Optimisation of lateral car dynamics taking into account parameter uncertainties

Simulation studies on an active all-wheel-steering car show that disturbance of vehicle parameters have high influence on lateral car dynamics. This motivates the need of robust design against such parameter uncertainties. A specific parametrisation is established combining deterministic, velocity-dependent steering control parameters with partly uncertain, velocity-independent vehicle parameters for simultaneous use in a numerical optimisation process. Model-based objectives are formulated and summarised in a multi-objective optimisation problem where especially the lateral steady-state behaviour is improved by an adaption strategy based on measurable uncertainties. The normally distributed uncertainties are generated by optimal Latin hypercube sampling and a response surface based strategy helps to cut down time consuming model evaluations which offers the possibility to use a genetic optimisation algorithm. Optimisation results are discussed in different criterion spaces and the achieved improvements confirm the validity of the proposed procedure.     

An easy procedure to determine Magic Formula parameters: a comparative study between the starting value optimization technique and the IMMa optimization algorithm

In 2004, a new searching algorithm for Magic Formula tyre model parameters was presented. Now, a summary of the results, for pure and combined slip, that this algorithm is able to achieve is presented. The Magic Formula tyre model needs a set of parameters to describe the tyre properties. The determination of these parameters is dealt with in this article. A new method, called IMMa Optimization Algorithm (IOA), based on genetic techniques, is used to determine these parameters. Here, we show the computational cost that has been used to obtain the optimum parameters of every characteristic of the Magic Formula tyre model, called Delft Tyre 96. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. Hence, to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters (null sensitivity to starting values). The search can be started with a randomly generated set of parameters between [0, 1]. Nowadays, MF-Tool, an application developed by TNO, uses an optimization technique to fit Magic Formula parameters from Matlab toolbox [van Oosten, J.J.M. and Bakker, E., 1993, {Determination of magic tyre model parameters}. Vehicle System Dynamics, 21, 19–29; van Oosten, J.J.M., Savi, C., Augustin, M., Bouhet, O., Sommer, J. and Colinot, J.P., 1999, {Time, tire, measurements, forces and moments, a new standard for steady state cornering tyre testing}. EAEC Conference, Barcelona, 30 June–2 July.]. We refer to that algorithm as the starting value optimization technique. The comparison between the optimization technique employed by TNO and the proposed IOA method is discussed in this article. In order to give a relative idea of adjustment accuracy, the sum-squared error and the mean-squared error, from the curves of the tyre model with the parameters optimized by both applications compared with test data are evaluated.     

Multiobjective optimisation of bogie suspension to boost speed on curves

To improve safety and maximum admissible speed on different operational scenarios, multiobjective optimisation of bogie suspension components of a one-car railway vehicle model is considered. The vehicle model has 50 degrees of freedom and is developed in multibody dynamics software SIMPACK. Track shift force, running stability, and risk of derailment are selected as safety objective functions. The improved maximum admissible speeds of the vehicle on curves are determined based on the track plane accelerations up to 1.5?m/s². To attenuate the number of design parameters for optimisation and improve the computational efficiency, a global sensitivity analysis is accomplished using the multiplicative dimensional reduction method (M-DRM). A multistep optimisation routine based on genetic algorithm (GA) and MATLAB/SIMPACK co-simulation is executed at three levels. The bogie conventional secondary and primary suspension components are chosen as the design parameters in the first two steps, respectively. In the last step semi-active suspension is in focus. The input electrical current to magnetorheological yaw dampers is optimised to guarantee an appropriate safety level. Semi-active controllers are also applied and the respective effects on bogie dynamics are explored. The safety Pareto optimised results are compared with those associated with in-service values. The global sensitivity analysis and multistep approach significantly reduced the number of design parameters and improved the computational efficiency of the optimisation. Furthermore, using the optimised values of design parameters give the possibility to run the vehicle up to 13% faster on curves while a satisfactory safety level is guaranteed. The results obtained can be used in Pareto optimisation and active bogie suspension design problems.     

Improved calibration of simulation models in railway dynamics: application of a parameter identification process to the multi-body model of a TGV train

This paper aims at estimating the vehicle suspension parameters of a TGV (Train à Grande Vitesse) train from measurement data. A better knowledge of these parameters is required for virtual certification or condition monitoring applications. The estimation of the parameter values is performed by minimising a misfit function describing the distance between the measured and the simulated vehicle response. Due to the unsteady excitation from the real track irregularities and nonlinear effects in the vehicle behaviour, the misfit function is defined in the time domain using a least squares estimation. Then an optimisation algorithm is applied in order to find the best parameter values within the defined constraints. The complexity of the solution surface with many local minima requires the use of global optimisation methods. The results show that the model can be improved by this approach providing a response of the simulation model closer to the measurements.     

A comparison of various algorithms to extract Magic Formula tyre model coefficients for vehicle dynamics simulations

Tyre models are a prerequisite for any vehicle dynamics simulation. Tyre models range from the simplest mathematical models that consider only the cornering stiffness to a complex set of formulae. Among all the steady-state tyre models that are in use today, the Magic Formula tyre model is unique and most popular. Though the Magic Formula tyre model is widely used, obtaining the model coefficients from either the experimental or the simulation data is not straightforward due to its nonlinear nature and the presence of a large number of coefficients. A common procedure used for this extraction is the least-squares minimisation that requires considerable experience for initial guesses. Various researchers have tried different algorithms, namely, gradient and Newton-based methods, differential evolution, artificial neural networks, etc. The issues involved in all these algorithms are setting bounds or constraints, sensitivity of the parameters, the features of the input data such as the number of points, noisy data, experimental procedure used such as slip angle sweep or tyre measurement (TIME) procedure, etc. The extracted Magic Formula coefficients are affected by these variants. This paper highlights the issues that are commonly encountered in obtaining these coefficients with different algorithms, namely, least-squares minimisation using trust region algorithms, Nelder–Mead simplex, pattern search, differential evolution, particle swarm optimisation, cuckoo search, etc. A key observation is that not all the algorithms give the same Magic Formula coefficients for a given data. The nature of the input data and the type of the algorithm decide the set of the Magic Formula tyre model coefficients.     

Real-time implementation of a traction control algorithm on a scaled roller rig

Traction control is a very important aspect in railway vehicle dynamics. Its optimisation allows improvement of the performance of a locomotive by working close to the limit of adhesion. On the other hand, in case the adhesion limit is surpassed, the wheels are subjected to heavy wear and there is also a big risk that vibrations in the traction occur. Similar considerations can be made in the case of braking. The development and optimisation of a traction/braking control algorithm is a complex activity, because it is usually performed on a real vehicle on the track, where many uncertainties are present due to environmental conditions and vehicle characteristics. This work shows the use of a scaled roller rig to develop and optimise a traction control algorithm on a single wheelset. Measurements performed on the wheelset are used to estimate the optimal adhesion forces by means of a wheel/rail contact algorithm executed in real time. This allows application of the optimal adhesion force.     

Identification of nonlinear systems using modified particle swarm optimisation: a hydraulic suspension system

This paper presents a novel modified particle swarm optimisation (MPSO) algorithm to identify nonlinear systems. The case of study is a hydraulic suspension system with a complicated nonlinear model. One of the main goals of system identification is to design a model-based controller such as a nonlinear controller using the feedback linearisation. Once the model is identified, the found parameters may be used to design or tune the controller. We introduce a novel mutation mechanism to enhance the global search ability and increase the convergence speed. The MPSO is used to find the optimum values of parameters by minimising the fitness function. The performance of MPSO is compared with genetic algorithm and alternative particle swarm optimisation algorithms in parameter identification. The presented comparisons confirm the superiority of MPSO algorithm in terms of the convergence speed and the accuracy without the premature convergence problem. Furthermore, MPSO is improved to detect any changes of system parameters, which can be used for designing an adaptive controller. Simulation results show the success of the proposed algorithm in tracking time-varying parameters.     

Wear/comfort Pareto optimisation of bogie suspension

Pareto optimisation of bogie suspension components is considered for a 50 degrees of freedom railway vehicle model to reduce wheel/rail contact wear and improve passenger ride comfort. Several operational scenarios including tracks with different curve radii ranging from very small radii up to straight tracks are considered for the analysis. In each case, the maximum admissible speed is applied to the vehicle. Design parameters are categorised into two levels and the wear/comfort Pareto optimisation is accordingly accomplished in a multistep manner to improve the computational efficiency. The genetic algorithm (GA) is employed to perform the multi-objective optimisation. Two suspension system configurations are considered, a symmetric and an asymmetric in which the primary or secondary suspension elements on the right- and left-hand sides of the vehicle are not the same. It is shown that the vehicle performance on curves can be significantly improved using the asymmetric suspension configuration. The Pareto-optimised values of the design parameters achieved here guarantee wear reduction and comfort improvement for railway vehicles and can also be utilised in developing the reference vehicle models for design of bogie active suspension systems.     

Magic Formula轮胎模型参数辨识的一种混合优化方法

Magic Formula(MF)轮胎模型能够准确描述轮胎的侧偏特性,广泛应用于车辆动力学的研究。由于MF轮胎模型参数多,且高度非线性,从大量的试验数据中准确辨识这些参数相当困难。提出一种基于遗传算法和数值优化算法的混合优化方法,采用由粗到精的辨识过程,先利用遗传算法得出近似最优解,再利用数值优化算法辨识出精确的参数。利用辨识出的参数计算轮胎的侧偏特性,计算结果与试验数据吻合良好,表明该方法是辨识MF轮胎模型参数的有效手段。     

Optimisation of active suspension control inputs for improved vehicle handling performance

Active suspension is commonly considered under the framework of vertical vehicle dynamics control aimed at improvements in ride comfort. This paper uses a collocation-type control variable optimisation tool to investigate to which extent the fully active suspension (FAS) application can be broaden to the task of vehicle handling/cornering control. The optimisation approach is firstly applied to solely FAS actuator configurations and three types of double lane-change manoeuvres. The obtained optimisation results are used to gain insights into different control mechanisms that are used by FAS to improve the handling performance in terms of path following error reduction. For the same manoeuvres the FAS performance is compared with the performance of different active steering and active differential actuators. The optimisation study is finally extended to combined FAS and active front- and/or rear-steering configurations to investigate if they can use their complementary control authorities (over the vertical and lateral vehicle dynamics, respectively) to further improve the handling performance.     

Non-fragile multi-objective static output feedback control of vehicle active suspension with time-delay

This paper presents an approach to design a delay-dependent non-fragile H_∞/L₂–L_∞ static output feedback (SOF) controller for active suspension with input time-delay. The control problem of quarter-car active suspension with actuator time-delay is formulated to a H_∞/L₂–L_∞ control problem. By employing a delay-dependent Lyapunov function, new existence conditions of delay-dependent non-fragile SOF H_∞ controller and L₂–L_∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities (BMIs). Then, a procedure based on linear matrix inequality optimisation and a hybrid algorithm of the particle swarm optimisation and differential evolution is used to solve an optimisation problem with BMI constraints. Design and simulation results of non-fragile H_∞/L₂–L_∞ controller for active suspension show that the designed controller not only can achieve the optimal performance and stability of the closed-loop system in spite of the existence of the actuator time-delay, but also has significantly improved the non-fragility characteristics over controller perturbations.     

Integration of vehicle yaw stabilisation and rollover prevention through nonlinear hierarchical control allocation

This work presents an approach to rollover prevention that takes advantage of the modular structure and optimisation properties of the control allocation paradigm. It eliminates the need for a stabilising roll controller by introducing rollover prevention as a constraint on the control allocation problem. The major advantage of this approach is the control authority margin that remains with a high-level controller even during interventions for rollover prevention. In this work, the high-level control is assigned to a yaw stabilising controller. It could be replaced by any other controller. The constraint for rollover prevention could be replaced by or extended to different control objectives. This work uses differential braking for actuation. The use of additional or different actuators is possible. The developed control algorithm is computationally efficient and suitable for low-cost automotive electronic control units. The predictive design of the rollover prevention constraint does not require any sensor equipment in addition to the yaw controller. The method is validated using an industrial multi-body vehicle simulation environment.     

Multi-objective geometrical optimization of full toroidal CVT

The objective of this research is geometrical and kinematical optimization of full-toroidal continuously variable transmission (CVT) in order to achieve high power transmission efficiency and low mass. At first, a dynamic analysis is performed for the system. A computer model is developed to simulate elastohydrodynamic (EHL) contact between disks and roller and consequently, calculate CVT efficiency. The validity of EHL model is investigated by comparing output of this model and experimental data. Geometrical parameters are obtained by means of Particle Swarm Optimization algorithm, while the optimization objective is to maximize CVT efficiency and minimize its mass. The algorithm is run for different values of selected input parameters that are oil temperature, roller tilting angle (speed ratio). Optimization results show that optimized geometrical parameters are approximately constant for various values of input parameters. Also, it is observed that, increasing values of oil temperature and roller tilting angle (in clockwise direction), will decrease power transmission efficiency. An average power transmission efficiency of 86.7% is achieved over a wide range of input parameters, using optimized geometry.     

Modelling minimum-time manoeuvering with global optimisation of local receding horizon control

In this paper, we explore the notion that a human driver uses a receding horizon model predictive control (MPC) scheme for minimum-time manoeuvering. However, MPC is an inherently sub-optimal control scheme because not all future information is incorporated into its finite preview horizon. In many practical applications, this sub-optimality is tolerated as the solution is sufficiently close to optimal. However, it is known that professional drivers have the ability to learn driving circuits and exploit its features to minimise their global manoeuvering time. In this paper, we will model their process with a cascaded optimisation structure. Therein, the inner-loop features a local MPC scheme tasked with finding the control inputs that achieve a blended objective of minimising time and maximising velocity in each preview horizon/distance. The outer loop of this cascaded structure computes the best set of weights for the two components of the local objectives in order to minimise the global manoeuvering time. The proposed cascaded optimisation and control approach is compared against a straight-forward fixed-cost time optimal MPC applied to minimum-time manoeuvering over two well-known race courses. The paper also includes an extended literature review and details of the computational formulation of the model approach.     

基于分子动力学的相变微胶囊与沥青相容性及增强机理研究

微胶囊法是相变材料（PCM）封装的一种重要手段，为了改善加入相变微胶囊后沥青路面的低温性能，采用分子动力学方法，对相变微胶囊的相变机制、与沥青共混后的相容性和抗拉强度等进行模拟分析。对沥青四组分（As，R，S，Ar）、三聚氰胺甲醛树脂（MF）、沥青四组分与MF共混体系、沥青四组分与石墨烯（CG）共混体系、MF与CG共混体系、沥青体系、沥青与MF共混体系、沥青与CG共混体系等17个分子体系分别进行了溶度参数和内聚能密度计算，分析了MF，CG与沥青四组分之间的相容性变化规律，评价了MF，CG对沥青四组分抗拉强度的影响。对以MF为壁材、正十四烷为芯材的3种不同微观结构PCM分子模型和以石墨烯复合三聚氰胺甲醛树脂（CGMF）为壁材、正十四烷为芯材的2种不同微观结构PCM分子模型进行了升温过程相变性能模拟研究，分析了壁材厚度、芯材体积大小对PCM相变性能的影响，并比较了不同种类壁材PCM的热效率。通过对CGMF为壁材的PCM降温过程的相变性能模拟研究，进一步分析了CG对PCM热效率的影响。研究结果表明：采用CGMF为壁材制备PCM，可以提升PCM的热效率，CGMFPCM2031的能量效率比MFPCM2026平均增加141.15%，在沥青体系中加入CGMF为壁材的PCM，可以提高沥青组分之间的相容性和抗拉强度，有利于增强沥青体系的低温抗裂性能。     

Optimisation of full-toroidal continuously variable transmission in conjunction with fixed ratio mechanism using particle swarm optimisation

The aim of this research is the optimisation of full-toroidal continuously variable transmission (CVT) in conjunction with the fixed ratio (FR) mechanism, while the optimisation objective is to minimise fuel consumption (FC) of the vehicle in the new European driving cycle. After the dynamic analysis of the power train, a computer model is developed to simulate contact between CVT elements and consequently calculate its efficiency. Then an algorithm is presented to calculate FC of the vehicle in the driving cycle. Then, an optimisation using particle swarm optimisation on the CVT geometry and FR mechanism (which is embedded between CVT and final drive) is carried out to minimise FC. It is found that by utilisation of the optimised CVT; FC will be about 11% and 8% lower, compared with the application of a five-speed manual transmission and conventional CVT, respectively. Finally, effects of the roller tilt angle and oil temperature on the FC are investigated.     

基于数据驱动的人机混驾多车协同控制算法

针对多车协同控制系统中，传统控制算法需要准确获取系统中与驾驶员驾驶行为相关的参数以及与车辆系统动力学相关参数等问题，提出基于数据驱动的自适应动态规划控制算法。以有人与无人驾驶车辆混行的多车协同控制系统为研究对象，通过分析系统的横纵向控制模型，推导出系统状态方程，采用递推数值方法在线逼近最优解，并通过对最优反馈控制矩阵进行优化求解，得到最优控制输入。该算法简化了系统的控制输入参数，仅仅利用V2X通信获得的车辆的前轮转角以及车辆期望的纵向加速度作为控制输入，即可实现无人驾驶车辆的优化控制。基于Carsim和Simulink进行联合仿真测试验证，结果表明，该算法控制参数简单、收敛速度快、控制精度高、适应性强，能够控制无人驾驶车辆在多车系统中保持期望的车速并且与前车保持期望的车间距，同时在任意曲率道路上行驶时与车道中心线之间的横向误差趋于0。      

Adaptive impedance control of a hydraulic suspension system using particle swarm optimisation

This paper presents a novel active control approach for a hydraulic suspension system subject to road disturbances. A novel impedance model is used as a model reference in a particular robust adaptive control which is applied for the first time to the hydraulic suspension system. A scheme is introduced for selecting the impedance parameters. The impedance model prescribes a desired behaviour of the active suspension system in a wide range of different road conditions. Moreover, performance of the control system is improved by applying a particle swarm optimisation algorithm for optimising control design parameters. Design of the control system consists of two interior loops. The inner loop is a force control of the hydraulic actuator, while the outer loop is a robust model reference adaptive control (MRAC). This type of MRAC has been applied for uncertain linear systems. As another novelty, despite nonlinearity of the hydraulic actuator, the suspension system and the force loop together are presented as an uncertain linear system to the MRAC. The proposed control method is simulated on a quarter-car model. Simulation results show effectiveness of the method.     

Optimal preview game theory approach to vehicle stability controller design

Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.