}={f}_{L}\left({\Delta }_{Rack}\right)\\ {\delta }_{R}={f}_{R}\left({\Delta }_{Rack}\right)\end{array}$`

`off`

Block uses two tables:

• fL — Function of rack travel displacement

• fR — Function of rack travel displacement

`$\begin{array}{l}{\Delta }_{Rack}={\delta }_{in}\cdot Gr\\ {\delta }_{L}={f}_{L}\left({\Delta }_{Rack}\right)\\ {\delta }_{R}={f}_{R}\left({\Delta }_{Rack}\right)\end{array}$`

The block uses a gear ratio to adjust the rack travel displacement. To use a

• Constant gear ratio, set Gear ratio parameterized by to `Constant`.

• Gear ratio as a function of steering angle, set Gear ratio parameterized by to ```Lookup table```.

The equations use these variables.

 δin Steering wheel angle δSpdF Steering wheel angle speed factor δSuprImp Superimposed steering wheel angle δL, δR Left and right wheel angles, respectively ΔRack Rack travel displacement Gr Gear ratio

## Ports

### Input

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Use the parameter to specify a steering angle range. By default, the value is set to 1.25*pi, which limits the steering angle to a range of -1.25*pi to 1.25*pi.

Vehicle speed, Vehspd, in m/s.

#### Dependencies

To create this port, select Speed dependent.

### Output

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Bus signal containing these block calculations.

SignalDescriptionVariableUnit

`AngLft`

Left wheel angle

δL

`AngRght`

Left wheel angle

δR

Left wheel angle, δL, in rad.

Right wheel angle, δR, in rad.

## Parameters

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Options

Select to use speed-dependent tables.

#### Dependencies

Selecting this parameter creates input port `VehSpd`.

If you set Steering type to ```Steering wheel angle```, the block implements these tables.

Speed DependentImplementation
`on` (default)

Block uses three tables:

• fs — Function of vehicle speed

• fL — Function of superimposed steering wheel angle

• fR — Function of superimposed steering wheel angle

`off`

Block uses two tables:

• fL — Function of steering wheel angle

• fR — Function of steering wheel angle

If you set Steering type to ```Rack travel displacement```, the block implements these tables.

Speed DependentImplementation
`on` (default)

Block uses three tables:

• fs — Function of vehicle speed

• fL — Function of rack travel displacement

• fR — Function of rack travel displacement

`off`

Block uses two tables:

• fL — Function of rack travel displacement

• fR — Function of rack travel displacement

#### Dependencies

If you set Steering type to ```Rack travel displacement```, to enable this parameter, set Gear ratio parameterized by to `Lookup table`.

Rack travel displacement breakpoints, in mm.

#### Dependencies

To enable this parameter, set Steering type to `Rack travel displacement` and Gear ratio parameterized by to `Lookup table`.

Gear ratio table as a function of rack travel displacement, in mm/rev.

#### Dependencies

To enable this parameter, set Steering type to `Rack travel displacement` and Gear ratio parameterized by to `Lookup table`.

Gear ratio constant, in mm/rev.

#### Dependencies

To enable this parameter, set Steering type to `Rack travel displacement` and Gear ratio parameterized by to `Constant`.

Left wheel angle table, δL, in rad.

Right wheel angle table, δR, in rad.

Vehicle speed breakpoints, in m/s.

#### Dependencies

To create this parameter, select Speed dependent.

Superimposed speed factor table, ƒs, dimensionless. The table is a factor of vehicle speed, v.

#### Dependencies

To create this parameter, select Speed dependent.

## References

[1] Crolla, David, David Foster, et al. Encyclopedia of Automotive Engineering. Volume 4, Part 5 (Chassis Systems) and Part 6 (Electrical and Electronic Systems). Chichester, West Sussex, United Kingdom: John Wiley & Sons Ltd, 2015.

[2] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers, 1992.

[3] Vehicle Dynamics Standards Committee. Vehicle Dynamics Terminology. SAE J670. Warrendale, PA: Society of Automotive Engineers, 2008.

## Version History

Introduced in R2018a