Path Following Control System

Examples

Lane Following Control with Sensor Fusion and Lane Detection

Simulate and generate code for an automotive lane-following controller.

(Automated Driving Toolbox)

Highway Lane Following

Simulate a lane-following controller and monocular camera-based perception algorithm in the Unreal Engine^® simulation environment.

(Automated Driving Toolbox)

Ports

Input

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Set velocity — Ego vehicle velocity setpoint
nonnegative scalar

Ego vehicle velocity setpoint in m/s. When there is no lead vehicle, the controller tracks this velocity.

Time gap — Safe time gap
nonnegative scalar

Safe time gap in seconds between the lead vehicle and the ego vehicle. This time gap is used to calculate the minimum safe following distance constraint. For more information, see Safe Following Distance.

Relative distance — Distance between lead vehicle and ego vehicle
positive scalar

Distance in meters between lead vehicle and ego vehicle. To calculate this signal, subtract the ego vehicle position from the lead vehicle position.

Relative velocity — Velocity difference between lead vehicle and ego vehicle
scalar

Velocity difference in meters per second between lead vehicle and ego vehicle. To calculate this signal, subtract the ego vehicle velocity from the lead vehicle velocity.

Longitudinal velocity — Ego vehicle velocity
nonnegative scalar

Ego vehicle velocity in m/s.

Curvature — Road curvature
scalar | vector

Road curvature, specified as 1/R, where R is the radius of the curve in meters.

The road curvature is:

Positive when the road curves toward the positive Y axis of the global coordinate system.
Negative when the road curves toward the negative Y axis of the global coordinate system.
Zero for a straight road.

The controller models the road curvature as a measured disturbance with previewing. You can specify the curvature as a:

Scalar signal — Specify the curvature for the current control interval. The controller uses this curvature value across the prediction horizon.
Vector signal with length less than or equal to the Prediction Horizon parameter — Specify the current and predicted curvature values across the prediction horizon. If the length of the vector is less than the prediction horizon, then the controller uses the final curvature value in the vector for the remainder of the prediction horizon.

Lateral deviation — Ego vehicle lateral deviation
scalar

Ego vehicle lateral deviation in meters from the centerline of the lane. The lateral deviation e₁ is positive when the ego vehicle is to the right of the centerline and negative when the ego vehicle is to the left of the centerline.

Relative yaw angle — Angle from lane centerline
scalar

Ego vehicle longitudinal axis angle in radians from the centerline of the lane, defined as:

$e_{2} = θ_{e} - θ_{c}$

Here, θ_e is the ego vehicle angle and θ_c is the centerline angle, with both angles defined in the global coordinate frame.

Minimum longitudinal acceleration — Minimum ego vehicle acceleration
scalar

Minimum ego vehicle longitudinal acceleration constraint in m/s². Use this input port when the minimum acceleration varies at run time.

Dependencies

To enable this port, select corresponding Use external source parameter.

Maximum longitudinal acceleration — Maximum ego vehicle acceleration
scalar

Maximum ego vehicle longitudinal acceleration constraint in m/s². Use this input port when the maximum acceleration varies at run time.

Dependencies

To enable this port, select corresponding Use external source parameter.

Minimum steering angle — Minimum front steering angle
scalar

Minimum front steering angle constraint in radians. Use this input port when the minimum steering angle varies at run time.

Dependencies

To enable this port, select corresponding Use external source parameter.

Maximum steering angle — Maximum front steering angle
scalar

Maximum front steering angle constraint in radians. Use this input port when the maximum steering angle varies at run time.

Dependencies

To enable this port, select corresponding Use external source parameter.

Enable optimization — Controller optimization enable signal
scalar

Controller optimization enable signal. When this signal is:

Nonzero, the controller performs optimization calculations and generates the Longitudinal acceleration and Steering angle control signals.
Zero, the controller does not perform optimization calculations. In this case, the Longitudinal acceleration and Steering angle output signals remain at the values they had when the optimization was disabled. The controller continues to update its internal state estimates.

Dependencies

To enable this port, select the Use external signal to enable or disable optimization parameter.

External control signal — Control signals applied to ego vehicle
vector of length two

Actual control signals applied to the ego vehicle. The first element of this signal is the longitudinal acceleration in m/s², and the second element is the steering angle in radians. The controller uses these signals to estimate the ego vehicle model states. Use this input port when the control signals applied to the ego vehicle do not match the optimal control signals computed by the model predictive controller. This mismatch can occur when, for example:

The Path Following Control System is not the active controller. Maintaining an accurate state estimate when the controller is not active prevents bumps in the control signals when the controller becomes active.
The steering or acceleration actuator fails and does not provide the correct control signal to the ego vehicle.

Dependencies

To enable this port, select the Use external control signal for bumpless transfer between PFC and other controllers parameter.

Vehicle dynamics matrix A — State matrix of ego vehicle predictive model
square matrix

State matrix of ego vehicle predictive model. The number of rows in the state matrix corresponds to the number of states in the predictive model. This matrix must be square.

The ego vehicle predictive model defined by Vehicle dynamics matrix A, Vehicle dynamics matrix B, and Vehicle dynamics matrix C must be minimal.

Dependencies

To enable this port, select the Use vehicle model parameter.

Vehicle dynamics matrix B — Input-to-state matrix of ego vehicle predictive model
matrix with two columns

Input-to-state matrix of ego vehicle predictive model. The number of rows in this signal must match the number of rows in Vehicle dynamics matrix A.

The ego vehicle predictive model defined by Vehicle dynamics matrix A, Vehicle dynamics matrix B, and Vehicle dynamics matrix C must be minimal.

Dependencies

To enable this port, select the Use vehicle model parameter.

Vehicle dynamics matrix C — State-to-output matrix of ego vehicle predictive model
matrix with three rows

State-to-output matrix of ego vehicle predictive model. The number of columns in this signal must match the number of rows in Vehicle dynamics matrix A.

The ego vehicle predictive model defined by Vehicle dynamics matrix A, Vehicle dynamics matrix B, and Vehicle dynamics matrix C must be minimal.

Dependencies

To enable this port, select the Use vehicle model parameter.

Output

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Longitudinal acceleration — Acceleration control signal
scalar

Acceleration control signal in m/s² generated by the controller.

Steering angle — Front steering angle control signal
scalar

Front steering angle control signal in radians generated by the controller. The front steering angle is the angle of the front tires from the longitudinal axis of the vehicle. The steering angle is positive towards the positive lateral axis of the ego vehicle.

Parameters

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Parameters Tab

Ego Vehicle

Use vehicle parameters — Define ego vehicle model using vehicle properties
`on` (default) | `off`

Select this parameter to define the ego vehicle model used by the MPC controller by specifying properties of the ego vehicle. The ego vehicle model is the linear model from the longitudinal acceleration and front steering angle to the longitudinal velocity, lateral velocity, and yaw angle rate.

To define the vehicle model, specify the following block parameters:

Total mass
Yaw moment of inertia
Longitudinal distance from center of gravity to front tires
Longitudinal distance from center of gravity to rear tires
Cornering stiffness of front tires
Cornering stiffness of rear tires
Longitudinal acceleration tracking time constant

For more information on the ego vehicle model, see Ego Vehicle Predictive Model.

Selecting this parameter clears the Use vehicle model parameter.

Programmatic Use

Block Parameter: ModelType

Type: string, character vector

Default: "Use vehicle parameters"

Use vehicle model — Define ego vehicle model using state-space matrices
`off` (default) | `on`

Select this parameter to define the state-space matrices of the ego vehicle model used by the MPC controller. The ego vehicle model is the linear model from the longitudinal acceleration and front steering angle to the longitudinal velocity, lateral velocity, and yaw angle rate.

To define the initial internal model, specify the A, B, and C state-space matrices. The internal model must be a minimal realization with no direct feedthrough, and the dimensions of A, B, and C must be consistent.

Typically, the ego vehicle model is velocity-dependent, and therefore, it varies over time. To update the internal model at run time, use the Vehicle dynamics A, Vehicle dynamics B, and Vehicle dynamics C input ports.

For more information on the ego vehicle model, see Ego Vehicle Predictive Model

Selecting this parameter clears the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: ModelType

Type: string, character vector

Default: "Use vehicle parameters"

Total mass — Ego vehicle mass
`1575` (default) | positive scalar

Ego vehicle mass in kg.

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: VehicleMass

Type: string, character vector

Default: "1575"

Yaw moment of inertia — Moment of inertia about the ego vehicle vertical axis
`2875` (default) | positive scalar

Moment of inertia about the ego vehicle vertical axis in Kg·m².

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: VehicleYawInertia

Type: string, character vector

Default: "2875"

Longitudinal distance from center of gravity to front tires — Distance from the ego vehicle center of mass to its front tires
`1.2` (default) | positive scalar

Distance from the ego vehicle center of mass to its front tires in meters, measured along the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: LengthToFront

Type: string, character vector

Default: "1.2"

Longitudinal distance from center of gravity to rear tires — Distance from the ego vehicle center of mass to its rear tires
`1.6` (default) | positive scalar

Distance from the ego vehicle center of mass to its rear tires in meters, measured along the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: LengthToRear

Type: string, character vector

Default: "1.6"

Cornering stiffness of front tires — Front tire stiffness
`19000` (default) | positive scalar

Front tire stiffness in N/rad, defined as the relationship between the side force on the front tires and the angle of the tires to the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: FrontTireStiffness

Type: string, character vector

Default: "19000"

Cornering stiffness of rear tires — Rear tire stiffness
`33000` (default) | positive scalar

Rear tire stiffness in N/rad, defined as the relationship between the side force on the rear tires and the angle of the tires to the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: RearTireStiffness

Type: string, character vector

Default: "33000"

Longitudinal acceleration tracking time constant — Time constant for acceleration tracking
`0.5` (default) | positive scalar

Time constant for tracking longitudinal acceleration, specified in seconds.

Dependencies

To enable this parameter, select the Use vehicle parameters parameter.

Programmatic Use

Block Parameter: AccelTimeConstant

Type: string, character vector

Default: "0.5"

A — Initial state matrix of ego vehicle predictive model
square matrix

Initial state matrix of ego vehicle predictive model. The number of rows in the state matrix corresponds to the number of states in the predictive model. This matrix must be square.

The initial ego vehicle predictive model defined by A, B, and C must be minimal.

Typically, the ego vehicle model varies over time. To update the state matrix at run time, use the Vehicle dynamics A input port.

Dependencies

To enable this parameter, select the Use vehicle model parameter.

Programmatic Use

Block Parameter: EgoModelMatrixA

Type: string, character vector

Default:

"[-4.4021
                                        ,-12.4603;1.3913,-5.1868]"

B — Initial input-to-state matrix of ego vehicle predictive model
matrix with two columns

Initial input-to-state matrix of ego vehicle predictive model. The number of rows in this parameter must match the number of rows in A.

The initial ego vehicle predictive model defined by A, B, and C must be minimal.

Typically, the ego vehicle model varies over time. To update the input-to-state matrix at run time, use the Vehicle dynamics B input port.

Dependencies

To enable this parameter, select the Use vehicle model parameter.

Programmatic Use

Block Parameter: EgoModelMatrixB

Type: string, character vector

Default: "[24.1270;15.8609]"

C — Initial state-to-output matrix of ego vehicle predictive model
matrix with three rows

Initial state-to-output matrix of ego vehicle predictive model. The number of columns in this parameter must match the number of rows in A.

The initial ego vehicle predictive model defined by A, B, and C must be minimal.

Typically, the ego vehicle model varies over time. To update the state-to-output matrix at run time, use the Vehicle dynamics C input port.

Dependencies

To enable this parameter, select the Use vehicle model parameter.

Programmatic Use

Block Parameter: EgoModelMatrixC

Type: string, character vector

Default: "[1,0;0,1]"

Initial longitudinal velocity — Initial velocity of the ego vehicle model
`15` (default) | nonnegative scalar

Initial velocity of the ego vehicle model in m/s, which can differ from the actual ego vehicle initial velocity.

This value is used to configure the initial conditions of the model predictive controller. For more information, see Initial Conditions.

Note

A very small initial velocity, for example eps, can produce a nonminimal realization for the controller plant model, causing an error. To prevent this error, set the initial velocity to a larger value, for example 1e-3.

Programmatic Use

Block Parameter: InitialLongVel

Type: string, character vector

Default: "15"

Transport lag between model inputs and outputs — Total transport lag in ego vehicle model
`0` (default) | nonnegative scalar

Total transport lag, τ, in the ego vehicle model in seconds. This lag includes actuator, sensor, and communication lags. For each input-output channel, the transport lag model is:

$\frac{1}{τ s + 1}$

Programmatic Use

Block Parameter: TransportLag

Type: string, character vector

Default: "0"

Spacing Control

Maintain safe distance between lead vehicle and ego vehicle — Enable spacing control
`on` (default) | `off`

To configure the safe following distance, set the Default spacing parameter. For more information on the safe following distance used by the controller, see Safe Following Distance.

Programmatic Use

Block Parameter: spaceCtrl

Type: string, character vector

Default: "on"

Default spacing — Minimum spacing to lead vehicle
`10` (default) | nonnegative scalar

Minimum spacing in meters between the lead vehicle and the ego vehicle. This value corresponds to the target relative distance between the ego and lead vehicles when the ego vehicle velocity is zero.

This value is used to calculate the:

Minimum safe following distance. For more information, see Safe Following Distance.
Controller initial conditions. For more information, see Initial Conditions.

Dependencies

To enable this parameter, select the Maintain safe distance between lead vehicle and ego vehicle parameter.

Programmatic Use

Block Parameter: DefaultSpacing

Type: string, character vector

Default: "10"

Controller Tab

Path Following Controller Constraints

Minimum steering angle — Minimum front steering angle
`-0.26` (default) | scalar between `-pi/2` and `pi/2`

Minimum front steering angle constraint in radians.

If the minimum steering angle varies over time, add the Minimum steering angle input port to the block by selecting Use external source.

Dependencies

This parameter must be less than the Maximum steering angle parameter.

Programmatic Use

Block Parameter: MinSteering

Type: string, character vector

Default: "-0.26"

Maximum steering angle — Maximum front steering angle
`0.26` (default) | scalar between `-pi/2` and `pi/2`

Maximum front steering angle constraint in radians.

If the maximum steering angle varies over time, add the Maximum steering angle input port to the block by selecting Use external source.

Dependencies

This parameter must be greater than the Minimum steering angle parameter.

Programmatic Use

Block Parameter: MaxSteering

Type: string, character vector

Default: "0.26"

Minimum longitudinal acceleration — Minimum ego vehicle acceleration
`-3` (default) | scalar

Minimum ego vehicle longitudinal acceleration constraint in m/s².

If the minimum acceleration varies over time, add the Minimum longitudinal acceleration input port to the block by selecting Use external source.

Programmatic Use

Block Parameter: MinAcceleration

Type: string, character vector

Default: "-3"

Maximum longitudinal acceleration — Maximum ego vehicle acceleration
`2` (default) | scalar

Maximum ego vehicle longitudinal acceleration constraint in m/s².

If the maximum acceleration varies over time, add the Maximum longitudinal acceleration input port to the block by selecting Use external source.

Programmatic Use

Block Parameter: MaxAcceleration

Type: string, character vector

Default: "2"

Model Predictive Controller Settings

Sample time — Controller sample time
`0.1` (default) | positive scalar

Controller sample time in seconds.

Programmatic Use

Block Parameter: Ts

Type: string, character vector

Default: "0.1"

Prediction horizon — Controller prediction horizon
`10` (default) | positive integer

Controller prediction horizon steps. The controller prediction time is the product of the sample time and the prediction horizon.

Programmatic Use

Block Parameter: PredictionHorizon

Type: string, character vector

Default: "30"

Control horizon — Controller control horizon
`3` (default) | positive integer | vector of positive integers

Controller control horizon, specified as one of the following:

Positive integer less than or equal to the Prediction horizon parameter. In this case, the controller computes m free control moves occurring at times k through k+m-1, and holds the controller output constant for the remaining prediction horizon steps from k+m through k+p-1. Here, k is the current control interval.
Vector of positive integers, [m₁, m₂, …], where the sum of the integers equals the Prediction horizon parameter. In this case, the controller computes M blocks of free moves, where M is the length of the control horizon vector. The first free move applies to times k through k+m₁-1, the second free move applies from time k+m₁ through k+m₁+m₂-1, and so on. Using block moves can improve the robustness of your controller.

Programmatic Use

Block Parameter: ControlHorizon

Type: string, character vector

Default: "3"

Controller Behavior

Weight on velocity tracking — Tuning weight for longitudinal velocity tracking
`0.1` (default) | positive scalar

Tuning weight for longitudinal velocity tracking. To produce smaller velocity-tracking errors, increase this weight.

Programmatic Use

Block Parameter: LongWeight

Type: string, character vector

Default: "0.1"

Weight on lateral error — Tuning weight for lateral error
`1` (default) | positive scalar

Tuning weight for lateral error. To produce smaller lateral errors, increase this weight.

Programmatic Use

Block Parameter: LateralWeight

Type: string, character vector

Default: "1"

Weight on change of longitudinal acceleration — Tuning weight for change in longitudinal acceleration
`0.1` (default) | positive scalar

Tuning weight for changes in longitudinal acceleration. To produce less-aggressive vehicle acceleration, increase this weight.

Programmatic Use

Block Parameter: AccelRateWeight

Type: string, character vector

Default: "0.1"

Weight on change of steering angle — Tuning weight for change in steering angle
`0.1` (default) | positive scalar

Tuning weight for changes in steering angle. To produce less-aggressive steering angle changes, increase this weight.

Programmatic Use

Block Parameter: SteerRateWeight

Type: string, character vector

Default: "0.1"

Block Tab

Use suboptimal solution — Apply suboptimal solution after specified number of iterations
`off` (default) | `on`

Configure the controller to apply a suboptimal solution after a specified maximum number of iterations, which guarantees the worst-case execution time for your controller.

For more information, see Suboptimal QP Solution.

Dependencies

After selecting this parameter, specify the Maximum iteration number parameter.

Programmatic Use

Block Parameter: suboptimal

Type: string, character vector

Default: "off"

Maximum iteration number — Maximum optimization iterations
`10` (default) | positive integer

Maximum number of controller optimization iterations.

Dependencies

To enable this parameter, select the Use suboptimal solution parameter.

Programmatic Use

Block Parameter: maxiter

Type: string, character vector

Default: "10"

Use external signal to enable or disable optimization — Add port for enabling optimization
`off` (default) | `on`

To add the Enable optimization input port to the block, select this parameter.

Programmatic Use

Block Parameter: optmode

Type: string, character vector

Default: "off"

Use external signal for bumpless transfer between PFC and other controllers — Add external control signal input port
`off` (default) | `on`

To add the External control signal input port to the block, select this parameter.

Programmatic Use

Block Parameter: trackmode

Type: string, character vector

Default: "off"

Create PFC subsystem — Create custom controller
button

Generate a custom PFC subsystem, which you can modify for your application. The configuration data for the custom controller is exported to the MATLAB^® workspace as a structure.

You can modify the custom controller subsystem to:

Modify default MPC settings or use advanced MPC features.
Modify the default controller initial conditions.
Use different application settings, such as a custom safe following distance definition.

Algorithms

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Ego Vehicle Predictive Model

The default ego vehicle predictive model for path-following control is the combination of two state-space models, one for adaptive cruise control and one for lane keeping.

Adaptive Cruise Control Predictive Model

The predictive state-space model for adaptive cruise control is:

$\begin{array}{l} A_{1} = [\begin{matrix} - 1 / τ & 0 \\ 1 & 0 \end{matrix}] \\ B_{1} = [\begin{matrix} 1 / τ \\ 0 \end{matrix}] \\ C_{1} = [\begin{matrix} 0 & 1 \end{matrix}] \\ D_{1} = 0 \end{array}$

Here, τ is the Longitudinal acceleration tracking time constant parameter.

The input to this model is the longitudinal acceleration in m/s², and the output is the longitudinal velocity in meters per second.

Lane-Keeping Predictive Model

The predictive state-space model for lane keeping is:

$\begin{array}{l} A_{2} = [\begin{matrix} - 2 (C_{F} + C_{R}) / m / V_{X} & - V_{X} - 2 (C_{F} L_{F} - C_{R} L_{R}) / m / V_{X} \\ - 2 (C_{F} L_{F} - C_{R} L_{R}) / I_{Z} / V_{X} & - 2 (C_{F} L_{F}^{2} + C_{R} L_{R}^{2}) / I_{Z} / V_{X} \end{matrix}] \\ B_{2} = 2 C_{F} [\begin{matrix} 1 / m \\ L_{F} / I_{Z} \end{matrix}] \\ C_{2} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \\ D_{2} = [\begin{matrix} 0 \\ 0 \end{matrix}] \end{array}$

Here:

V_X is the longitudinal velocity of the car. At the start of the simulation, this velocity is equal to the Initial condition for longitudinal velocity parameter. At run time, this velocity is equal to the Longitudinal velocity input signal.
m is the Total mass parameter.
I_Z is the Yaw moment of inertia parameter.
L_F is the Longitudinal distance from center of gravity to front tires parameter.
L_R is the Longitudinal distance from center of gravity to rear tires parameter.
C_F is the Cornering stiffness of front tires parameter.
C_R is the Cornering stiffness of rear tires parameter.

The input to this model is the steering angle in radians. The outputs are the lateral velocity in meters per second and yaw angle rate in radians per second.

Combined Path-Following Predictive Model

The Path Following Control System block combines these models as follows:

$\begin{array}{l} A = [\begin{matrix} A_{1} & 0 \\ 0 & A_{2} \end{matrix}] \\ B = [\begin{matrix} B_{1} & 0 \\ 0 & B_{2} \end{matrix}] \\ C = [\begin{matrix} C_{1} & 0 \\ 0 & C_{2} \end{matrix}] \\ D = [\begin{matrix} D_{1} & 0 \\ 0 & D_{2} \end{matrix}] \end{array}$

The inputs to this combined model are the longitudinal acceleration in m/s² and steering angle in radians. The outputs are the longitudinal velocity in meters per second, lateral velocity in meters per second, and yaw angle rate in radians per second.

The controller creates its internal predictive model by augmenting the ego vehicle dynamic model. The augmented model includes the road curvature as a measured disturbance input signal.

Define a Custom Model

To define a different ego vehicle predictive model, select the Use vehicle model parameter, and specify the initial state-space model. Then, specify the run-time values of the state-space matrices using the Vehicle dynamics A, Vehicle dynamics B, and Vehicle dynamics C input signals.

Safe Following Distance

When the Maintain safe distance between lead vehicle and ego vehicle parameter is selected, the model predictive controller computes the safe following distance constraint; that is, the minimum relative distance between the lead and ego vehicle, as:

$D_{R} = D_{S} + G_{T} * V_{E}$

Here:

D_S is the Default spacing parameter.
G_T is the Time gap input signal.
V_E is the Longitudinal velocity input signal.

To define a different safe following distance constraint, create a custom path-following control system by, on the Block tab, clicking Create PFC subsystem.

Initial Conditions

By default, the model predictive controller assumes the following initial conditions for the ego vehicle:

Longitudinal velocity is equal to the Initial longitudinal velocity parameter.
Longitudinal acceleration is zero.
Lateral velocity is zero.
Steering angle is zero.
Yaw angle rate is zero.

When the Maintain safe distance between lead vehicle and ego vehicle parameter is selected, the controller assumes the following additional initial conditions:

The lead vehicle longitudinal velocity is equal to the Initial longitudinal velocity parameter.
Relative distance between the lead vehicle and ego vehicle is:
$D_{R} = D_{S} + G_{T} * V_{E}$
Here:
- D_S is the Default spacing parameter.
- G_T is the time gap and is assumed to be 1.4.
- V_E is the Initial longitudinal velocity parameter.

If the initial conditions in your model do not match these conditions, the Steering angle and Longitudinal acceleration outputs can exhibit initial bumps at the start of the simulation.

To modify the controller initial conditions to match your simulation, create a custom path-following control system by, on the Block tab, clicking Create PFC subsystem.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Version History

Introduced in R2019a

Path Following Control System

Description

Examples

Lane Following Control with Sensor Fusion and Lane Detection

Highway Lane Following

Ports

Input

Set velocity — Ego vehicle velocity setpoint nonnegative scalar

Time gap — Safe time gap nonnegative scalar

Relative distance — Distance between lead vehicle and ego vehicle positive scalar

Relative velocity — Velocity difference between lead vehicle and ego vehicle scalar

Longitudinal velocity — Ego vehicle velocity nonnegative scalar

Curvature — Road curvature scalar | vector

Lateral deviation — Ego vehicle lateral deviation scalar

Relative yaw angle — Angle from lane centerline scalar

Minimum longitudinal acceleration — Minimum ego vehicle acceleration scalar

Dependencies

Maximum longitudinal acceleration — Maximum ego vehicle acceleration scalar

Dependencies

Minimum steering angle — Minimum front steering angle scalar

Dependencies

Maximum steering angle — Maximum front steering angle scalar

Dependencies

Enable optimization — Controller optimization enable signal scalar

Dependencies

External control signal — Control signals applied to ego vehicle vector of length two

Dependencies

Vehicle dynamics matrix A — State matrix of ego vehicle predictive model square matrix

Dependencies

Vehicle dynamics matrix B — Input-to-state matrix of ego vehicle predictive model matrix with two columns

Dependencies

Vehicle dynamics matrix C — State-to-output matrix of ego vehicle predictive model matrix with three rows

Dependencies

Output

Longitudinal acceleration — Acceleration control signal scalar

Steering angle — Front steering angle control signal scalar

Parameters

Parameters Tab

Use vehicle parameters — Define ego vehicle model using vehicle properties on (default) | off

Programmatic Use

Use vehicle model — Define ego vehicle model using state-space matrices off (default) | on

Programmatic Use

Total mass — Ego vehicle mass 1575 (default) | positive scalar

Dependencies

Programmatic Use

Yaw moment of inertia — Moment of inertia about the ego vehicle vertical axis 2875 (default) | positive scalar

Dependencies

Programmatic Use

Longitudinal distance from center of gravity to front tires — Distance from the ego vehicle center of mass to its front tires 1.2 (default) | positive scalar

Dependencies

Programmatic Use

Longitudinal distance from center of gravity to rear tires — Distance from the ego vehicle center of mass to its rear tires 1.6 (default) | positive scalar

Dependencies

Programmatic Use

Cornering stiffness of front tires — Front tire stiffness 19000 (default) | positive scalar

Dependencies

Programmatic Use

Cornering stiffness of rear tires — Rear tire stiffness 33000 (default) | positive scalar

Dependencies

Programmatic Use

Longitudinal acceleration tracking time constant — Time constant for acceleration tracking 0.5 (default) | positive scalar

Dependencies

Programmatic Use

A — Initial state matrix of ego vehicle predictive model square matrix

Dependencies

Programmatic Use

B — Initial input-to-state matrix of ego vehicle predictive model matrix with two columns

Dependencies

Programmatic Use

C — Initial state-to-output matrix of ego vehicle predictive model matrix with three rows

Dependencies

Programmatic Use

Initial longitudinal velocity — Initial velocity of the ego vehicle model 15 (default) | nonnegative scalar

Programmatic Use

Transport lag between model inputs and outputs — Total transport lag in ego vehicle model 0 (default) | nonnegative scalar

Programmatic Use

Maintain safe distance between lead vehicle and ego vehicle — Enable spacing control on (default) | off

Programmatic Use

Default spacing — Minimum spacing to lead vehicle 10 (default) | nonnegative scalar

Dependencies

Set velocity — Ego vehicle velocity setpoint
nonnegative scalar

Time gap — Safe time gap
nonnegative scalar

Relative distance — Distance between lead vehicle and ego vehicle
positive scalar

Relative velocity — Velocity difference between lead vehicle and ego vehicle
scalar

Longitudinal velocity — Ego vehicle velocity
nonnegative scalar

Curvature — Road curvature
scalar | vector

Lateral deviation — Ego vehicle lateral deviation
scalar

Relative yaw angle — Angle from lane centerline
scalar

Minimum longitudinal acceleration — Minimum ego vehicle acceleration
scalar

Maximum longitudinal acceleration — Maximum ego vehicle acceleration
scalar

Minimum steering angle — Minimum front steering angle
scalar

Maximum steering angle — Maximum front steering angle
scalar

Enable optimization — Controller optimization enable signal
scalar

External control signal — Control signals applied to ego vehicle
vector of length two

Vehicle dynamics matrix A — State matrix of ego vehicle predictive model
square matrix

Vehicle dynamics matrix B — Input-to-state matrix of ego vehicle predictive model
matrix with two columns

Vehicle dynamics matrix C — State-to-output matrix of ego vehicle predictive model
matrix with three rows

Longitudinal acceleration — Acceleration control signal
scalar

Steering angle — Front steering angle control signal
scalar

Use vehicle parameters — Define ego vehicle model using vehicle properties
`on` (default) | `off`

Use vehicle model — Define ego vehicle model using state-space matrices
`off` (default) | `on`

Total mass — Ego vehicle mass
`1575` (default) | positive scalar

Yaw moment of inertia — Moment of inertia about the ego vehicle vertical axis
`2875` (default) | positive scalar

Longitudinal distance from center of gravity to front tires — Distance from the ego vehicle center of mass to its front tires
`1.2` (default) | positive scalar

Longitudinal distance from center of gravity to rear tires — Distance from the ego vehicle center of mass to its rear tires
`1.6` (default) | positive scalar

Cornering stiffness of front tires — Front tire stiffness
`19000` (default) | positive scalar

Cornering stiffness of rear tires — Rear tire stiffness
`33000` (default) | positive scalar

Longitudinal acceleration tracking time constant — Time constant for acceleration tracking
`0.5` (default) | positive scalar

A — Initial state matrix of ego vehicle predictive model
square matrix

B — Initial input-to-state matrix of ego vehicle predictive model
matrix with two columns

C — Initial state-to-output matrix of ego vehicle predictive model
matrix with three rows

Initial longitudinal velocity — Initial velocity of the ego vehicle model
`15` (default) | nonnegative scalar

Transport lag between model inputs and outputs — Total transport lag in ego vehicle model
`0` (default) | nonnegative scalar

Maintain safe distance between lead vehicle and ego vehicle — Enable spacing control
`on` (default) | `off`

Default spacing — Minimum spacing to lead vehicle
`10` (default) | nonnegative scalar

Minimum steering angle — Minimum front steering angle
`-0.26` (default) | scalar between `-pi/2` and `pi/2`

Maximum steering angle — Maximum front steering angle
`0.26` (default) | scalar between `-pi/2` and `pi/2`

Minimum longitudinal acceleration — Minimum ego vehicle acceleration
`-3` (default) | scalar

Maximum longitudinal acceleration — Maximum ego vehicle acceleration
`2` (default) | scalar

Sample time — Controller sample time
`0.1` (default) | positive scalar

Prediction horizon — Controller prediction horizon
`10` (default) | positive integer

Control horizon — Controller control horizon
`3` (default) | positive integer | vector of positive integers

Weight on velocity tracking — Tuning weight for longitudinal velocity tracking
`0.1` (default) | positive scalar

Weight on lateral error — Tuning weight for lateral error
`1` (default) | positive scalar

Weight on change of longitudinal acceleration — Tuning weight for change in longitudinal acceleration
`0.1` (default) | positive scalar

Weight on change of steering angle — Tuning weight for change in steering angle
`0.1` (default) | positive scalar

Use suboptimal solution — Apply suboptimal solution after specified number of iterations
`off` (default) | `on`

Maximum iteration number — Maximum optimization iterations
`10` (default) | positive integer

Use external signal to enable or disable optimization — Add port for enabling optimization
`off` (default) | `on`

Use external signal for bumpless transfer between PFC and other controllers — Add external control signal input port
`off` (default) | `on`

Create PFC subsystem — Create custom controller
button

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