Constant Radius Maneuver

This reference application represents a full vehicle dynamics model undergoing a constant radius test maneuver. For information about similar maneuvers, see standards SAE J266_199601^[4] and ISO 4138:2012^[5]. You can create your own versions, establishing a framework to test that your vehicle meets the design requirements under normal and extreme driving conditions. Use this reference application in ride and handling studies and chassis controls development to characterize the steering and lateral vehicle dynamics.

You can configure the reference application for open-loop and closed-loop tests:

• Open-loop — Maintain the target velocity and steering wheel angle to determine the lateral acceleration, side-slip characteristics, and steering angles for specific accelerations and subsequent test maneuvers. For the open-loop test, set the Reference Generator block Maneuver parameter to Increasing Steer.

• Closed-loop — Use the predictive driver to maintain a prespecified turn radius at different velocities for drivability and handling performance studies. For the closed-loop test, set the Reference Generator block Maneuver parameter to Constant radius.

To create and open a working copy of the constant radius reference application, enter

vdynblksConstRadiusStart 

This table summarizes the blocks and subsystems in the reference application. Some subsystems contain variants.

Reference Application Element	Description	Variants
Reference Generator	Sets the parameters that configure the maneuver and 3D visualization environment. By default, the block is set for the constant radius maneuver with the 3D simulation engine environment disabled. For the minimum 3D visualization environment hardware requirements, see Unreal Engine Simulation Environment Requirements and Limitations. To enable 3D visualization, on the 3D Engine tab, select Enabled.	✓
Driver Commands	Implements the driver model that the reference application uses to generate acceleration, braking, gear, and steering commands. By default, Driver Commands subsystem variant is the Predictive Driver block.	✓
Environment	Implements wind and road forces.	✓
Controllers	Implements controllers for engine control units (ECUs), transmissions, anti-lock braking systems (ABS), and active differentials.	✓
Passenger Vehicle	Implements the: Body, suspension, and wheels Engine Steering, transmission, driveline, and brakes	✓
Visualization	Provides the vehicle trajectory and driver response. Note Simulating models in the 3D visualization environment requires Simulink® 3D Animation™.	✓

To override the default variant, on the Modeling tab, in the Design section, click the drop-down. In the General section, select Variant Manager. In the Variant Manager, navigate to the variant that you want to use. Right-click and select Override using this Choice.

Reference Generator

The Reference Generator block sets the parameters that configure the maneuver and 3D simulation environment. By default, the block is set for the constant radius maneuver with the 3D simulation engine environment disabled.

Use the Maneuver parameter to specify the type of maneuver. You can specify the double lane change, swept sine, sine with dwell, and slowly increasing maneuvers.

If you select the Use maneuver-specific driver, initial position, and scene parameter, the reference application sets the driver, initial position, and scene for the maneuver that you specified.

For more information, see Reference Generator.

Driver Commands

The Driver Commands block implements the driver model that the reference application uses to generate acceleration, braking, gear, and steering commands. By default, if you select the Reference Generator block parameter Use maneuver-specific driver, initial position, and scene, the reference application selects the driver for the maneuver that you specified.

Vehicle Command Mode Setting	Implementation
Longitudinal Driver	Longitudinal Driver block — 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. Use the block to model the dynamic response of a driver or to generate the commands necessary to track a longitudinal drive cycle.
Predictive Driver	Predictive Driver block — Controller that generates normalized steering, acceleration, and braking commands to track longitudinal velocity and a lateral reference displacement. The normalized commands can vary between -1 to 1. The controller uses a single-track (bicycle) model for optimal single-point preview control.
Predictive Stanley Driver (default)	Predictive Driver block — Controller that generates normalized steering, acceleration, and braking commands to track longitudinal velocity and a lateral reference displacement. The normalized commands can vary between -1 to 1. For longitudinal control, the block uses a single-track (bicycle) model for optimal single-point preview control. For lateral control, the block uses a Stanley controller to minimize the position and angle error of the current path with respect to a reference path.
Open Loop	Implements an open-loop system so that you can configure the reference application for constant or signal-based steering, acceleration, braking, and gear command input.

Environment

The Environment subsystem generates the wind and ground forces. The reference application has these environment variants.

Environment	Variant	Description
Ground Feedback	3D Engine	Uses Simulation 3D Terrain Sensor block to implement a multipoint terrain sensor in 3D environment
	Constant (default)	Implements a constant friction value

Controllers

The Controllers subsystem generates engine torque, transmission gear, brake pressure, and differential pressure commands.

ECU

The ECU controller generates the engine torque command. The controller prevents over-revving the engine by limiting the engine torque command to the value specified by model workspace variable EngRevLim. By default, the value is 7000 rpm. If the differential torque command exceeds the limited engine torque command, the ECU sets the engine torque command to the commanded differential torque.

Transmission Control

The Transmission Controller subsystem generates the transmission gear command. The controller includes these variants.

Variant	Description
Driver - No Clutch	Open loop transmission control. The controller sets the gear command to the gear request.
PRNDL Controller (default)	Implements a transmission control module (TCM) that uses Stateflow® logic to generate the gear command based on the vehicle acceleration, brake command, wheel speed, engine speed, and gear request.
Paddles	Implements a paddle controller that uses the vehicle acceleration and engine speed to generate the gear command.
Transmission Controller	Implements a transmission control module (TCM) that uses Stateflow logic to generate the gear command based on the vehicle acceleration, wheel speed, and engine speed.

Brake Pressure Control

The Brake Controller subsystem implements a Brake Pressure Control subsystem to generate the brake pressure command. The Brake Pressure Control subsystem has these variants.

Variant	Description
Bang Bang ABS	Implements an anti-lock braking system (ABS) feedback controller that switches between two states to regulate wheel slip. The bang-bang control minimizes the error between the actual slip and desired slip. For the desired slip, the controller uses the slip value at which the mu-slip curve reaches a peak value. This desired slip value is optimal for minimum braking distance.
Open Loop (default)	Open loop brake control. The controller sets the brake pressure command to a reference brake pressure based on the brake command.
Five-State ABS	Five-state ABS control when you simulate the maneuver.1,2,3 The five-state ABS controller uses logic-switching based on wheel deceleration and vehicle acceleration to control the braking pressure at each wheel. Consider using five-state ABS control to prevent wheel lock-up, decrease braking distance, or maintain yaw stability during the maneuver. The default ABS parameters are set to work on roads that have a constant friction coefficient scaling factor of 0.6.

Active Differential Control

The Active Differential Control subsystem generates the differential pressure command. To calculate the command, the subsystem has these variants.

Variant	Description
Rear Diff Controller	Implements a controller that generates the differential pressure command based on the: Steer angle Vehicle pitch, yaw, and roll Brake command Wheel speed Gear Vehicle acceleration
No Control (default)	Does not implement a controller. Sets the differential pressure command to 0.

Passenger Vehicle

The Passenger Vehicle subsystem has an engine, controllers, and a vehicle body with four wheels. Specifically, the vehicle contains these subsystems.

Body, Suspension, Wheels Subsystem	Variant	Description
PassVeh7DOF	PassVeh7DOF	Vehicle with four wheels: Vehicle body has three degrees-of-freedom (DOFs) — Longitudinal, lateral, and yaw Each wheel has one DOF — Rolling Subsystem has variants for the tires, including: Fiala Magic Formula
PassVeh14DOF	PassVeh14DOF (default)	Vehicle with four wheels. Vehicle body has six DOFs — Longitudinal, lateral, vertical and pitch, yaw, and roll Each wheel has two DOFs — Vertical and rolling Subsystem has variants for the suspension, including: Double Wishbone Independent Mapped Front Kinematics and Compliance Independent Suspension Subsystem has variants for the tires, including: Fiala Magic Formula Dugoff

Engine Subsystem	Variant	Description
Mapped Engine	SiMappedEngine (default)	Mapped spark-ignition (SI) engine

Steering, Transmission, Driveline, and Brakes Subsystem		Variant	Description
Driveline Ideal Fixed Gear	Driveline model	All Wheel Drive	Configure the driveline for all-wheel, front-wheel, rear-wheel, or rear-wheel active differential drive and specify the type of torque coupling.
		Front Wheel Drive
		Rear Wheel Drive
		Rear Wheel Drive Active Differential (default)
	Transmission	Ideal (default)	Implements an ideal fixed gear transmission.
	Brake Hydraulics	NA	Implements the heuristic response of a hydraulic system when the controller applies a brake command to a cylinder. Includes front and rear wheel bias coefficients. The subsystem converts the applied pressure to a cylinder spool position. To generate the brake pressure, the spool applies a flow downstream to the cylinders.

Visualization

When you run the simulation, the Visualization subsystem provides driver, vehicle, and response information. The reference application logs vehicle signals during the maneuver, including steering, vehicle and engine speed, and lateral acceleration. You can use the Simulation Data Inspector to import the logged signals and examine the data.

Element	Description
Driver Commands	Driver commands: Handwheel angle Acceleration command Brake command
Vehicle Response	Vehicle response: Engine speed Vehicle speed Lateral acceleration
Steer, Velocity, Lat Accel Scope block	SteerAngle — Steering angle versus time <xdot> — Longitudinal vehicle velocity versus time <ay> — Lateral acceleration versus time
Vehicle XY Plotter	Vehicle longitudinal versus lateral distance
ISO 15037-1:2006 block	Display ISO standard measurement signals in the Simulation Data Inspector, including steering wheel angle and torque, longitudinal and lateral velocity, and sideslip angle

If you enable 3D visualization on the Reference Generator block 3D Engine tab by selecting Enabled, you can view the vehicle response in the Simulation 3D Viewer.

Note

Simulating models in the 3D visualization environment requires Simulink 3D Animation.

To smoothly change the camera views, use these keyboard shortcuts.

Keyboard Shortcut	Camera View
1	Back left	View Animated GIF
2	Back
3	Back right
4	Left
5	Internal
6	Right
7	Front left
8	Front
9	Front right
0	Overhead

For additional camera controls, use these keyboard shortcuts.

Keyboard Shortcut	Camera Control
Tab	Cycle the view between all vehicles in the scene.  View Animated GIF
Mouse scroll wheel	Control the camera distance from the vehicle.  View Animated GIF
L	Toggle a camera lag effect on or off. When you enable the lag effect, the camera view includes: Position lag, based on the vehicle translational acceleration Rotation lag, based on the vehicle rotational velocity This lag improves visualization of overall vehicle acceleration and rotation.  View Animated GIF
F	Toggle the free camera mode on or off. When you enable the free camera mode, you can use the mouse to change the pitch and yaw of the camera. This mode allows you to orbit the camera around the vehicle.  View Animated GIF

References

[1] Pasillas-Lépine, William. "Hybrid modeling and limit cycle analysis for a class of five-phase anti-lock brake algorithms." Vehicle System Dynamics 44, no. 2 (2006): 173-188.

[2] Gerard, Mathieu, William Pasillas-Lépine, Edwin De Vries, and Michel Verhaegen. "Improvements to a five-phase ABS algorithm for experimental validation." Vehicle System Dynamics 50, no. 10 (2012): 1585-1611.

[3] Bosch, R. "Bosch Automotive Handbook." 10th ed. Warrendale, PA: SAE International, 2018.

[4] J266_199601. Steady-State Directional Control Test Procedures for Passenger Cars and Light Trucks. Warrendale, PA: SAE International, 1996.

[5] ISO 4138:2012. Passenger cars — Steady-state circular driving behaviour — Open-loop test methods. Geneva: ISO, 2012.