A receding horizon sliding control approach for electric powertrains with backlash and flexible half-shafts

Active control of electric powertrains is challenging, due to the fact that backlash and structural flexibility in transmission components can cause severe performance degradation or even instability of the control system. Furthermore, high impact forces in transmissions reduce driving comfort and possibly lead to damage of the mechanical elements in contact. In this paper, a nonlinear electric powertrain is modelled as a piecewise affine (PWA) system. The novel receding horizon sliding control (RHSC) idea is extended to constrained PWA systems and utilised to systematically address the active control problem for electric powertrains. Simulations are conducted in Matlab/Simulink in conjunction with the high fidelity Carsim software. RHSC shows superior jerk suppression and target wheel speed tracking performance as well as reduced computational cost over classical model predictive control (MPC). This indicates the newly proposed RHSC is an effective method to address the active control problem for electric powertrains.     

Modelling and model predictive control for a bicycle-rider system

This study proposes a bicycle-rider control model based on model predictive control (MPC). First, a bicycle-rider model with leaning motion of the rider’s upper body is developed. The initial simulation data of the bicycle rider are then used to identify the linear model of the system in state-space form for MPC design. Control characteristics of the proposed controller are assessed by simulating the roll-angle tracking control. In this riding task, the MPC uses steering and leaning torques as the control inputs to control the bicycle along a reference roll angle. The simulation results in different cases have demonstrated the applicability and performance of the MPC for bicycle-rider modelling.     

A nonlinear virtual rider for motorcycles

This work presents a virtual rider for the guidance of a nonlinear motorcycle model. The target motion is defined in terms of roll angle and speed. The virtual rider inputs are the steering torque, the rear-wheel driving/braking torque and front-wheel braking torque. The virtual rider capability is assessed by guiding the nonlinear motorcycle model in demanding manoeuvres with roll angles of 50° and longitudinal accelerations up to 0.8 g. Considerations on the effective preview distance used by the virtual rider are included.     

A theoretical justification of the sine with dwell manoeuvre

The sine with dwell (SWD) manoeuvre has received much attention within the context of vehicle stability testing. This manoeuvre is used in a test developed by the NHTSA, designed to certificate electronic stability control systems in light vehicles. The test is used in legislations as well as in consumer tests all over the globe. The SWD manoeuvre was designed using test vehicles on a test track and experimentally validated. The paper at hand uses optimal control theory to theoretically justify the use of the SWD manoeuvre to produce a severe lateral motion and over-steering based on steering input. It is shown that a manoeuvre similar to the SWD manoeuvre can be obtained from an optimal control problem using simple vehicle dynamics models. The optimal control method is further used to analyse the manoeuvre's robustness with respect to vehicle dimensions and tyre properties. It is shown that the manoeuvre is robust in dimensions, which theoretically motivates its application for various sizes of vehicles.     

基于非线性模型预测控制的车辆纵向队列协调控制

本文中针对基于分层控制结构的车辆队列上、下层控制缺少联系的问题,提出了车辆队列跟驰与个体车辆动力学稳定性协调控制的思路,其基本思想是在保证队列中个体车辆安全稳定行驶的同时,尽可能实现队列跟驰控制的目标。基于非线性模型预测控制(nonlinear model predictive control, NMPC)方法设计了车辆队列协调控制方案,设计了包括跟驰间距误差、跟驰速度误差以及车速与车轮圆周速度差3个子目标的优化目标函数,将队列跟驰与车辆动力学稳定性的协调控制转化为约束优化控制问题;基于序列二次规划(sequential quadratic programming, SQP)方法进行求解,得到车辆前、后轴的制动/驱动力矩来实现上层决策输出的期望跟驰加速度。基于由3车辆组成的非线性队列模型对控制方案进行了仿真分析,结果表明,所提出的基于NMPC的车辆队列协调控制策略可以在大范围操纵工况下,在保证车辆安全稳定行驶的基础上实现队列的跟驰控制。     

A nonlinear model predictive control formulation for obstacle avoidance in high-speed autonomous ground vehicles in unstructured environments

This paper presents a nonlinear model predictive control (MPC) formulation for obstacle avoidance in high-speed, large-size autono-mous ground vehicles (AGVs) with high centre of gravity (CoG) that operate in unstructured environments, such as military vehicles. The term ‘unstructured’ in this context denotes that there are no lanes or traffic rules to follow. Existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a new nonlinear MPC formulation is developed to navigate an AGV from its initial position to a target position at high-speed safely. First, a new cost function formulation is used that aims to find the shortest path to the target position, since no reference trajectory exists in unstructured environments. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms the obstacle-free region can assume due to the presence of multiple obstacles in the prediction horizon in an unstructured environment. Third, the no-wheel-lift-off condition, which is the major dynamical safety concern for high-speed, high-CoG AGVs, is ensured by limiting the steering angle within a range obtained offline using a 14 degrees-of-freedom vehicle dynamics model. Thus, a safe, high-speed navigation is enabled in an unstructured environment. Simulations of an AGV approaching multiple obstacles are provided to demonstrate the effectiveness of the algorithm.     

极限工况下主动前轮转向汽车稳定性控制

轮胎对汽车稳定性有重要影响,研究和利用轮胎的非线性特性有助于扩展汽车的稳定域。本文基于非线性轮胎模型,提出一种改进型线性时变模型预测控制(LTV-MPC)方法。该方法能扩展主动前轮转向汽车的稳定范围,提高极限工况下主动前轮转向汽车的稳定性。仿真结果表明,该方法比传统的LTV-MPC方法具有更好的稳定性控制效果。     

A combined-slip predictive control of vehicle stability with experimental verification

In this paper, a model predictive vehicle stability controller is designed based on a combined-slip LuGre tyre model. Variations in the lateral tyre forces due to changes in tyre slip ratios are considered in the prediction model of the controller. It is observed that the proposed combined-slip controller takes advantage of the more accurate tyre model and can adjust tyre slip ratios based on lateral forces of the front axle. This results in an interesting closed-loop response that challenges the notion of braking only the wheels on one side of the vehicle in differential braking. The performance of the proposed controller is evaluated in software simulations and is compared to a similar pure-slip controller. Furthermore, experimental tests are conducted on a rear-wheel drive electric Chevrolet Equinox equipped with differential brakes to evaluate the closed-loop response of the model predictive control controller.     

Non-linear modelling and control of semi-active suspensions with variable damping

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f–v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief–desire–intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.     

Utilisation of optimisation solutions to control active suspension for decreased braking distance

This work deals with how to utilise active suspension on individual vehicle wheels in order to improve the vehicle performance during straight-line braking. Through numerical optimisation, solutions have been found as regards how active suspension should be controlled and coordinated with friction brakes to shorten the braking distance. The results show that, for the studied vehicle, the braking distance can be shortened by more than 1?m when braking from 100?km/h. The applicability of these results is studied by investigating the approach for different vehicle speeds and actuator stroke limitations. It is shown that substantial improvements in the braking distance can also be found for lower velocities, and that the actuator strokes are an important parameter. To investigate the potential of implementing these findings in a real vehicle, a validated detailed vehicle model equipped with active struts is analysed. Simplified control laws, appropriate for on-board implementation and based on knowledge of the optimised solution, are proposed and evaluated. The results show that substantial improvements of the braking ability, and thus safety, can be made using this simplified approach. Particle model simulations have been made to explain the underlying physical mechanisms and limitations of the approach. These results provide valuable guidance on how active suspension can be used to achieve significant improvements in vehicle performance with reasonable complexity and energy consumption.     

Model predictive control with constraints for a nonlinear adaptive cruise control vehicle model in transition manoeuvres

A vehicle following control law, based on the model predictive control method, to perform transition manoeuvres (TMs) for a nonlinear adaptive cruise control (ACC) vehicle is presented in this paper. The TM controller ultimately establishes a steady-state following distance behind a preceding vehicle to avoid collision, keeping account of acceleration limits, safe distance, and state constraints. The vehicle dynamics model is for continuous-time domain and captures the real dynamics of the sub-vehicle models for steady-state and transient operations. The ACC vehicle can execute the TM successfully and achieves a steady-state in the presence of complex dynamics within the constraint boundaries.     

Lane-keeping benefits of practical rear axle steer

The classic two-degree-of-freedom yaw-plane or ‘bicycle’ vehicle model is augmented with two additional states to describe lane-keeping behaviour and further augmented with an additional control input to steer the rear axle. A simple driver model is hypothesised where the driver closes a loop on a projected lateral lane position. The driver can select the preview distance to compensate driver/vehicle dynamics, consistent with the ‘cross-over’ model found in the literature. A rear axle steer control law is found to be a function of the front axle steering input and vehicle speed that exhibits stability similar to a positive-real system, while at the same time improving the ability of the driver/vehicle system to track a complex curved lane and improving steady-state manoeuvrability. The theoretically derived control law bears similarity to practical embodiments allowing a deeper understanding of the functional value of steering a rear axle.     

Vehicle dynamics control of an electric-all-wheel-drive hybrid electric vehicle using tyre force optimisation and allocation

ABSTRACT

Hybrid Electric Vehicles (HEV) offer improved fuel efficiency compared to conventional vehicles at the expense of adding complexity and at times, reduced total power. As a result, HEV generally lack the dynamic performance that customers enjoy. To address this issue, the paper presents a HEV with electric All-Wheel-Drive capabilities via the use of torque vectoring electric rear axle drive (TVeRAD) to power the rear axle. The addition of TVeRAD to a front wheel drive HEV improves the total power output. To improve the handling characteristics of the vehicle, the TVeRAD provides torque vectoring at the rear axle. A bond graph model of the drivetrain is developed and used in co-simulation with CarSim. The paper proposes a control system which utilises control allocation to optimise tyre forces. The proposed control system is tested in the simulation environment with a high fidelity CarSim vehicle model. Simulation results show the control system is able to maximise vehicle longitudinal performance while avoiding tyre saturation on low mu surfaces. More importantly, the control system is able to track the desired yaw moment request on a high speed double lane change manoeuvre through the use of the TVeRAD to improve the handling characteristic of the vehicle.     

Wheel slip control with torque blending using linear and nonlinear model predictive control

Modern hybrid electric vehicles employ electric braking to recuperate energy during deceleration. However, currently anti-lock braking system (ABS) functionality is delivered solely by friction brakes. Hence regenerative braking is typically deactivated at a low deceleration threshold in case high slip develops at the wheels and ABS activation is required. If blending of friction and electric braking can be achieved during ABS events, there would be no need to impose conservative thresholds for deactivation of regenerative braking and the recuperation capacity of the vehicle would increase significantly. In addition, electric actuators are typically significantly faster responding and would deliver better control of wheel slip than friction brakes. In this work we present a control strategy for ABS on a fully electric vehicle with each wheel independently driven by an electric machine and friction brake independently applied at each wheel. In particular we develop linear and nonlinear model predictive control strategies for optimal performance and enforcement of critical control and state constraints. The capability for real-time implementation of these controllers is assessed and their performance is validated in high fidelity simulation.     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.     

A model of driver steering control incorporating the driver's sensing of steering torque

Steering feel, or steering torque feedback, is widely regarded as an important aspect of the handling quality of a vehicle. Despite this, there is little theoretical understanding of its role. This paper describes an initial attempt to model the role of steering torque feedback arising from lateral tyre forces. The path-following control of a nonlinear vehicle model is implemented using a time-varying model predictive controller. A series of Kalman filters are used to represent the driver's ability to generate estimates of the system states from noisy sensory measurements, including the steering torque. It is found that under constant road friction conditions, the steering torque feedback reduces path-following errors provided the friction is sufficiently high to prevent frequent saturation of the tyres. When the driver model is extended to allow identification of, and adaptation to, a varying friction condition, it is found that the steering torque assists in the accurate identification of the friction condition. The simulation results give insight into the role of steering torque feedback arising from lateral tyre forces. The paper concludes with recommendations for further work.     

Vehicle control synthesis using phase portraits of planar dynamics

ABSTRACT

Phase portraits provide control system designers strong graphical insight into nonlinear system dynamics. These plots readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and system inputs. This paper extends the usage of phase portraits in vehicle dynamics to control synthesis by illustrating the relationship between the boundaries of stable vehicle operation and the state derivative isoclines in the yaw rate–sideslip phase plane. Closed-loop phase portraits demonstrate the potential for augmenting a vehicle's open-loop dynamics through steering and braking. The paper concludes by applying phase portrait analysis to an envelope control algorithm for yaw stability and a sliding surface controller for stabilising a saddle point equilibrium in drifting.     

A new flatness-based control of lateral vehicle dynamics

This paper presents a new concept for vehicle dynamics control (VDC). The control of the longitudinal vehicle dynamics is not discussed, since we are assuming that it is much slower and weakly coupled to the lateral and yawing dynamics. The actuators are considered to be the traction and the braking torques of the individual wheels and only the standard sensors of the common VDC system are used. A modular interface to the subordinate wheel control system is provided by choosing the yaw torque as a fictitious control input. The VDC system is designed by means of a two degrees-of-freedom control scheme. It comprises a flatness-based feedforward part and a stabilising feedback part. The reference trajectory generation is introduced for the flat output which is given by the lateral velocity of the vehicle. Thus an advantageous kind of body side-slip angle control is provided with the standard VDC system hardware. Extensive simulation studies show excellent performance of the designed control concept.     

On model-based longitudinal feed-forward motion control for low velocities on known road profiles

ABSTRACT

So far, longitudinal motion control has focused on situations like highway driving, where disturbances of the road profile can be neglected. In this paper, we show how the Two Point Tire Model can be used to derive a novel feed-forward control law for a vehicle's longitudinal motion that considers the effects of the road profile and can complement existing control approaches. For this purpose, we recapitulate the basic model assumptions and equations and briefly discuss how it can be used on arbitrary road profiles. Two approaches for implementation in a real vehicle are presented. Comparisons of these approaches in simulation and to a human driver of an experimental vehicle show that the controller can deal with stepped obstacles of up to 14?cm in height. However, the control performance is essentially limited by the actuator delay and human drivers outperform the controller due to their ability of sensing subtle vehicle motions. The results indicate that the control performance can be further improved by using a preview on the necessary drive torque, which can be provided by the solution that we propose.