Documentation

# 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`

`$y=\frac{{K}_{ff}}{{v}_{nom}}{v}_{ref}+\frac{{K}_{p}{e}_{ref}}{{v}_{nom}}+\int \left(\frac{{K}_{i}{e}_{ref}}{{v}_{nom}}+{K}_{aw}{e}_{out}\right)dt+{K}_{g}\theta$`

```Scheduled PI```

`$y=\frac{{K}_{ff}\left(v\right)}{{v}_{nom}}{v}_{ref}+\frac{{K}_{p}\left(v\right){e}_{ref}}{{v}_{nom}}+\int \left(\frac{{K}_{i}\left(v\right){e}_{ref}}{{v}_{nom}}+{K}_{aw}{e}_{out}\right){e}_{ref}dt+{K}_{g}\left(v\right)\theta$`

`$\begin{array}{l}\text{where:}\\ \\ {e}_{ref}={v}_{ref}-v\\ {e}_{out}={y}_{sat}-y\\ \\ {y}_{sat}=\left\{\begin{array}{cc}-1& y<-1\\ y& -1\le y\le 1\\ 1& 1`

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

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

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

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. 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

#### Vehicle Dynamics

For longitudinal motion, the block implements these linear dynamics.

`$\begin{array}{l}{x}_{1}=v\\ {\stackrel{˙}{x}}_{1}={x}_{2}=\frac{{K}_{pt}}{m}-g\mathrm{sin}\left(\gamma \right)+{F}_{r}{x}_{1}\end{array}$`

In matrix notation:

The block uses this equation for the rolling resistance.

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.

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).

`$J=\frac{1}{T}{\int }_{t}^{t+T}{\left[f\left(\eta \right)-y\left(\eta \right)\right]}^{2}d\eta$`

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 ahead1, 2, 3.

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

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.

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

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

expand all

Reference velocity, vref, in m/s.

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

Road grade angle, θ or γ, in deg.

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

expand all

Bus signal containing these block calculations.

SignalVariableDescription
`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`$\underset{0}{\overset{t}{\int }}{e}_{ref}{}^{2}dt$

Integrated square of error

`ErrMax`$\mathrm{max}\left({e}_{ref}\left(t\right)\right)$

Maximum error during simulation

`ErrMin`$\mathrm{min}\left({e}_{ref}\left(t\right)\right)$

Minimum error during simulation

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

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

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

expand all

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.

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.

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, dimensionless.

#### Dependencies

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

Proportional gain, Ki, dimensionless.

#### Dependencies

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

Velocity feed-forward gain, Kff, dimensionless.

#### Dependencies

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

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

#### Dependencies

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

Velocity gain breakpoints, VehVelVec, dimensionless.

#### Dependencies

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

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, as a function of vehicle velocity, dimensionless.

#### Dependencies

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

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, as a function of vehicle velocity, in 1/deg.

#### Dependencies

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

Nominal vehicle speed, vnom, 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 gain, Kaw, dimensionless.

#### Dependencies

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

Error filter time constant, τerr, 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, in kg.

#### Dependencies

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

Effective vehicle total tractive force, Kp, in N.

#### Dependencies

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

Driver response time, τ, in s.

#### Dependencies

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

Driver preview distance, L, in m.

#### Dependencies

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

Static rolling and driveline resistance coefficient, aR, 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, 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, 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, in m/s^2.

#### Dependencies

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

### Shift

#### Reverse, Neutral, Drive

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, 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

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`.

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 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 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, in s.

#### Dependencies

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

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

#### Dependencies

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

Time required to engage park from neutral, tPark, 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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