Steering System

Steering system for Ackermann and rack-and-pinion steering mechanisms

Since R2022b

• 

Libraries:
Vehicle Dynamics Blockset / Steering

Description

The Steering System block implements dynamic steering to calculate the wheel steer angles for rack-and-pinion mechanisms with friction^[4], compliance, and Ackermann steering features. The block uses the steering wheel input angle or torque input, vehicle speed, caster angle, and right and left wheel feedbacks to calculate the wheel steer angles. The block uses the vehicle coordinate system.

If you select the Power assist parameter, you can specify a torque assist lookup table that is a function of the vehicle speed and steering wheel input torque. The block uses the steering wheel input torque and torque assist to calculate the steering dynamics. If you select the Ackerman steering parameter, you can specify a lookup table of percentage Ackermann values to calculate the Ackermann steering effects, or a constant Ackermann percentage, where 100 percent means perfect Ackermann steering.

If you select the Power assist, Ackerman steering, or Kingpin moment^[5] parameters in the Input signals section, you can specify additional inputs for the external power assist torques, percent Ackermann values, or kingpin moments.

Use the Steered axle parameter to specify whether the front or rear axle is steered.

Setting	Implementation
Front	Front axle steering
Rear	Rear axle steering

Steering Type

Rack-and-Pinion

For rack-and-pinion steering, pinion rotation causes linear motion of the rack, which steers the wheels through the tie rods and steering arms.

To calculate the steered wheel angles, the block uses these equations.

$$\begin{array}{l}{l}_1=\frac{TW-l_{rack}}{2}-\Delta P\\ \\ l_2{}^2=l_1{}^2+D^2\\ \\ \Delta P=r{\delta }_{in}\\ \\ \beta =\frac{\pi }{2}-{\tan }^{-1}\left[\frac{D}{l_1}\right]-{\cos }^{-1}\left[\frac{l_{arm}{}^2+l_2{}^2-l_{rod}{}^2}{2l_{arm}{l}_2}\right]\end{array}$$

The illustration and equations use these variables.

δin	Pinion angle (steering shaft angle into pinion)
δL	Left wheel steer angle
δR	Right wheel steer angle
TW	Track width
r	Pinion radius
ΔP	Linear change in rack position from "straight ahead" position
D	Longitudinal distance between rack and steered axle
lrack	Rack length (distance between inner tie-rod ends)
larm	Steering arm length
lrod	Tie rod length

Steering Effects

Ackerman

For ideal Ackerman steering, the wheel angles have a common turning circle.

To calculate the ideal wheel angles, the block uses these equations.

$$\begin{array}{l}\cot ({\delta }_L)-\cot ({\delta }_R)=\frac{TW}{WB}\\ \\ {\delta }_{Ack}=\frac{{\delta }_{in}}{\gamma }\\ \\ {\delta }_L={\tan }^{-1}\left(\frac{WB\tan ({\delta }_{Ack})}{WB+0.5TW\tan ({\delta }_{Ack})}\right)\\ {\delta }_R={\tan }^{-1}\left(\frac{WB\tan ({\delta }_{Ack})}{WB-0.5TW\tan ({\delta }_{Ack})}\right)\end{array}$$

After the block calculates the ideal wheel angles, it uses the Ackerman percentage to adjust the outside wheel angle.

$${\delta }_o={\delta }_i-p_{Ack}({\delta }_i-{\delta }_{Ack})$$

The outside wheel angle depends on the turn direction.

• Right turn

  • Outside angle, δ_o, is left wheel angle, δ_L

  • Inside angle, δ_i, is right wheel angle, δ_R

• Left turn

  • Outside angle, δ_o, is right wheel angle, δ_R

  • Inside angle, δ_i, is left wheel angle, δ_L

The illustration and equations use these variables.

δin	Steering angle
δL	Left wheel angle
δR	Right wheel angle
δo	Outside wheel angle
δi	Inside wheel angle
pAck	Ackerman percentage
TW	Track width
WB	Wheel base
γ	Steering ratio

Kingpin Moment and Tie Rod Force

If you do not select the Kingpin moment parameter in the Input signals section to specify right and left kingpin moment inputs, the block implements the total kingpin moment using these equations:

$$\begin{array}{l}{M}_{kp}=M_{k{p}_{fx}}+M_{k{p}_{fy}}+M_{k{p}_{fz}}+M_{k{p}_{mx}}+M_{k{p}_{my}}+M_{k{p}_{mz}}\\ \\ \text{where}\\ \\ M_{k{p}_{fx}}=0\\ \\ M_{k{p}_{fy}}=-F_y(n_T\cos (\nu ))\cos (\delta )\\ \\ n_T=H_l+(r_{sl}\tan (\nu ))\\ \\ M_{k{p}_{fz}}=-(F_z\sin (\lambda )r_s\sin (\delta ))+(F_z\sin (\nu )r_s\cos (\delta ))\\ \\ r_s=K{p}_{offset}-(r_{sl}\tan (\lambda ))\\ \\ M_{k{p}_{mx}}=0\\ \\ M_{k{p}_{my}}=0\\ \\ M_{k{p}_{mz}}=M_z\cos ({(}^{{\lambda }^2})\end{array}$$

The illustration and equations use these variables.

Mkp	Total kingpin moment
Mkpfx	Moment due to tractive force
Mkpfy	Moment due to cornering force
Mkpfz	Moment due to vertical force
Mkpmx	Tire overturning moment
Mkpmy	Tire rolling resistance moment
Mkpmz	Tire aligning moment
Fy	Fy tire input
nT	Caster trail
ν	Dynamic caster angle input
δ	Dynamic steering angle
ƛ	Kingpin inclination angle
Fz	Fz tire input
rs	Scrub radius
Mz	Mz tire input
Kpoffset	Kingpin offset
Hl	Hub lead
rsl	Static loaded radius

The block implements the tie rod force using these equations:

$$\begin{array}{l}{F}_{tie}=\frac{M_{kp}}{L_{sa}\cos (\lambda )\cos (\delta )}\\ \\ \text{where}\\ \\ L_{sa}=(\frac{r_s{k}_r\cos (\lambda )\cos (\nu )}{\pi })\end{array}$$

The illustration and equations use these variables.

Ftie	Tie rod force
Mkp	Kingpin moment
Lsa	Swing arm length for rack and pinon steering
ƛ	Kingpin inclination angle
δ	Dynamic steering angle
rs	Overall steer ratio
kr	Rack gain
ν	Dynamic caster angle input

Examples

Double Lane Change Reference Application

Simulate a full vehicle dynamics model undergoing a double lane change maneuver standard ISO 3888-2. Use for vehicle dynamics ride and handling analysis and chassis controls development, including yaw stability and lateral acceleration limits.

• Open Script

Ports

Input

VehSpd — Vehicle speed

scalar

Vehicle speed, v, in m/s, specified as a scalar. This is the magnitude of the vehicle CG longitudinal velocity vector.

Dependencies

To enable this parameter, select the Power assist Block Option.

CstrAng — Wheel caster angle

1-by-2 vector

Wheel caster angle, τ_L, in radians, specified as a 1-by-2 vector. The first element is the angle for the left wheel and the second is the angle for the right wheel.

Dependencies

To enable this port, clear Input signals > Kingpin moment.

WhlAngFdk — Wheel steer angle feedback

1-by-2 vector

Wheel steer angle feedback, in radians, specified as a 1-by-2 vector. The first element is the angle feedback from the left wheel and the second element is the angle feedback from the right wheel:

• AngLft

• AngRght

You can specify the wheel steer angle feedback using steering angle responses from a vehicle plant model or the wheel angle outputs from this block.

Dependencies

To enable this port, clear Input signals > Kingpin moment.

AngIn — Steering wheel angle input

scalar

Steering wheel angle input from driver, in radians, specified as a scalar.

Dependencies

To enable this port, select Steering inputs > Angle.

TrqIn — Steering torque input

scalar

Steering wheel torque input from driver, in N*m, specified as a scalar.

Dependencies

To enable this port, select Steering inputs > Torque.

PwrAstTrq — Power assist torque

scalar

The torque value of power assist on the steering shaft, in N*m, specified as a scalar. The value is supplied externally into this port.

Dependencies

To enable this port, select Input signals > Power assist.

PctAck — Percent Ackermann value

scalar

The Ackermann value in percent, specified as a scalar. The value is supplied externally into this port.

Dependencies

To enable this port, select Input signals > Ackerman steering.

TireFdk — Tire forces and moments feedback

1-by-12 vector

Tire forces and moments feedback from both right and left tires, specified as a 1-by-12 vector that contains the following values, in the order specified in this table:

Description	Unit
x-directional Force, Left	N
x-directional Force, Right	N
y-directional Force, Left	N
y-directional Force, Right	N
z-directional Force, Left	N
z-directional Force, Right	N
x-directional Moment, Left	N*m
x-directional Moment, Right	N*m
y-directional Moment, Left	N*m
y-directional Moment, Right	N*m
z-directional Moment, Left	N*m
z-directional Moment, Right	N*m

Dependencies

To enable this port, clear Input signals > Kingpin moment.

LftKpM — Left kingpin moment

scalar

Left kingpin moment, in N*m, specified as a scalar.

Dependencies

To enable this port, select Input signals > Kingpin moment.

RghtKpM — Right kingpin moment

scalar

Right kingpin moment, in N*m, specified as a scalar.

Dependencies

To enable this port, select Input signals > Kingpin moment.

Output

Info — Vehicle dynamics information

bus

Vehicle dynamics information, returned as a bus signal that contains these signals:

Signal	Description	Unit
StrWhlAngFdk	Steering wheel angle	rad
AstTrq	Torque applied by power assist	N·m
AstPwr	Power applied by power assist	W
LftTieRodForce	Axial force in left tie rod	N
RghtTieRodForce	Axial force in right tie rod	N
LftKpM	Left kingpin moment	N·m
RghtKpM	Right kingpin moment	N·m
LftWhlAng	Left wheel steer angle	rad
RghtWhlAng	Right wheel steer angle	rad
LftWhlSpd	Left wheel steer angle velocity	rad/s
RghtWhlSpd	Right wheel steer angle velocity	rad/s
TrqIn	Torque applied by driver on steering wheel	N·m

AngLft — Left wheel steer angle

scalar

Left wheel steer angle, δ_L, in radians, returned as a scalar.

AngRght — Right wheel steer angle

scalar

Right wheel steer angle, δ_R, in radians, returned as a scalar.

Parameters

Block Options

Type — Steering type

Rack and pinion (default)

Set the steering type for the steering system.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrgType
Values:	Rack and pinion (default)
Data Types:	character vector

Intermediate shaft type — Intermediate shaft type

Single Cardan joint (default) | Double Cardan joints

Select whether to model the intermediate shaft type using single or double Cardan joints.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	IntmdShaftType
Values:	Single Cardan joint (default) | Double Cardan joints
Data Types:	character vector

Power assist — Option to model power assist

on (default) | off

Select this parameter to model power assist within the steering system.

Dependencies

To enable this parameter, in the Input signals section, clear Power assist.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PwrAst
Values:	on (default) | off
Data Types:	character vector

Ackerman steering — Option to use Ackermann steering

on (default) | off

Select this parameter to set the Ackermann steering percentage within the Steering System block.

Dependencies

To enable this parameter, in the Input signals section, clear Ackerman steering.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	AckStr
Values:	on (default) | off
Data Types:	character vector

Input Signals

Power assist — External power assist torque

off (default) | on

Select this parameter to enable the PwrAstTrq port.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PwrAstOverride
Values:	off (default) | on
Data Types:	character vector

Ackerman steering — External Ackermann percent

off (default) | on

Select this parameter to enable the PctAck port.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	AckStrOverride
Values:	off (default) | on
Data Types:	character vector

Kingpin moment — Left and right kingpin moments

off (default) | on

Select this parameter to enable the LftKpM and RghtKpM ports.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	KingpinOverride
Values:	off (default) | on
Data Types:	character vector

Steered axle — Location of steering system

Front (default) | Rear

Select either the front or rear axle as the location of the Steering System.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Loc
Values:	Front (default) | Rear
Data Types:	character vector

Steering inputs — Steering wheel angle or torque

Angle (default) | Torque

Select either the AngIn or TrqIn port as the driver input.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrIn
Values:	Angle (default) | Torque
Data Types:	character vector

General

Track width, TrckWdth — Track width

1 (default) | scalar

Track width, TW, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TrckWdth
Values:	1 (default) | scalar
Data Types:	double

Steering angle input range, StrRng — Steering wheel range

1.25*pi (default) | scalar

Steering wheel angle from straight-ahead to either left or right lock, in rad, specified as a scalar. This parameter causes both steered wheels to remain within their designed steering range.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrRng
Values:	1.25*pi (default) | scalar
Data Types:	double

Steering angle input deadband width, DbWdth — Steering angle input deadband width

0 (default) | scalar

Steering wheel deadband angle, in radians, from left-engagement to right-engagement.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	DbWdth
Values:	0 (default) | scalar
Data Types:	double

Steering wheel inertia, StrWhlInert — Steering wheel inertia

0.1 (default) | scalar

Steering wheel moment of inertia, in kg*m², specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrWhlInert
Values:	0.1 (default) | scalar
Data Types:	double

Steering shaft inertia, StrColInert — Inertia of steering shaft

0.01 (default) | scalar

Steering shaft moment of inertia, in kg*m², specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrCollnert
Values:	0.01 (default) | scalar
Data Types:	double

Kingpin offset, KngpnOfst — Kingpin offset

0.075 (default) | scalar

Kingpin offset, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	KngpnOfst
Values:	0.075 (default) | scalar
Data Types:	character vector

Kingpin inclination angle, Lambda — Kingpin inclination angle

0.2094 (default) | scalar

Kingpin inclination angle, in rad, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Lambda
Values:	0.2094 (default) | scalar
Data Types:	double

Hub lead, HbLead — Hub lead

4.00E-05 (default) | scalar

Hub lead, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	HbLead
Values:	4.00E-05 (default) | scalar
Data Types:	double

Static loaded radius, StcLdRadius — Static loaded radius

0.4 (default) | scalar

Static loaded tire radius, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StcLdRadius
Values:	0.4 (default) | scalar
Data Types:	double

Overall steering ratio, OvrlStrRatio — Overall steering ratio

17.42 (default) | scalar

Overall steering ratio, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	OvrlStrRatio
Values:	17.42 (default) | scalar
Data Types:	double

Steering angle breakpoints, StrgAngBpts — Steering wheel angle breakpoints

[-6.2832 -5.0265 -3.7699 -2.5133 -1.2566 0 1.2566 2.5133 3.7699 5.0265 6.2832] (default) | 1-by-11 vector

Steering wheel angle breakpoints, in rad, specified as a 1-by-11 vector. These breakpoints are used to parameterize either Ackermann value or rack gain.

Dependencies

To enable this parameter, set one of these parameters to Lookup table:

• Rack and pinion > Rack gain parameterized by

• Ackerman steering > Percent Ackerman parameterized by

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrgAngBpts
Values:	[-6.2832 -5.0265 -3.7699 -2.5133 -1.2566 0 1.2566 2.5133 3.7699 5.0265 6.2832] (default) | 1-by-11 vector
Data Types:	double

CstrAng — Caster angle

0 (default) | scalar

Caster angle, in rad, specified as a scalar.

Dependencies

To enable this parameter, select Input signals > Kingpin moment.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	CstrAng
Values:	0 (default) | scalar
Data Types:	double

Rack and Pinion

Rack gain parameterized by — Rack gain parameterization

Constant (default) | Lookup table

Whether to parameterize the rack gain as a constant value or by using a lookup table.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrgRatioType
Values:	Constant (default) | Lookup table
Data Types:	character vector

Rack gain, RckGn — Rack gain

0.062 (default) | scalar

Rack gain, in m/rev, specified as a scalar.

Dependencies

To enable this parameter, set Rack gain parameterized by to Constant.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	RckGn
Values:	0.062 (default) | scalar
Data Types:	double

Rack gain table, RckGnTbl — Rack gain table

ones(1,11)*0.0057*2*pi (default) | 1-by-11 vector

Rack gain table, in m/rev, specified as a 1-by-11 vector.

Dependencies

To enable this parameter, set Rack gain parameterized by to Lookup table.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	RckGnTbl
Values:	ones(1,11)*0.0057*2*pi (default) | 1-by-11 vector
Data Types:	double

Steering arm length, StrgArmLngth — Steering arm length

0.1 (default) | scalar

Steering arm length, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	StrgArmLngth
Values:	0.1 (default) | scalar
Data Types:	double

Rack casing length, RckCsLngth — Rack length

0.5 (default) | scalar

Rack length (distance between inner tie rod ends), in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	RckCsLngth
Values:	0.5 (default) | scalar
Data Types:	double

Tie rod length, TieRodLngth — Tie rod length

0.248 (default) | scalar

Tie rod length, l_rod, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TieRodLngth
Values:	0.248 (default) | scalar
Data Types:	double

Distance between axis and rack, Dst — Distance between axle and rack

0.2 (default) | scalar

Longitudinal distance between the steered axle and rack centerline, D, in m, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Dst
Values:	0.2 (default) | scalar
Data Types:	double

Efficiency of gears, Epsilon — Efficiency of gears

0.9 (default) | scalar

Efficiency of the rack and pinion mechanism, ɛ, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Epsilon
Values:	0.9 (default) | scalar
Data Types:	double

Pinion inertia, PnInert — Pinion inertia

0.1 (default) | scalar

Pinion inertia, in kg*m², specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PnInert
Values:	0.1 (default) | scalar
Data Types:	double

Single Cardan Joint

Spatial angle for the single Cardan joint, SptlAng — Spatial angle for the single Cardan joint

2.6178 (default) | scalar

Spatial angle for the single Cardan joint, in rad, specified as a scalar.

Dependencies

To enable this parameter, set Intermediate shaft type to Single Cardan joint.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	SptlAng
Values:	2.6178 (default) | scalar
Data Types:	double

Double Cardan Joints

Spatial angle for the upper Cardan joint, Alpha_b — Spatial angle for upper Cardan joint

2.6178 (default) | scalar

Spatial angle for the upper Cardan joint, in rad, specified as a scalar.

Dependencies

To enable this parameter, set Intermediate shaft type to Double Cardan joints.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Alpha_b
Values:	2.6178 (default) | scalar
Data Types:	double

Spatial angle for the lower Cardan joint, Alpha_c — Spatial angle for lower Cardan joint

2.7051 (default) | scalar

Spatial angle for the lower Cardan joint, in rad, specified as a scalar.

Dependencies

To enable this parameter, set Intermediate shaft type to Double Cardan joints.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Alpha_c
Values:	2.7051 (default) | scalar
Data Types:	double

Edge view angle between the planes of the two joints, Sigma_bc — Edge view angle between planes of the two joints

0.2618 (default) | scalar

Edge view angle between the planes of the two joints, in rad, specified as a scalar.

Dependencies

To enable this parameter, set Intermediate shaft type to Double Cardan joints.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Sigma_bc
Values:	0.2618 (default) | scalar
Data Types:	double

Phase angle, Gamma — Phase angle

0.2618 (default) | scalar

Rotation phase angle between the two joints, in rad, specified as a scalar.

Dependencies

To enable this parameter, set Intermediate shaft type to Double Cardan joints.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Gamma
Values:	0.2618 (default) | scalar
Data Types:	double

Power Assist

Steering wheel torque breakpoints, TrqBpts — Steering wheel torque breakpoints

[-100 0 100] (default) | 1-by-M vector

Steering wheel torque breakpoints, in N·m, specified as a 1-by-M vector.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TrqBpts
Values:	[-100 0 100] (default) | 1-by-M vector
Data Types:	double

Vehicle speed breakpoints, VehSpdBpts — Vehicle speed breakpoints

[0 20] (default) | 1-by-N vector

Vehicle speed breakpoints, in m/s, specified as a 1-by-N vector.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	VehSpdBpts
Values:	[0 20] (default) | 1-by-N vector
Data Types:	double

Assisting torque table, TrqTbl — Torque assist table

[0 -100;0 0;0 100] (default) | M-by-N matrix

Torque assist table, ƒ_trq, in N·m, specified as an M-by-N matrix.

The torque assist lookup table is a function of the vehicle speed, v, and steering wheel input torque, τ_in:

$${\tau }_{ast}=f_{trq}(v,{\tau }_{in})$$.

The block applies the steering wheel input torque and torque assist to the pinion.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TrqTbl
Values:	[0 -100;0 0;0 100] (default) | M-by-N matrix
Data Types:	double

Assisting torque limit, TrqLmt — Torque assist limit

100 (default) | scalar

Torque assist limit, in N·m, specified as a scalar.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TrqLmt
Values:	100 (default) | scalar
Data Types:	double

Assisting power limit, PwrLmt — Assist power limit

1000 (default) | scalar

Assist power limit, in watts, specified as a scalar.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PwrLmt
Values:	1000 (default) | scalar
Data Types:	double

Assisting torque efficiency, Eta — Torque assist efficiency

1 (default) | scalar

Torque assist efficiency, specified as a scalar.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Eta
Values:	1 (default) | scalar
Data Types:	double

Cutoff frequency, CutOmege [rad/s] — Cutoff frequency

200 (default) | scalar

Cutoff frequency, in rad/s, specified as a scalar.

Dependencies

To enable this parameter, select the Power assist Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	omega_c
Values:	200 (default) | scalar
Data Types:	double

Ackerman Steering

Percent Ackerman parameterized by — Ackermann parameterization

Constant (default) | Lookup table

Whether to parameterize the Ackermann values as a constant value or by a lookup table.

Dependencies

To enable this parameter, select the Ackerman steering Block Option.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	AckParamType
Values:	Constant (default) | Lookup table
Data Types:	character vector

Percent Ackerman, PctAck — Percent Ackermann

100 (default) | scalar

Percent Ackermann, specified as a scalar.

Dependencies

To enable this parameter, select the Ackerman steering Block Option and set Percent Ackerman parameterized by to Constant.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PctAck
Values:	100 (default) | scalar
Data Types:	double

Percent Ackerman table, PctAckTbl — Percent Ackermann table

ones(1,11)*100 (default) | 1-by-11 vector

Percent Ackermann table, specified as a 1-by-11 vector.

Dependencies

To enable this parameter, select the Ackerman steering Block Option and set Percent Ackerman parameterized by to Lookup table.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PctAckTbl
Values:	ones(1,11)*100 (default) | 1-by-11 vector
Data Types:	double

Friction and Compliance

Sealing stiffness, SlgStf — Sealing stiffness

1.5e4 (default) | scalar

Sealing stiffness, in N*m/rad, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	SlgStf
Values:	1.5e4 (default) | scalar
Data Types:	double

Upper boundary friction, UpprFric — Upper boundary friction

1 (default) | scalar

Upper boundary friction, in N, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	UpprFric
Values:	1 (default) | scalar
Data Types:	double

Pressure change due to friction boundary increase, PrsFric — Pressure change due to friction boundary increase

1e-5 (default) | scalar

Pressure change due to friction boundary increase, in N/bar, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	PrsFric
Values:	1e-5 (default) | scalar
Data Types:	double

Maxwell element stiffness, MaxStf — Maxwell element stiffness

10000 (default) | scalar

Maxwell element stiffness, in N*m/rad, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	MaxStf
Values:	10000 (default) | scalar
Data Types:	double

Maxwell element upper boundary friction, MaxUpprFric — Maxwell element upper boundary friction

0.2 (default) | scalar

Maxwell element upper boundary friction, in N, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	MaxUpprFric
Values:	0.2 (default) | scalar
Data Types:	double

Maxwell linear damping coefficient, MaxDamp — Maxwell linear damping coefficient

1 (default) | scalar

Maxwell linear damping coefficient, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	MaxDamp
Values:	1 (default) | scalar
Data Types:	double

Torsion bar stiffness coefficient, TorStf — Torsional stiffness of steering shaft

30 (default) | scalar

Torsional stiffness of steering shaft, in N*m/rad, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TorStf
Values:	30 (default) | scalar
Data Types:	double

Torsion bar damping coefficient, TorDamp — Torsional viscous damping in steering shaft

1 (default) | scalar

Torsional viscous damping in steering shaft, in N*m*s/rad, specified as a scalar.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	TorDamp
Values:	1 (default) | scalar
Data Types:	double

Steering Torque Controller

Integral anti-windup gain, A [] — Integral anti-windup gain

0 (default) | scalar

Integral anti-windup gain, specified as a scalar.

Dependencies

To enable this parameter, select Steering inputs > Angle.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	A
Values:	0 (default) | scalar
Data Types:	double

Derivative gain, D [] — Derivative gain

0.1 (default) | scalar

Derivative gain, specified as a scalar.

Dependencies

To enable this parameter, select Steering inputs > Angle.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	D
Values:	0.1 (default) | scalar
Data Types:	double

Integral gain, I [] — Integral gain

5 (default) | scalar

Integral gain, specified as a scalar.

Dependencies

To enable this parameter, select Steering inputs > Angle.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	I
Values:	5 (default) | scalar
Data Types:	double

Steering torque output saturation lower limit, OutSatLowLmt [Nm] — Output saturation lower limit

-500 (default) | scalar

Steering torque output saturation lower limit, specified as a scalar, in Nm.

Dependencies

To enable this parameter, select Steering inputs > Angle.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	OutSatLowLmt
Values:	-500 (default) | scalar
Data Types:	double

Steering torque output saturation upper limit, OutSatUpLmt [Nm] — Steering torque output saturation upper limit

500 (default) | scalar

Steering torque output saturation upper limit, specified as a scalar, in Nm.

Dependencies

To enable this parameter, select Steering inputs > Angle.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	OutSatUpLmt
Values:	500 (default) | scalar
Data Types:	double

Proportional gain, P [] — Proportional gain

150 (default) | scalar

Proportional gain, specified as a scalar.

Dependencies

To enable this parameter, select Steering inputs > Angle.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	P
Values:	150 (default) | scalar
Data Types:	double

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.

[4] Pfeffer, P. E., M. Harrer, and D. N. Johnston. “Interaction of Vehicle and Steering System Regarding On-Centre Handling.” Vehicle System Dynamics 46, no. 5 (May 2008): 413–28. https://doi.org/10.1080/00423110701416519.

[5] Reimpell, Jörnsen, Helmut Stoll, and Jürgen W. Betzler. The Automotive Chassis: Engineering Principles Chassis and Vehicle Overall, Wheel Suspensions and Types of Drive, Axle Kinematics and Elastokinematics, Steering, Springing, Tyres, Construction and Calculations Advice. 2nd ed. Oxford: Butterworth Heinemann, 2001.

Extended Capabilities

C/C++ Code Generation
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Version History

Introduced in R2022b

R2024a: New steering torque controller parameters

Starting in R2024a, the Steering System block includes these parameters that you can specify to define a steering torque controller:

• Integral antiwindup gain

• Derivative gain

• Integral gain

• Output saturation lower limit

• Output saturation upper limit

• Proportional gain