An Adaptive Nonlinear Differentiable Friction Modeling for Tire-Road Friction Estimation

2015 ◽  
Author(s):  
Zhi-Jun Fu ◽  
Subhash Rakheja ◽  
Wen-Fang Xie ◽  
Xiao-Bin Ning ◽  
Wei-Dong Xie
Keyword(s):  
Parameter Estimation ◽  
Estimation Error ◽  
Friction Model ◽  
Least Square ◽  
Nonlinear Observer ◽  
Accurate Estimation ◽  
Vehicle Speed ◽  
Recursive Least Square ◽  
Friction Modeling ◽  
Road Friction

In this paper, a differentiable friction model is proposed to estimate the longitudinal tire-road friction force of vehicle systems. A novel adaptive nonlinear observer-based parameter estimation scheme has been developed to estimate the parameters of friction model, which requires the signals from the existing sensors signals such as wheel rotational speed and vehicle speed. Different from conventional gradient and recursive least square (RLS) methods, the filtered regression parameter estimation error is introduced in the novel adaptive laws, which can guarantee the observer error convergence to zero and the estimated parameter also convergence to their real value. The Lyapunov method is used to prove the stability of the proposed methods. The robustness of the developing method against bounded disturbances is also proved. Simulation results illustrate that the proposed method can realize relatively accurate estimation of the friction with variations in speed and road gradient.

scholarly journals Adaptive Nonlinear Tire-Road Friction Force Estimation for Vehicular Systems Based on a Novel Differentiable Friction Model

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Zhi-Jun Fu ◽  
Wei-Dong Xie ◽  
Xiao-Bin Ning
Keyword(s):  
Friction Force ◽  
Estimation Algorithm ◽  
Friction Model ◽  
Lyapunov Theory ◽  
Nonlinear Observer ◽  
Estimation Methods ◽  
Vehicle Speed ◽  
Force Estimation ◽  
Observer Error ◽  
Road Friction

A novel adaptive nonlinear observer-based parameter estimation scheme using a newly continuously differentiable friction model has been developed to estimate the tire-road friction force. The differentiable friction model is more flexible and suitable for online adaptive identification and control with the advantage of more explicit parameterizable form. Different from conventional estimation methods, the filtered regression estimation parameter is introduced in the novel adaptive laws, which can guarantee that both the observer error and parameter error exponentially converge to zero. Lyapunov theory has been used to prove the stability of the proposed methods. The effectiveness of the estimation algorithm is illustrated via a bus simulation model in the Trucksim software and simulation environment. The relatively accurate tire-road friction force was estimated just by the easily existing sensors signals wheel rotational speed and vehicle speed and the proposed method also displays strong robustness against bounded disturbances.

scholarly journals Path tracking of autonomous vehicle based on adaptive model predictive control

2019 ◽  
Vol 16 (5) ◽  
pp. 172988141988008 ◽  
Author(s):  
Fen Lin ◽  
Yuke Chen ◽  
Youqun Zhao ◽  
Shaobo Wang
Keyword(s):  
Friction Coefficient ◽  
Working Conditions ◽  
Autonomous Vehicle ◽  
Least Square ◽  
Vehicle Speed ◽  
Adaptive Model ◽  
Recursive Least Square ◽  
Tracking Accuracy ◽  
Road Friction ◽  
Road Friction Coefficient

In most cases, a vehicle works in a complex environment, with working conditions changing frequently. For most model predictive tracking controllers, however, the impacts of some important working conditions, such as speed and road conditions, are not concerned. In this regard, an adaptive model predictive controller is proposed, which improves tracking accuracy and stability compared with general model predictive controllers. First, the proposed controller utilizes the recursive least square algorithm to estimate tire cornering stiffness and road friction coefficient online. Then, the estimated tire cornering stiffness is used to update vehicle dynamics model and the estimated road friction coefficient is used to update the road adhesion constraint. Moreover, the control parameters consist of prediction horizon, control horizon, and sampling time, all of which are set according to vehicle speed. A co-simulation based on MATLAB/Simulink and CarSim is conducted. The simulation results illustrate that the proposed controller has a great adaptive ability to changing working conditions, especially to speed and road conditions.

scholarly journals State of Charge Estimation of Composite Energy Storage Systems with Supercapacitors and Lithium Batteries

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Kai Wang ◽  
Chunli Liu ◽  
Jianrui Sun ◽  
Kun Zhao ◽  
Licheng Wang ◽  
...  
Keyword(s):  
Energy Storage ◽  
Kalman Filtering ◽  
Lithium Batteries ◽  
Estimation Error ◽  
Storage System ◽  
Energy Storage System ◽  
Least Square ◽  
Recursive Least Square ◽  
Soc Estimation ◽  
Composite Energy

This paper studies the state of charge (SOC) estimation of supercapacitors and lithium batteries in the hybrid energy storage system of electric vehicles. According to the energy storage principle of the electric vehicle composite energy storage system, the circuit models of supercapacitors and lithium batteries were established, respectively, and the model parameters were identified online using the recursive least square (RLS) method and Kalman filtering (KF) algorithm. Then, the online estimation of SOC was completed based on the Kalman filtering algorithm and unscented Kalman filtering algorithm. Finally, the experimental platform for SOC estimation was built and Matlab was used for calculation and analysis. The experimental results showed that the SOC estimation results reached a high accuracy, and the variation range of estimation error was [−0.94%, 0.34%]. For lithium batteries, the recursive least square method is combined with the 2RC model to obtain the optimal result, and the estimation error is within the range of [−1.16%, 0.85%] in the case of comprehensive weighing accuracy and calculation amount. Moreover, the system has excellent robustness and high reliability.

Vehicle Trajectory Prediction Based on Road Recognition

2014 ◽  
Vol 599-601 ◽  
pp. 760-766
Author(s):  
Qing Bo Shao ◽  
Hsin Guan ◽  
Xin Jia
Keyword(s):  
Autonomous Vehicle ◽  
Recognition Algorithm ◽  
Least Square ◽  
Prediction Algorithm ◽  
Recursive Least Square ◽  
Trajectory Prediction ◽  
Dynamic Correction ◽  
The Road ◽  
Road Friction ◽  
Vehicle Trajectory

Predicting vehicle trajectory accurately is a crucial task for an autonomous vehicle. It is also necessary for many Advanced Driver Assistance System to predict trajectory of the ego-vehicle’s. In recent years, some vehicles trajectory prediction algorithm is mainly based on a simple Motion Model. This paper puts forward a method which combines road recognition and the hypothesis of steady preview and dynamic correction for trajectory prediction. In the road recognition algorithm, both methods of Kalman Filter (KF) and Recursive Least-Square (RLS) work well to estimate the road slope and road friction coefficient.

scholarly journals Application of Recursive Least Square Algorithm on Estimation of Vehicle Sideslip Angle and Road Friction

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Nenggen Ding ◽  
Saied Taheri
Keyword(s):  
Least Square ◽  
Recursive Least Square ◽  
Control Logic ◽  
Sideslip Angle ◽  
Active Steering ◽  
Direct Yaw Moment Control ◽  
Road Friction ◽  
Yaw Moment Control ◽  
Moment Control ◽  
Yaw Moment

A recursive least square (RLS) algorithm for estimation of vehicle sideslip angle and road friction coefficient is proposed. The algorithm uses the information from sensors onboard vehicle and control inputs from the control logic and is intended to provide the essential information for active safety systems such as active steering, direct yaw moment control, or their combination. Based on a simple two-degree-of-freedom (DOF) vehicle model, the algorithm minimizes the squared errors between estimated lateral acceleration and yaw acceleration of the vehicle and their measured values. The algorithm also utilizes available control inputs such as active steering angle and wheel brake torques. The proposed algorithm is evaluated using an 8-DOF full vehicle simulation model including all essential nonlinearities and an integrated active front steering and direct yaw moment control on dry and slippery roads.

scholarly journals Online Parameter Identification of Lithium-Ion Batteries Using a Novel Multiple Forgetting Factor Recursive Least Square Algorithm

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 3180 ◽  
Author(s):  
Bizhong Xia ◽  
Rui Huang ◽  
Zizhou Lao ◽  
Ruifeng Zhang ◽  
Yongzhi Lai ◽  
...  
Keyword(s):  
Parameter Identification ◽  
Lithium Ion ◽  
Least Square ◽  
Estimation Methods ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Recursive Least Square ◽  
Forgetting Factor ◽  
Temperature State

The model parameters of the lithium-ion battery are of great importance to model-based battery state estimation methods. The fact that parameters change in different rates with operation temperature, state of charge (SOC), state of health (SOH) and other factors calls for an online parameter identification algorithm that can track different dynamic characters of the parameters. In this paper, a novel multiple forgetting factor recursive least square (MFFRLS) algorithm was proposed. Forgetting factors were assigned to each parameter, allowing the algorithm to capture the different dynamics of the parameters. Particle swarm optimization (PSO) was utilized to determine the optimal forgetting factors. A state of the art SOC estimator, known as the unscented Kalman filter (UKF), was combined with the online parameter identification to create an accurate estimation of SOC. The effectiveness of the proposed method was verified through a driving cycle under constant temperature and three different driving cycles under varied temperature. The single forgetting factor recursive least square (SFFRLS)-UKF and UKF with fixed parameter were also tested for comparison. The proposed MFFRLS-UKF method obtained an accurate estimation of SOC especially when the battery was running in an environment of changing temperature.

An Adaptive Semiactive Control Algorithm for Vehicle Suspension Systems

2003 ◽  
Author(s):  
Xubin Song ◽  
Mehdi Ahmadian ◽  
Steve Southward
Keyword(s):  
Dynamic System ◽  
Adaptive Algorithm ◽  
Control Algorithm ◽  
Suspension System ◽  
Least Square ◽  
Vehicle Suspension ◽  
Semiactive Control ◽  
Vehicle Speed ◽  
Recursive Least Square ◽  
Line System

In general, a vehicle suspension system can be characterized as a nonlinear dynamic system that is subjected to unknown vibration sources, dependent on road roughness and vehicle speed. In this paper, we will present a nonlinear-model-based adaptive semiactive control algorithm developed for nonlinear systems exposed to broadband non-stationary random vibration sources that are assumed to be unknown or not measurable. If there exist unknown and/or varying parameters of the dynamic system such as mass and stiffness, then the adaptive algorithm can include a recursive least square (RLS) method for on-line system identification. Since the adaptive algorithm is developed for semiactive systems, stability is guaranteed based on the fact that the system is energy conservative. The convergence of the adaptive system, however is not guaranteed, and is investigated through a numerical approach for a specific case. The simulation results for a magneto-rheological seat suspension system with the suggested adaptive control are presented. The results are compared with low-damping and high-damping cases, as well æ other configurations of skyhook control, in order to show the extent of the procurement that can be expected with the suggested adaptive skyhook control provides a better broadbandk performance for the suspension, as compared to the other damping configurations that are included here.

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