Optimal Braking Research Articles

Mathematical Simulations and Analyses of Proportional Electro-Hydraulic Brakes and Anti-Lock Braking Systems in Motorcycles

In the motorcycle industry, the safety of motorcycles operating at high speeds has received increasing attention. If a motorcycle is equipped with an anti-lock braking system (ABS), it can automatically adjust the size of the brake force to prevent the wheels from locking and achieve an optimal braking effect, ensuring operation stability. In an ABS, the brake force is controlled by an electro-hydraulic brake (EHB). The control valve inside the EHB was replaced with a proportional valve in this study, which differed from the general use of a solenoid valve. The purpose for this change was to precisely control the brake force and prevent hydraulic pressure oscillating in the piping. This study employed MATLAB/Simulink and block diagrams to establish a complete motorcycle ABS simulation model, including a proportional electro-hydraulic brake (PEHB), motorcycle motion, tire, and controller models. In an analysis of ABS simulation results, when traveling on different road surfaces, the PEHB could effectively reduce braking distance and solve the problem of hydraulic pressure oscillation during braking. The research demonstrated that this proportional pressure control valve can substitute the general solenoid valve in commercial braking systems. This can assist the ABS in achieving more precise slip control and improved motorcycle safety.

MPC-based Slip Control System for In-wheel-motor Drive EV

A new slip control system for electric vehicles (EVs) equipped with four in-wheel motors is presented in this paper to solve the problem of the risk of locking up of EV wheels on brakes. This controller is designed on the basis of a model predictive control (MPC) scheme. Thus, the proposed MPC slip controller guarantees the optimal braking torque on each wheel by individually controlling the slip ratio of each tire within the stable zone over a considerably shortened response time. The wheel slip control performance is improved given the shortened response of the regenerative braking system. Theoretical analyses and simulation show that the proposed controller delivers an effective antilock performance.

Mixed Slip-Deceleration PID Control of Aircraft Wheel Braking System

Aircraft antiskid braking system is designed to prevent the main wheels from locking and additionally seeking the optimal braking performance. Wheel deceleration is the traditional controlled target used in antiskid system, since it can be easily measured by angular velocity transducer. However the optimal target value is hard to find due to the changing of road-surface and aircraft velocity. An alternative controlled target is the wheel longitudinal slip which is more robustly controllable under all conditions. But the wheel slip cannot be measured directly, that will definitely result in control error from the poor estimated aircraft speed. In this work a PID control scheme based on mixed slip-deceleration input variable is proposed for aircraft antiskid braking system. This control algorithm is able to stabilize the wheel slip around any equilibrium point. Moreover, it inherits all the appealing characteristics of slip control, while overcoming its sensitivity to slip measurement errors.

Dynamic Optimization of Multibody System Using Multithread Calculations and a Modification of Variable Metric Method

The paper presents dynamic optimization methods used to calculate the optimal braking torques applied to wheels of an articulated vehicle in the lane following/changing maneuver in order to prevent a vehicle rollover. In the case of unforeseen obstacles, the nominal trajectory of the articulated vehicle has to be modified, in order to avoid collisions. Computing the objective function requires an integration of the equation of motions of the vehicle in each optimization step. Since it is rather time-consuming, a modification of the classical gradient method—variable metric method (VMM)—was proposed by implementing parallel computing on many cores of computing unit processors. Results of optimization calculations providing stable motion of a vehicle while performing a maneuver and a description and results of parallel computing are presented in this paper.

Vehicle optimal road departure prevention via model predictive control

This article addresses the problem of road departure prevention using integrated brake control. The scenario considered is when a high-speed vehicle leaves the highway on a curve and enters the shoulder or another lane, owing to excessive speed or a reduction in the friction of the road due to adverse weather conditions. In such a scenario, the vehicle speed is too high for the available tyre–road friction and road departure is inevitable; however, its effect can be minimized with an optimal braking strategy. To achieve online implementation, the task is formulated as a receding horizon optimization problem and solved in a linear model predictive control (MPC) framework. In this formulation, a nonlinear tyre model is adopted in order to work properly at the friction limits. The optimization results are close to those obtained previously using a particle model optimization, parabolic path reference (PPR), coupled to a control algorithm, the modified Hamiltonian algorithm (MHA), specifically designed to operate at the vehicle friction limits. This shows that the MPC formulation may be equally effective for vehicle control at the friction limits. The major difference here, compared with the earlier PPR/MHA control formulation, is that the proposed MPC strategy directly generates an optimal brake sequence, while PPR provides an optimal reference first, then MHA responds to the reference to give closed-loop actuator control. The presented MPC approach has the potential for use in future vehicle systems as part of the overall active safety control to improve overall vehicle agility and safety.

Выбор оптимальной тормозной силы на колесной паре с учетом неидеальности противоюзных устройств

В статье поставлена и решена задача о выборе оптимальной тормозной силы на колесной паре по критерию минимизации потерь из-за увеличения тормозных путей. Для постановки задачи оптимизации исследовано соотношение выигрыша от сокращения тормозных путей при хорошем сцеплении и проигрыша от их увеличения при плохом сцеплении из-за неидеальной работы противоюзных устройств. Проведенный анализ результатов моделирования показывает, что выбор ограничения сверху для коэффициента сцепления = 0,3, заложенного в государственном стандарте на электропоезда, достаточно обоснован. С другой стороны, из анализа коэффициентов эффективности использования сцепления современных противоюзных устройств следует, что минимальное значение величины на оси электропоезда при экстренном торможении разумно задавать не менее 0,2.

Slip Control of Electric Vehicle Based on Tire-Road Friction Coefficient Estimation

The real-time change of tire-road friction coefficient is one of the important factors that influence vehicle safety performance. Besides, the vehicle wheels’ locking up has become an important issue. In order to solve these problems, this paper comes up with a novel slip control of electric vehicle (EV) based on tire-road friction coefficient estimation. First and foremost, a novel method is proposed to estimate the tire-road friction coefficient, and then the reference slip ratio is determined based on the estimation results. Finally, with the reference slip ratio, a slip control based on model predictive control (MPC) is designed to prevent the vehicle wheels from locking up. In this regard, the proposed controller guarantees the optimal braking torque on each wheel by individually controlling the slip ratio of each tire within the stable zone. Theoretical analyses and simulation show that the proposed controller is effective for better braking performance.

High-speed trains subject to abrupt braking

ABSTRACTThe dynamic response of high-speed train subject to braking is investigated using the moving element method. Possible sliding of wheels over the rails is accounted for. The train is modelled as a 15-DOF system comprising of a car body, two bogies and four wheels interconnected by spring-damping units. The rail is modelled as a Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The interaction between the moving train and track-foundation is accounted for through the normal and tangential wheel–rail contact forces. The effects of braking torque, wheel–rail contact condition, initial train speed and severity of railhead roughness on the dynamic response of the high-speed train are investigated. For a given initial train speed and track irregularity, the study revealed that there is an optimal braking torque that would result in the smallest braking distance with no occurrence of wheel sliding, representing a good compromise between train instability and safety.

Analysis of torque transmitting behavior and wheel slip prevention control during regenerative braking for high speed EMU trains

The wheel-rail adhesion control for regenerative braking systems of high speed electric multiple unit trains is crucial to maintaining the stability, improving the adhesion utilization, and achieving deep energy recovery. There remain technical challenges mainly because of the nonlinear, uncertain, and varying features of wheel-rail contact conditions. This research analyzes the torque transmitting behavior during regenerative braking, and proposes a novel methodology to detect the wheel-rail adhesion stability. Then, applications to the wheel slip prevention during braking are investigated, and the optimal slip ratio control scheme is proposed, which is based on a novel optimal reference generation of the slip ratio and a robust sliding mode control. The proposed methodology achieves the optimal braking performance without the wheel-rail contact information. Numerical simulation results for uncertain slippery rails verify the effectiveness of the proposed methodology.

Biomechanical Energy Harvesting System With Optimal Cost-of-Harvesting Tracking Algorithm

Biomechanical energy harvesting can provide an attractive alternative for powering portable electronics, such as laptops and mobile communication devices. This unique type of energy is particularly advantageous to those who do not have direct access to the utility grid for extended periods of time. This paper presents an innovative biomechanical energy harvesting system based on the regenerative braking concept applied to the human natural motion. To determine the optimal braking profile, previous studies used an offline procedure based on constant external load to determine the optimal braking profile. The new concept of this paper continuously optimizes the maximum amount of energy that can be extracted during human motion while minimizing the subject's effort (metabolic rate). This is achieved by an energy harvesting system equipped with a programmable braking profile and a unique power extraction algorithm, which adaptively changes the braking profile to obtain the optimal ratio of energy to effort. These are facilitated by a brushless dc generator that is connected to boost converter. A digital current-programmed control of the boost converter enables an adaptive torque variation according to biofeedback (the measure of effort) and electrical feedback. This paper focuses on the human knee joint as the energy source, since most of this joint's work during level walking is negative (muscles are acting as brakes). Since this paper is preliminary and more oriented to the novel concept of adaptive profile and optimal power extraction, the operation of the energy harvester is demonstrated on a full-scale laboratory prototype based on a walking emulator. Initial experiments on human subjects have been initiated and are also reported. The results exhibit ultimate power extraction capabilities as well as adaptation to the walking pattern.

Design of the filling-rate controller for water medium retarders on the basis of coolant circulation

Water medium retarders are auxiliary braking devices which can reduce the vehicle speed by converting the mechanical energy of a driving vehicle to the total energy of the working fluid. These retarders can replace service brakes in non-emergency braking conditions. This study analysed the dynamic and thermodynamic characteristics of water medium retarders. An observer was designed to identify the optimal braking power of the water medium retarder under different braking conditions. The braking process involving the retarder can be divided into three stages. The controller was designed separately at each stage to control the braking torque of the water medium retarder according to braking requirements. A combined dynamic and thermodynamic vehicle model was also constructed with MATLAB/Simulink. The effects of the controller on the vehicle feedback control system were analysed. The results show that the controller equipped with the observer can effectively control the water medium retarder to satisfy the braking requirements of vehicles on the assumption that the coolant circulation is sufficiently radiated. Finally, an experiment was conducted to determine the performance of the controller and to validate the simulation results.

Model-based vehicle stability control with tyre force and instantaneous cornering stiffness estimation

A model-based vehicle stability controller is proposed in this paper. Since a model-based controller highly depends on the model accuracy, the lateral forces of the tyres and the instantaneous cornering stiffnesses of the predictive vehicle model are estimated online in order to deal with the model mismatch. The model-based controller calculates a desired yaw moment according to the prevailing errors in the the yaw rate and the side-slip angles of the vehicle. Then, by using linearization, an optimal braking force allocation algorithm is proposed to allocate the yaw moments to the target slip ratios of each wheel. Simulations are carried out with a full-vehicle model in CarSim software. The effectiveness and the robustness of the proposed control algorithm are evaluated through simulation cases of open-loop and closed-loop manoeuvres.

DETERMINATION OF BRAKING OPTIMAL MODE OF CONTROLLED CUT OF DESIGN GROUP

Purpose. The application of automation systems of breaking up process on the gravity hump is the efficiency improvement of their operation, absolute provision of trains breaking up safety demands, as well as improvement of hump staff working conditions. One of the main tasks of the indicated systems is the assurance of cuts reliable separation at all elements of their rolling route to the classification track. This task is a sophisticated optimization problem and has not received a final decision. Therefore, the task of determining the cuts braking mode is quite relevant. The purpose of this research is to find the optimal braking mode of control cut of design group. Methodology. In order to achieve the purpose is offered to use the direct search methods in the work, namely the Box complex method. This method does not require smoothness of the objective function, takes into account its limitations and does not require calculation of the function derivatives, and uses only its value. Findings. Using the Box method was developed iterative procedure for determining the control cut optimal braking mode of design group. The procedure maximizes the smallest controlled time interval in the group. To evaluate the effectiveness of designed procedure the series of simulation experiments of determining the control cut braking mode of design group was performed. The results confirmed the efficiency of the developed optimization procedure. Originality. The author formalized the task of optimizing control cut braking mode of design group, taking into account the cuts separation of design group at all elements (switches, retarders) during cuts rolling to the classification track. The problem of determining the optimal control cut braking mode of design group was solved. The developed braking mode ensures cuts reliable separation of the group not only at the switches but at the retarders of brake position. Practical value. The developed procedure can be successfully used to determine the optimal braking modes of cuts in automation systems of trains breaking up on the gravity humps.

Simulated and Experimental Comparisons of Slip and Torque Control Strategies for Regenerative Braking in Instances of Parametric Uncertainties

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270003/02.jpg"" width=""340"" />Slip efficiency map & control law</div> A three-wheel hybrid recreational vehicle was studied for the purpose of regenerative braking control. In order to optimize the amount of energy recovered from electrical braking, most of the existing literature presents optimal methods which consist in defining the optimal braking torque as a function of vehicle speed. The originality of the present study is to propose a new strategy based on the control of rear wheel slip. A simulator based on MATLAB/Simulink and validated with experimental measurements compared the two strategies and their sensitivities to variations in mass, slope and road conditions. Numerical simulations and experimental tests show that regenerative braking based on a slip controller was less affected by the majority of the parametric changes. Moreover, since the slip was limited, the longitudinal stability of the vehicle was thereby improved. It thus becomes possible to ensure optimal energy recovery and vehicle stability even in instances of parametric uncertainties.

Antilock Braking System Using Dynamic Speed Estimation

Antilock braking systems use slip to control braking, for which the velocity of the car and wheel speeds of the wheels are required. The wheel speeds can be measured directly but the velocity of the vehicle is difficult to measure. Although the wheel speed can be used to calculate the linear velocity of the vehicle using the tire characteristic function, it depends upon various environmental and time varying parameters. The dominant factor in the characteristic function is the road friction coefficient. Due to the difficulties in proper estimation of the road friction, most systems calculate the optimal values offline and apply them at different speeds using switching functions. By using the tire model and the optimal friction coefficients, the velocity of the vehicle is estimated and used for calculating the optimal braking force, resulting in inappropriate control of braking creating longer braking distances. In the method proposed in this paper, an estimator will be used to estimate the velocity, which is proved to be more accurate than calculated from the wheel speeds. The estimated velocity and the pitch angle will be used to schedule the braking forces in order to reduce the braking time. The braking time of the proposed system lies between the ideal braking time and the conventional reference wheel speed related braking time, indicating an improvement in reducing the braking distance.

Study on Optimal Dynamic Braking Resistor of Induction Motor

In order to discuss the transient process of induction motors dynamic braking,analysis the impact of the brake resistance on the time, and then choose the best resistance.In Matlab / Simulink environment,based on motor simulation model,by repeatedly adjusting the rotor resistor, their impact on motor speed during braking time can be visually observed.By using the least squares method in Matlab, each discrete points of the resistor and the corresponding braking time can be fitted into continuous curve, resulting in the optimum braking resistor under the shortest brake time. With the optimum load resistance in the rotor, the motor brake fastest and more stable without fluctuations,and provide the theoretical guidance for other motor control and engineering.

Longitudinal changes of cycling peak power in overweight and normal weight boys

Summary Objective The purpose of this study was to assign cycling peak power (CPP) in overweight boys, and to determine the longitudinal changes in CPP over the period of 10 to 14 years of age. Methods Eleven overweight and fourteen normal weight boys took part in three exercise tests, which were conducted every two years. The force–velocity test was used to measure CPP. The workload in the force–velocity test was assigned in relation to fat-free mass (FFM). Optimal braking force was defined as the workload used during the sprint in which the highest cycling power was reached. Results The CPP (absolute, relative to free-fat mass, and to body mass raised to the 0.67 exponent) was comparable in overweight and normal weight boys. The relative to body mass CPP was significantly lower in the overweight boys. During growth, systematical increase in the difference in CPP between overweight and normal weight boys was noted. The cycling peak power was noted in both groups at a similar relative to the FFM optimal braking force. Conclusion Longitudinal changes of CPP indicated the constant impairment of anaerobic performance in overweight boys. During growth, the gain of relative to body mass and to FFM cycling peak power is lower in overweight than in normal weight boys. Optimal braking force in pre-pubertal boys remained at a similar level but significantly increased at puberty. This finding should be taken into account for planning measurements of CPP in pre-pubertal and circumpubertal children.

Cooperative regenerative braking control for front-wheel-drive hybrid electric vehicle based on adaptive regenerative brake torque optimization using under-steer index

In this study, cooperative regenerative braking control of front-wheel-drive hybrid electric vehicle is proposed to recover optimal braking energy while guaranteeing the vehicle lateral stability. In front-wheel-drive hybrid electric vehicle, excessive regenerative braking for recuperation of the maximum braking energy can cause under-steer problem. This is due to the fact that the resultant lateral force on front tire saturates and starts to decrease. Therefore, cost function with constraints is newly defined to determine optimum distribution of brake torques including the regenerative brake torque for improving the braking energy recovery as well as the vehicle lateral stability. This cost function includes trade-off relation of two objectives. The physical meaning of first objective of cost function is to maximize the regenerative brake torque for improving the fuel economy and that of second objective is to increase the mechanical-friction brake torques at rear wheels rather than regenerative brake torque at front wheels for preventing front tire saturation. And weighting factor in cost function is also proposed as a function of under-steer index representing current state of the vehicle lateral motion in order to generalize the constrained optimization problem including both normal and severe cornering situation. For example, as the vehicle approaches its handling limits, adaptation of weighting factor is possible to prioritize front tire saturation over increasing the recuperation of braking energy for driver safety and vehicle lateral stability. Finally, computer simulation of closed loop driver-vehicle system based on Carsim™ performed to verify the effectiveness of adaptation method in proposed controller and the vehicle performance of the proposed controller in comparison with the conventional controller for only considering the vehicle lateral stability. Simulation results indicate that the proposed controller improved the performance of braking energy recovery as well as guaranteed the vehicle lateral stability similar to the conventional controller.

Relationship Modeling for the Psychological Impact of Night Vision on Braking Distance

The traditional braking model does not consider the impact of drivers' visual distance error, which leads to deviation in determining the distance between vehicles, and therefore effective braking model cannot be built. In order to solve this problem, the paper proposes a modeling method reflecting the relationship between psychology of night vision and braking distance to get the optimal braking reaction speed thus realizing intelligent emergency brake control. The experimental results show that the model takes the relationship between psychology of night vision and braking distance into consideration, increases the braking reaction speed of the drivers, and has high robustness.

Designing a set of efficient regenerative braking strategies with a performance index tool

The goal of this study is to design efficient regenerative braking strategies for a recreational three-wheel rear-wheel-drive hybrid electric vehicle. Current studies provide several optimal regenerative braking strategies, but no tool to obtain a set of acceptable strategies. A performance index tool is thus proposed and used to evaluate the efficiency of a given strategy. With this tool it is then possible to define a set of efficient regenerative strategies. The performance index is based on knowledge of a global efficiency map defined as the ratio of the incoming battery power to the extracted kinetic power. Two simulators of the vehicle are implemented in MATLAB/Simulink: one with a rear-wheel slip model and the other without slip considerations. They also include the longitudinal dynamics of the vehicle and the efficiency of the electrical drive from the electric motor to the battery. They were validated with experimental measurements of several accelerations and decelerations on a dry asphalt road from 0 km/h to 60 km/h. The simulated global efficiency map was also experimentally validated by regenerative braking measurements on a dry asphalt road from 50 km/h to 0 km/h. The simulated global efficiency map is used to design the optimal strategy (with and without wheel slip considerations). The performance map deduced from the global efficiency map was used to define the boundaries for the optimal strategy deviations and hence to limit the regenerated energy drop. Simulations show that there is a wide range of acceptable strategies from 0 km/h to 50 km/h on a dry asphalt road and hence give the driver the possibility of modulating the regenerative braking within a good energy recapture level. Finally, the design methodology presented with a simulated global efficiency map is also applicable with an experimental efficiency map which can be updated online.