Real-time dynamic simulation of vehicles with electronic stability control: Modeling and validation
Weidong Pan and Yiannis E. Papelis
National Advanced Driving Simulator, The University of Iowa,
2401 Oakdale Blvd., Iowa City, IA 52242-5003, USA
E-mail: ,
Abstract: This paper presents an approach to real-time dynamic simulation of vehicles with electronic stability control (ESC). The approach involves the integration of ESC software into the powertrain and brake models of the real-time vehicle dynamic simulation environment of the National Advanced Driving Simulator (NADS). The ultimate goal of this integration is the use of ESC equipped vehicles in simulator-based human factors experimentation assessing the effectiveness of ESC in avoiding loss of control accidents. The effectiveness of this approach in simulating ESC is demonstrated through the development and validation of two vehicle models, one for a 2003 Ford Expedition and the other for a 2002 Oldsmobile Intrigue, both equipped with ESC. Results show close correlation of vehicle behavior between the test data and the simulation data. In addition, the timing and magnitude of the simulated ESC activity correlate closely with the test results.
Keywords: active safety systems, driving simulator, electronic stability control, multibody vehicle dynamics, real-time vehicle dynamic simulation, vehicle modeling and validation
Reference to this paper should be made as follows: Pan, Weidong, and Papelis, Yiannis E. (xxxx) ‘Real-time dynamic simulation of vehicles with electronic stability control: Modeling and validation’, Int. J. of Vehicle Systems Modelling and Testing, Vol. X, No. Y, pp. 000-000.
Biographical notes: Weidong Pan is an associate research engineer at the National Advanced Driving Simulator. He earned his Ph.D. in mechanical engineering from the University of Iowa. His academic and research career has focused on flexible multibody dynamics, vehicle dynamics modeling and real-time simulation, and high-fidelity tire-soil and tool-soil interaction modeling and simulation technology. He has published in journals such as Computer Methods in Applied Mechanics and Engineering and Mechanics of Structures and Machines.
Dr. Yiannis Papelis isa research scientist and chief technical officer at the National Advanced Driving Simulator. He earned a Ph.D. in electrical and computer engineering from the University of Iowa and has been involved in driving simulation research for the past 15 years. Dr. Papelis hasinitiated and led numeroustransportation safety research projects focusing on in-vehicle devices and vehicle design. He has also consulted with industry on simulator development projects in the U.S., Europe, and Asia. His research interests includetransportation safety research, synthetic environment modeling, and simulation, and he has published in journals such as IEEE Computer and Transactions on Software Engineering, as well as in numerous conference proceedings.
1 Introduction
Vehicle design has evolved significantly over the last decade, with new safety features available on more and more vehicles. The latest addition is electronic stability control (ESC). During severe maneuvers, such as obstacle avoidance, the ESC senses impending loss of control and selectively brakes individual wheels and intervenes in the engine-management system to help the driver maintain control of the vehicle. Early statistical studies have shown that vehicles with ESC have fewer accidents than vehicles without; however, there has been no empirical study of ESC effectiveness with normal drivers.
Testing a new design or studying the effectiveness of an existing safety system like ESC in the real world is difficult because such systems are designed to prevent accidents and thus function only in severe and risky situations. High-fidelity driving simulation, where the virtual environment ensures maximum driver immersion without the risks associated with the driving situations necessary to exhibit the potential benefits of ESC, is an ideal alternative. However, properly testing ESC on a driving simulator requires the modeling and integration of ESC into the vehicle dynamics used in the real-time simulation.
Real-time vehicle dynamics simulation is a key enabling technology in a high-fidelity driving simulator. Given the driver control over the steering wheel, brake pedal, accelerator pedal, and gear shift, vehicle dynamics must predict all information required by the motion system (velocity and acceleration), visual system (position and orientation), and audio system (powertrain, tires), in real time. The development of the NADSdyna software a decade ago represents an early effort to achieve this capability (CCAD, 1995). The software, with incremental enhancements over the years, now runs at the National Advanced Driving Simulator at the University of Iowa.
There are several challenges when integrating an ESC model into real-time dynamics code. First, the ESC system is only activated during very aggressive maneuvers, at which point, there are severe nonlinearities in the vehicle suspension and tires. The vehicle dynamics model must be of adequate fidelity and utilize high-quality data. For example, the tire model must adequately simulate large slip angles and slip ratios. This problem was addressed by obtaining, in a test laboratory environment, tire data for large slip angles and slip ratios. This data was used to calibrate the simulation models, thus ensuring close match to real-world aggregate vehicle performance.
Secondly, the ESC system implementation uses complicated proprietary algorithms that are not easily reproduced. In this case, this problem was addressed by two ESC manufacturers willingness to provide a library containing the actual software that runs in the vehicle ESC controller to the University of Iowa. This software was integrated into the NADS vehicle model, thus ensuring identical behavior of the ESC system between the real world and the simulation.
The two ESC-equipped vehicles that were modeled are the 2003 Ford Expedition and the 2002 Oldsmobile Intrigue. The ultimate purpose of this modeling effort was to utilize these models in a simulator-based human factors study comparing loss of control with and without ESC, under typical loss-of-control driving situations (Papelis et al., 2004).
This paper is organized as follows. The approach to incorporating ESC software into NADSdyna is presented in Section 2. In Section 3, the development of the real-time model of a passenger car and the real-time model of a sports utility vehicle (SUV) is presented. In Section 4, effectiveness of the vehicle dynamics modeling approach is demonstrated by comparing simulation results and test data for several relevant maneuvers. The integration time step-size for all simulations presented in this paper is 1/960 second, and the sampling rate of ESC software is 960 Hz.
2 Incorporating ESC into powertrain and brake model
Before the advent of ESC, the most popular active driving safety systems were the Antilock Brake System (ABS) and the Traction Control System (TCS). The primary function of ABS is to control the brake slip of the wheels to within a narrow range around the slip value at which the longitudinal tire force peaks. The range is also where the tire lateral force response to slip angle is usually sufficient to keep the vehicle stable and steerable (Pacejka, 2002). ABS uses wheel speed sensors to compute wheel slip and achieves its control objectives by modulating wheel brake pressure.
The primary function of TCS is to control the drive slip of the driven wheels so that it is around the slip value at which the longitudinal tire force peaks. A TCS system uses the same wheel speed sensors as the ABS but calculates drive slip as input to the control algorithm that decides the appropriate brake pressure at driven wheels. To obtain optimal results, TCS sometimes intervenes with the engine management to reduce engine power. TCS prevents wheel spin during straight-line acceleration. It also prevents skidding when accelerating too much in a turn.
Both ABS and TCS monitor wheel speed and take action based on the value of computed wheel slip (brake slip and drive slip, respectively). ESC contains all the capabilities of ABS and TSC. In addition, it also monitors steering wheel angle, accelerator position (read from engine ECU), primer pump pressure in the brake system, vehicle lateral acceleration, and vehicle yaw rate (Robert Bosch GmbH, 1999a). Based on this additional information, the ESC estimates driver intention, computes vehicle behavior, and then develops a control strategy to steer and/or slow the vehicle through brake application and engine intervention during situations where the vehicle is about to go out of control.
For TCS/ESC to intervene with engine management, an electronic throttle control (ETC), also known as drive-by-wire, must replace the conventional mechanical linkage between the accelerator pedal and the internal combustion engine throttle valve (or diesel injection pump). Let be the accelerator pedal angle, be the commanded throttle by the TCS/ESC system, and be a Boolean variable with a 1 indicating the TCS/ESC command should be honored and a 0 indicating the command should be disregarded. An ETC model can be expressed using the following equation:
(1)
where is the actual throttle passed to engine model. Note that in a drive-by-wire system, control commands from TCS/ESC have higher priority than commands from the driver (Robert Bosch GmbH, 1999b).
2.1 Definition of the inputs and outputs of driving safety systems
Based on the above discussion, one can summarize that an ESC takes three groups of information--driver inputs; chassis and wheel translational and rotational velocity and acceleration (vehicle states); and powertrain states--and achieves its control objectives through braking and engine/powertrain intervention. Thus, a generic interface for describing ESC in the context of vehicle dynamic simulation can be defined as shown in Fig. 1. The interface is general because all driver, vehicle, and powertrain information is included as input and different types of brake and engine intervention are included as output. It is expected that the interface will cover current and future driving safety systems to a great extent. Details of the inputs and outputs are described in the following paragraphs. Information that is not used by today’s ESC systems is intentionally included, with the assumption that future sensor technology and vehicle control algorithms will lead to more advanced driving safety systems that can use the information.
The vector of driver inputs consists of accelerator pedal position , brake pedal force, steering wheel angle , steering wheel velocity, and current gear selection; i.e.,
(2)
The vector of wheel kinematic information consists of wheel spin velocity, and wheel spin acceleration , at previous time step; i.e.,
(3)
The vector of powertrain information consists of engine speed, engine output torque, the current gear in transmission gear box, transmission output torque, powertrain operation model (two-wheel drive, four-wheel drive, or all-wheel drive), differential operation mode (locked, unlocked, or controllable), transfer case operation mode, and transfer case torque split ratio; i.e.,
(4)
The vector of chassis kinematic information, assuming use of the SAE vehicle coordinate system, is
(5)
where are the roll, pitch, and yaw angles; are the roll, pitch, and yaw rates; are the roll, pitch, and yaw accelerations at the previous time step; are the longitudinal, lateral, and vertical velocities at the center of gravity; and are the longitudinal, lateral, and vertical acceleration at the center of gravity at the previous time step. These quantities can be computed from chassis location, orientation matrix, angular velocity, and CG location relative to the origin of the chassis body reference frame, all reported by multibody dynamics, using the following equations:
(6)
(7)
(8)
The contents of depends on the ESC software to be integrated. While some of these values are often hard-coded, for the purpose of simulation it is beneficial to have the ability to disable ESC to facilitate the necessary comparison. Thus, a Boolean flag is included in the vector and is defined as follows:
(9)
On the output side, the generic interface lists three quantities for engine-intervention;, , and. They are redundant, and only one is active for a specific ESC model. The redundancy is necessary to make the interface useful for integrating ESC software developed by different manufacturers. A flag,, must be included in the vector to indicate which channel is to be used by multibody vehicle dynamics. The flag is defined as follows:
(10)
Similarly, the brake intervention quantities, and, are redundant, and only one is active for a specific ESC model. Another flag, , must be defined in the vector, as follows:
(11)
2.2 Integration into vehicle dynamics
As shown in Section 2.1, ESC outputs are directed to powertrain (via engine intervention) and brake systems. In real-time vehicle dynamics formulation, a powertrain model consists of models for the engine, torque converter, automatic transmission, transfer case, differential, and final drive. The inputs to the engine model are throttle opening and current engine speed; the output is engine torque. The inputs to the torque converter are engine torque and the speed ratio of torque convert input shaft (which equals engine speed) to the transmission input shaft speed. Outputs are the load applied on the engine flywheel and the driving torque applied on the transmission input shaft. The primary function of all other components, including transmission, transfer case (if applicable), differential, and final drive, is to transmit the torque at the transmission input shaft to individual driven wheels through a sequence of gear pairs and shafts connected by universal joints or constant velocity joints. Depending on the value of , the ESC engine intervention is achieved in different ways involving different components of the powertrain model.
When , ESC directly computes the desired engine throttle engine. This control can be realized by simply feeding the desire throttle to the ETC model in Eq. 1; i.e.,
(12)