Longitudinal Driver

Longitudinal speed-tracking controller

• Library:

• Powertrain Blockset / Vehicle Scenario Builder

  Vehicle Dynamics Blockset / Vehicle Scenarios / Driver

Description

The Longitudinal Driver block implements a longitudinal speed-tracking controller. Based on reference and feedback velocities, the block generates normalized acceleration and braking commands that can vary from 0 through 1. You can use the block to model the dynamic response of a driver or to generate the commands necessary to track a longitudinal drive cycle.

Configurations

Controller

Use the Control type, cntrlType parameter to specify one of these control options.

Setting	Block Implementation
PI	Proportional-integral (PI) control with tracking windup and feed-forward gains.
Scheduled PI	PI control with tracking windup and feed-forward gains that are a function of vehicle velocity.
Predictive	Optimal single-point preview (look ahead) control model developed by C. C. MacAdam1, 2, 3. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block: Represents the dynamics as a linear single track (bicycle) vehicle Minimizes the previewed error signal at a single point T* seconds ahead in time Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Shift

Use the Shift type, shftType parameter to specify one of these shift options.

Setting	Block Implementation
None	No transmission. Block outputs a constant gear of 1. Use this setting to minimize the number of parameters you need to generate acceleration and braking commands to track forward vehicle motion. This setting does not allow reverse vehicle motion.
Reverse, Neutral, Drive	Block uses a Stateflow® chart to model reverse, neutral, and drive gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using simple reverse, neutral, and drive gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses the initial gear and time required to shift to shift the vehicle up into drive or down into reverse or neutral. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
Scheduled	Block uses a Stateflow chart to model reverse, neutral, park, and N-speed gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using reverse, neutral, park, and N-speed gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses these parameters to determine the: Initial gear Upshift and downshift accelerator pedal positions Upshift and downshift velocity Timing for shifting and engaging forward and reverse from neutral For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
External	Block uses the input gear, vehicle state, and velocity feedback to generate acceleration and braking commands to track forward and reverse vehicle motion. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.

Controller: PI Speed-Tracking

If you set the control type to PI or Scheduled PI, the block implements proportional-integral (PI) control with tracking windup and feed-forward gains. For the Scheduled PI configuration, the block uses feed forward gains that are a function of vehicle velocity.

To calculate the speed control output, the block uses these equations.

Setting	Equation
PI	$$y=\frac{K_{ff}}{v_{nom}}{v}_{ref}+\frac{K_p{e}_{ref}}{v_{nom}}+{\displaystyle \int \left(\frac{K_i{e}_{ref}}{v_{nom}}+K_{aw}{e}_{out}\right)dt+K_g\theta }$$
Scheduled PI	$$y=\frac{K_{ff}(v)}{v_{nom}}{v}_{ref}+\frac{K_p(v)e_{ref}}{v_{nom}}+{\displaystyle \int \left(\frac{K_i(v)e_{ref}}{v_{nom}}+K_{aw}{e}_{out}\right)e_{ref}dt+K_g(v)\theta }$$

$$\begin{array}{l}\text{where:}\\ \\ e_{ref}=v_{ref}-v\\ e_{out}=y_{sat}-y\\ \\ y_{sat}=\{\begin{array}{cc}-1& y<-1\\ y& -1\le y\le 1\\ 1& 1<y\end{array}\end{array}$$

The velocity error low-pass filter uses this transfer function.

$$H(s)=\frac{1}{{\tau }_{err}s+1}\text{ for }{\tau }_{err}>0$$

To calculate the acceleration and braking commands, the block uses these equations.

$$\begin{array}{l}{y}_{acc}=\{\begin{array}{cc}0& y_{sat}<0\\ y_{sat}& 0\le y_{sat}\le 1\\ 1& 1<y_{sat}\end{array}\\ \\ y_{dec}=\{\begin{array}{cc}0& y_{sat}>0\\ -y_{sat}& -1\le y_{sat}\le 0\\ 1& y_{sat}<-1\end{array}\end{array}$$

The equations use these variables.

vnom	Nominal vehicle speed
Kp	Proportional gain
Ki	Integral gain
Kaw	Anti-windup gain
Kff	Velocity feed-forward gain
Kg	Grade feed-forward gain
θ	Grade angle
τerr	Error filter time constant
y	Nominal control output magnitude
ysat	Saturated control output magnitude
eref	Velocity error
eout	Difference between saturated and nominal control outputs
yacc	Acceleration signal
ydec	Braking signal
v	Velocity feedback signal
vref	Reference velocity signal

Controller: Predictive Speed-Tracking

If you set the Control type, cntrlType parameter to Predictive, the block implements an optimal single-point preview (look ahead) control model developed by C. C. MacAdam^{1, 2, 3}. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block:

• Represents the dynamics as a linear single track (bicycle) vehicle

• Minimizes the previewed error signal at a single point T* seconds ahead in time

• Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Vehicle Dynamics

For longitudinal motion, the block implements these linear dynamics.

$$\begin{array}{l}{x}_1=v\\ {\dot{x}}_1=x_2=\frac{K_{pt}}{m}-g\sin (\gamma )+F_r{x}_1\end{array}$$

In matrix notation:

$$\begin{array}{l}\dot{x}=Fx+g\overline{u}\\ \\ \text{where:}\\ \\ x=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]\\ F=\left[\begin{array}{cc}0& 1\\ \frac{F_r}{m}& 0\end{array}\right]\\ g=\left[\begin{array}{c}\begin{array}{c}0\\ \frac{K_{pt}}{m}\end{array}\end{array}\right]\\ \overline{u}=u- \frac{m^2}{K_{pt}}g\text{sin}(\gamma )\end{array}$$

The block uses this equation for the rolling resistance.

$F_r=-\left[\tanh (x_1)( \frac{a_r}{x_1}+c_r{x}_1)+b_r\right]$

The single-point model assumes a minimum previewed error signal at a single point T* seconds ahead in time. a* is the driver ability to predict the future vehicle response based on the current steering control input. b* is the driver ability to predict the future vehicle response based on the current vehicle state. The block uses these equations.

$$\begin{array}{l}a*=(T*)m^T\left[I+{\displaystyle \sum _{n=1}^{\infty }\frac{F^n{(T*)}^n}{(n+1)!}}\right]ge\\ \\ b*=m^T\left[I+{\displaystyle \sum _{n=1}^{\infty }\frac{F^n{(T*)}^n}{n!}}\right]\\ \\ \text{where: }\\ \\ m^T=\left[\begin{array}{cc}1& 1\end{array}\right]\end{array}$$

The equations use these variables.

a, b	Forward and rearward tire location, respectively
m	Vehicle mass
I	Vehicle rotational inertia
a*, b*	Driver prediction scalar and vector gain, respectively
x	Predicted vehicle state vector
v	Longitudinal velocity
F	System matrix
Kpt	Tractive force and brake limit
γ	Grade angle
g	Control coefficient vector
g	Gravitational constant
T*	Preview time window
ƒ(t+T*)	Previewed path input T* seconds ahead
U	Forward vehicle velocity
mT	Constant observer vector; provides vehicle lateral position
Fr	Rolling resistance
ar	Static rolling and driveline resistance
br	Linear rolling and driveline resistance
cr	Aerodynamic rolling and driveline resistance

Optimization

The single-point model implemented by the block finds the steering command that minimizes a local performance index, J, over the current preview interval, (t, t+T).

$$J=\frac{1}{T}{\displaystyle {\int }_t^{t+T}{[f(\eta )-y(\eta )]}^2}d\eta$$

To minimize J with respect to the steering command, this condition must be met.

$$\frac{dJ}{du}=0$$

You can express the optimal control solution in terms of a current non-optimal and corresponding nonzero preview output error T* seconds ahead^{1, 2, 3}.

$$u^o(t)=u(t)+\frac{e(t+T*)}{a*}$$

The equations use these variables.

ƒ(t+T*)	Previewed path input T* sec ahead
y(t+T*)	Previewed plant output T* sec ahead
e(t+T*)	Previewed error signal T* sec ahead
u(t), uo(t)	Steer angle and optimal steer angle, respectively
J	Performance index

Driver Lag

The single-point model implemented by the block introduces a driver lag. The driver lag accounts for the delay when the driver is tracking tasks. Specifically, it is the transport delay deriving from perceptual and neuromuscular mechanisms. To calculate the driver transport delay, the block implements this equation.

$$H(s)=e^{-s\tau }$$

The equations use these variables.

τ	Driver transport delay
y(t+T*)	Previewed plant output T* sec ahead
e(t+T*)	Previewed error signal T* sec ahead
u(t), uo(t)	Steer angle and optimal steer angle, respectively
J	Performance index

Ports

Input

VelRef — Reference vehicle velocity

scalar

Reference velocity, v_ref, in m/s.

VelFdbk — Longitudinal vehicle velocity

scalar

Longitudinal vehicle velocity, U, in vehicle-fixed frame, in m/s.

Grade — Road grade angle

scalar

Road grade angle, θ or γ, in deg.

ExtGear — Gear

scalar

Gear	Integer
Park	80
Reverse	-1
Neutral	0
Drive	1
Gear	Gear number

Dependencies

To create this port, set Shift type, shftType to External.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal	Variable	Description
Accel	yacc	Commanded vehicle acceleration, normalized from 0 through 1
Decel	ydec	Commanded vehicle deceleration, normalized from 0 through 1
Gear		Integer value of commanded gear
Clutch		Clutch command
Err	eref	Difference in reference vehicle speed and vehicle speed
ErrSqrSum	$${\displaystyle \underset{0}{\overset{t}{\int }}{e}_{ref}{}^2}dt$$	Integrated square of error
ErrMax	$$\max (e_{ref}(t))$$	Maximum error during simulation
ErrMin	$$\min (e_{ref}(t))$$	Minimum error during simulation

AccelCmd — Commanded vehicle acceleration

scalar

Commanded vehicle acceleration, y_acc, normalized from 0 through 1.

DecelCmd — Commanded vehicle deceleration

scalar

Commanded vehicle deceleration, y_dec, normalized from 0 through 1.

Gear — Commanded vehicle gear

scalar

Integer value of commanded vehicle gear.

Gear	Integer
Park	80
Reverse	-1
Neutral	0
Drive	1
Gear	Gear number

Dependencies

To create this port, select Output gear signal.

Parameters

Control type, cntrlType — Longitudinal control

PI (default) | Scheduled PI | Predictive

Type of longitudinal control.

Setting	Block Implementation
PI	Proportional-integral (PI) control with tracking windup and feed-forward gains.
Scheduled PI	PI control with tracking windup and feed-forward gains that are a function of vehicle velocity.
Predictive	Optimal single-point preview (look ahead) control model developed by C. C. MacAdam1, 2, 3. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block: Represents the dynamics as a linear single track (bicycle) vehicle Minimizes the previewed error signal at a single point T* seconds ahead in time Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Shift type, shftType — Shift type

None (default) | Reverse, Neutral, Drive | Scheduled | External

Shift type.

Setting	Block Implementation
None	No transmission. Block outputs a constant gear of 1. Use this setting to minimize the number of parameters you need to generate acceleration and braking commands to track forward vehicle motion. This setting does not allow reverse vehicle motion.
Reverse, Neutral, Drive	Block uses a Stateflow chart to model reverse, neutral, and drive gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using simple reverse, neutral, and drive gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses the initial gear and time required to shift to shift the vehicle up into drive or down into reverse or neutral. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
Scheduled	Block uses a Stateflow chart to model reverse, neutral, park, and N-speed gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using reverse, neutral, park, and N-speed gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses these parameters to determine the: Initial gear Upshift and downshift accelerator pedal positions Upshift and downshift velocity Timing for shifting and engaging forward and reverse from neutral For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
External	Block uses the input gear, vehicle state, and velocity feedback to generate acceleration and braking commands to track forward and reverse vehicle motion. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.

Reference and feedback units, velUnits — Velocity units

m/s (default)

Vehicle velocity reference and feedback units.

Dependencies

If you set Control type, cntrlType control type to Scheduled or Scheduled PI, the block uses the Reference and feedback units, velUnits for the Nominal speed, vnom parameter dimension.

If you set Shift Type, shftType to Scheduled, the block uses the Longitudinal velocity units, velUnits for these parameter dimensions:

• Upshift velocity data table, upShftTbl

• Downshift velocity data table, dwnShftTbl

Control

Longitudinal Nominal Gains

Proportional gain, Kp — Gain

scalar

Proportional gain, K_p, dimensionless.

Dependencies

To create this parameter, set Control type to PI.

Integral gain, Ki — Gain

scalar

Proportional gain, K_i, dimensionless.

Dependencies

To create this parameter, set Control type to PI.

Velocity feed-forward, Kff — Gain

scalar

Velocity feed-forward gain, K_ff, dimensionless.

Dependencies

To create this parameter, set Control type to PI.

Grade feed-forward, Kg — Gain

scalar

Grade feed-forward gain, K_g, in 1/deg.

Dependencies

To create this parameter, set Control type to PI.

Velocity gain breakpoints, VehVelVec — Breakpoints

array

Velocity gain breakpoints, VehVelVec, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Velocity feed-forward gain values, KffVec — Gain

array

Velocity feed-forward gain values, KffVec, as a function of vehicle velocity, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Proportional gain values, KpVec — Gain

array

Proportional gain values, KpVec, as a function of vehicle velocity, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Integral gain values, KiVec — Gain

array

Integral gain values, KiVec, as a function of vehicle velocity, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Grade feed-forward values, KgVec — Grade gain

array

Grade feed-forward values, KgVec, as a function of vehicle velocity, in 1/deg.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Nominal speed, vnom — Nominal vehicle speed

scalar

Nominal vehicle speed, v_nom, in units specified by the Reference and feedback units, velUnits parameter. The block uses the nominal speed to normalize the controller gains.

Dependencies

To create this parameter, set Control type to PI or Scheduled PI.

Anti-windup, Kaw — Gain

scalar

Anti-windup gain, K_aw, dimensionless.

Dependencies

To create this parameter, set Control type to PI or Scheduled PI.

Error filter time constant, tauerr — Filter

scalar

Error filter time constant, τ_err, in s. To disable the filter, enter 0.

Dependencies

To create this parameter, set Control type to PI or Scheduled PI.

Predictive

Vehicle mass, m — Mass

scalar

Vehicle mass, m, in kg.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Effective vehicle total tractive force, Kp — Tractive force

scalar

Effective vehicle total tractive force, K_p, in N.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Driver response time, tau — Tau

scalar

Driver response time, τ, in s.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Preview distance, L — Distance

scalar

Driver preview distance, L, in m.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Rolling resistance coefficient, aR — Resistance

scalar

Static rolling and driveline resistance coefficient, a_R, in N. Block uses the parameter to estimate the constant acceleration or braking effort.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Rolling and driveline resistance coefficient, bR — Resistance

scalar

Rolling and driveline resistance coefficient, b_R, in N·s/m. Block uses the parameter to estimate the linear velocity-dependent acceleration or braking effort.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Aerodynamic drag coefficient, cR — Drag

scalar

Aerodynamic drag coefficient, c_R, in N·s^2/m^2. Block uses the parameter to estimate the quadratic velocity-dependent acceleration or braking effort.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Gravitational constant, g — Gravitational constant

scalar

Gravitational constant, g, in m/s^2.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Shift

Reverse, Neutral, Drive

Initial gear, GearInit — Initial gear

scalar

Integer value of the initial gear. The block uses the initial gear to generate acceleration and braking commands to track forward and reverse vehicle motion.

Gear	Integer
Park	80
Reverse	-1
Neutral	0
Drive	1
Gear	Gear number

Dependencies

To create this parameter, set Shift type, shftType to Reverse, Neutral, Drive or Scheduled. If you specify Reverse, Neutral, Drive, the Initial Gear, GearInit parameter value can be only -1, 0, or 1.

Time required to shift, tShift — Time

scalar

Time required to shift, tShift, in s. The block uses the time required to shift to generate acceleration and braking commands to track forward and reverse vehicle motion using reverse, neutral, and drive gear shift scheduling.

Dependencies

To create this parameter, set Shift type, shftType to Reverse, Neutral, Drive.

Scheduled

Initial gear, GearInit — Initial gear

scalar

Integer value of the initial gear. The block uses the initial gear to generate acceleration and braking commands to track forward and reverse vehicle motion.

Gear	Integer
Park	80
Reverse	-1
Neutral	0
Drive	1
Gear	Gear number

Dependencies

To create this parameter, set Shift type, shftType to Reverse, Neutral, Drive or Scheduled. If you specify Reverse, Neutral, Drive, the Initial Gear, GearInit parameter value can be only -1, 0, or 1.

Up and down shift accelerator pedal positions, pdlVec — Pedal position breakpoints

[1-by-m] vector

Pedal position breakpoints for lookup tables when calculating upshift and downshift velocities, dimensionless. Vector dimensions are 1 by the number of pedal position breakpoints, m.

Dependencies

To create this parameter, set Shift type, shftType to Scheduled.

Upshift velocity data table, upShftTbl — Table

[m-by-n] array

Upshift velocity data as a function of pedal position and gear, in units specified by the Reference and feedback units, velUnits parameter. Upshift velocities indicate the vehicle velocity at which the gear should increase by 1.

The array dimensions are m pedal positions by n gears. The first column of data, when n equals 1, is the upshift velocity for the neutral gear.

Dependencies

To create this parameter, set Shift type, shftType to Scheduled.

Downshift velocity data table, dwnShftTbl — Table

[m-by-n] array

Downshift velocity data as a function of pedal position and gear, in units specified by the Reference and feedback units, velUnits parameter. Downshift velocities indicate the vehicle velocity at which the gear should decrease by 1.

The array dimensions are m pedal positions by n gears. The first column of data, when n equals 1, is the downshift velocity for the neutral gear.

Dependencies

To create this parameter, set Shift type, shftType to Scheduled.

Time required to shift, tClutch — Time

scalar

Time required to shift, t_Clutch, in s.

Dependencies

To create this parameter, set Shift type, shftType to Scheduled.

Time required to engage reverse from neutral, tRev — Time

scalar

Time required to engage reverse from neutral, t_Rev, in s.

Dependencies

To create this parameter, set Shift type, shftType to Scheduled.

Time required to engage park from neutral, tPark — Time

scalar

Time required to engage park from neutral, t_Park, in s.

Dependencies

To create this parameter, set Shift type, shftType to Scheduled.

References

[1] MacAdam, C. C. "An Optimal Preview Control for Linear Systems". Journal of Dynamic Systems, Measurement, and Control. Vol. 102, Number 3, Sept. 1980.

[2] MacAdam, C. C. "Application of an Optimal Preview Control for Simulation of Closed-Loop Automobile Driving ". IEEE Transactions on Systems, Man, and Cybernetics. Vol. 11, Issue 6, June 1981.

[3] MacAdam, C. C. Development of Driver/Vehicle Steering Interaction Models for Dynamic Analysis. Final Technical Report UMTRI-88-53. Ann Arbor, Michigan: The University of Michigan Transportation Research Institute, Dec. 1988.

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