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Keywords = anti-lock braking system

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18 pages, 3477 KiB  
Article
Optimization of Active Disturbance Rejection Control System for Vehicle Servo Platform Based on Artificial Intelligence Algorithm
by Fei Yang, Xiaopeng Su and Xuemei Ren
Electronics 2025, 14(4), 752; https://doi.org/10.3390/electronics14040752 - 14 Feb 2025
Viewed by 348
Abstract
The rapid growth of automotive intelligence and automation technology has made it difficult for traditional in-vehicle servo systems to satisfy the demands of modern intelligent systems when facing complex problems such as external disturbances, nonlinearity, and parameter uncertainty. To improve the anti-interference ability [...] Read more.
The rapid growth of automotive intelligence and automation technology has made it difficult for traditional in-vehicle servo systems to satisfy the demands of modern intelligent systems when facing complex problems such as external disturbances, nonlinearity, and parameter uncertainty. To improve the anti-interference ability and control accuracy of the system, this study proposes a joint control method of electronic mechanical braking control combined with the anti-lock braking system. This method has developed a new type of actuator in the electronic mechanical brake control system and introduced a particle swarm optimization algorithm to optimize the parameters of the self-disturbance rejection control system. At the same time, it combines an adaptive inversion algorithm to optimize the anti-lock braking system. The results indicated that the speed variation of the developed actuator and the actual signal completely stopped at 1.9 s. During speed control and deceleration, the actuator could respond quickly and accurately to control commands as expected. On an asphalt pavement, the maximum slip rate error of the optimized control method was 0.0428, while the original control method was 0.0492. The optimized method reduced the maximum error by about 12.9%. On icy and snowy roads, the maximum error of the optimization method was 0.0632, significantly lower than the original method’s 0.1266. The optimization method could significantly reduce slip rate fluctuations under extreme road conditions. The proposed method can significantly improve the control performance of the vehicle-mounted servo platform, reduce the sensitivity of the system to external disturbances, and has high practical value. Full article
(This article belongs to the Section Electrical and Autonomous Vehicles)
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<p>EMB system structure and working mechanism.</p>
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<p>Composition of EMB actuator model constructed.</p>
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<p>ADRC structure diagram.</p>
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<p>PSO algorithm participating in optimizing ADRC controller process.</p>
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<p>Joint control structure.</p>
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<p>Optimize the control framework of ABS system.</p>
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<p>Joint control model architecture.</p>
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<p>Performance comparison of EMB actuators.</p>
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<p>Clamping force comparison.</p>
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<p>Effect of the EMB multi-stage control approach.</p>
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<p>Asphalt pavement test results.</p>
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<p>Ice pavement test results.</p>
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17 pages, 2850 KiB  
Review
Enhanced Anti-Lock Braking System Performance: A Comparative Study of Adaptive Terminal Sliding Mode Control Approaches
by Salma Khatory, Houcine Chafouk and El Mehdi Mellouli
Vehicles 2025, 7(1), 14; https://doi.org/10.3390/vehicles7010014 - 10 Feb 2025
Viewed by 460
Abstract
Sliding Mode Control (SMC) has gained significant attention due to its simplicity, robustness, and rapid response in ensuring system stability, particularly with the Lyapunov approach. Despite its advantages, SMC faces challenges such as chattering near equilibrium, sensitivity to parameter variations, and delayed convergence. [...] Read more.
Sliding Mode Control (SMC) has gained significant attention due to its simplicity, robustness, and rapid response in ensuring system stability, particularly with the Lyapunov approach. Despite its advantages, SMC faces challenges such as chattering near equilibrium, sensitivity to parameter variations, and delayed convergence. To address these issues, advanced techniques like Terminal Sliding Mode Control (TSMC) and Integral Terminal Sliding Mode Control (ITSMC) have been proposed. TSMC ensures finite-time convergence while mitigating chattering, while ITSMC further handles singularities and disturbances. Additionally, Adaptive Switching Control (ASC) based on Particle Swarm Optimization (PSO) is applied to achieve faster convergence, suppress chattering, and enhance system robustness. The adaptive control law, utilizing a Lyapunov-based approach, is employed to estimate and compensate for external disturbances, further improving system performance under uncertainties. Gain tuning, essential for optimizing system performance and reducing tracking errors, is achieved using the efficient Teaching–Learning-Based Optimization (TLBO) algorithm. This study applies TSMC, ITSMC, and ASC-based PSO to an Anti-Lock Braking System (ABS), aiming to enhance robustness, stability, and finite-time convergence while reducing chattering. Stability is analyzed through the Lyapunov theory, ensuring rigorous validation. MATLAB simulations demonstrate the effectiveness of the proposed methods in improving ABS performance, offering a valuable contribution to robust control techniques for systems operating under dynamic and uncertain conditions. Full article
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<p>TLBO algorithm structure.</p>
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<p>ABS system for quarter-car model.</p>
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<p>Wheel slip ratio tracking for different TSMC and ITSMC control strategies.</p>
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<p>External disturbances.</p>
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<p>Control law input for TSMC and ITSMC.</p>
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<p>Sliding surface for TSMC and ITSMC.</p>
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15 pages, 3936 KiB  
Article
Research on a Hierarchical Control Strategy for Anti-Lock Braking Systems Based on Active Disturbance Rejection Control (ADRC)
by Shi Luo, Bing Zhang, Jiantao Ma and Xinyue Zheng
Appl. Sci. 2025, 15(3), 1294; https://doi.org/10.3390/app15031294 - 27 Jan 2025
Viewed by 542
Abstract
To improve the slip rate control effect for different road conditions during emergency braking of wheel hub motor vehicles, as well as to address the problems of uncertainty and nonlinearity of the system when the electro-mechanical braking system is used as the actuator [...] Read more.
To improve the slip rate control effect for different road conditions during emergency braking of wheel hub motor vehicles, as well as to address the problems of uncertainty and nonlinearity of the system when the electro-mechanical braking system is used as the actuator of the ABS, a hierarchical control strategy of the anti-lock braking system (ABS) using active disturbance rejection control (ADRC) is proposed. Firstly, a vehicle dynamics model and an ABS model based on the EMB system are established; secondly, a speed observer based on the dilated state observer is used in the upper layer to design a pavement recognition algorithm, which recognizes the current pavement and outputs the optimal slip rate; then, an ABS controller based on the ADRC algorithm is designed for the lower layer to track the optimal slip rate. In order to verify the performance of the pavement recognition method and control strategy, vehicle simulation software is used to establish the model and simulation. The results show that the road surface recognition method can quickly and effectively recognize the road surface, and comparing the emergency braking control effects of PID and SMC under different road surface conditions, the ADRC strategy has better robustness and reliability, and improves the braking effect. Full article
(This article belongs to the Section Transportation and Future Mobility)
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<p>Braking force diagram.</p>
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<p>Flowchart of road surface identification method.</p>
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<p>Electromechanical brake actuator structure.</p>
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<p>Structure of ABS control strategy in ADRC.</p>
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<p>The framework of the ADRC-based ABS control system.</p>
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<p>Simulation results of pavement identification. (<b>a</b>) Speed observation on dry cement road. (<b>b</b>) Speed observation on snowy road. (<b>c</b>) Dry cement road recognition. (<b>d</b>) Snow road recognition.</p>
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<p>Braking performance on dry cement pavement. (<b>a</b>) Braking distance. (<b>b</b>) Vehicle speed. (<b>c</b>) Wheel speed. (<b>d</b>) Slip.</p>
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<p>Braking performance on snowy pavement. (<b>a</b>) Braking distance. (<b>b</b>) Vehicle speed. (<b>c</b>) Wheel speed. (<b>d</b>) Slip.</p>
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<p>Braking performance on variable pavement. (<b>a</b>) Braking distance. (<b>b</b>) Vehicle speed. (<b>c</b>) Wheel speed. (<b>d</b>) Slip.</p>
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13 pages, 1067 KiB  
Article
Novel Approach to Diagnose Safe Electrical Power Distribution
by Lars Braun, Minh Le, Jürgen Motz and Kai Peter Birke
Energies 2024, 17(22), 5685; https://doi.org/10.3390/en17225685 - 14 Nov 2024
Viewed by 521
Abstract
The integrity of the 12Vdc power distribution system on a vehicle is essential to guarantee continuous power supply to safety-relevant consumers. Safety-relevant consumers are critical loads, for example, electric power steering, braking systems with functionalities like Anti-Lock Braking or Electronic Stability [...] Read more.
The integrity of the 12Vdc power distribution system on a vehicle is essential to guarantee continuous power supply to safety-relevant consumers. Safety-relevant consumers are critical loads, for example, electric power steering, braking systems with functionalities like Anti-Lock Braking or Electronic Stability Control, and autonomous drive systems. To prevent insufficient power supply for safety-relevant consumers due to an increased wiring harness resistance, a novel diagnostic approach is developed to determine the condition of the power distribution, especially the electrical resistance. The influence of measurement errors and bus commutation on the estimation is investigated by using a simulation. By using the diagnostic, a resistance determination in the milliohm range with a standard deviation of σ=0.3mΩ can be achieved under realistic conditions. This ensures that failures in the wiring harness can be identified, avoiding cascading effects and minimizing recalls. Compared to the state of the art, redundancies, costs, and weight can be saved with the proposed diagnostic system based on electrical resistance estimation. Full article
(This article belongs to the Section F1: Electrical Power System)
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<p>Typical components of a single wiring harness connection of an electric power steering system.</p>
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<p>Measurement points in wiring harness topology to determine the wiring harness path resistance.</p>
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<p>Functional design of the diagnostic.</p>
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<p>Estimation of wiring harness path resistance <math display="inline"><semantics> <msub> <mi>R</mi> <mi>EPS</mi> </msub> </semantics></math>. (<b>a</b>) Input with exemplary measurement errors and delay. (<b>b</b>) Resistance estimation, delay ratio, and error ratio bias out of the diagnostic.</p>
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<p>Resulting <math display="inline"><semantics> <msub> <mi>R</mi> <mi>EPS</mi> </msub> </semantics></math> after 1000 runs of Monte Carlo simulation. The estimated resistance has a mean value of <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>6.1</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> <mo>Ω</mo> </mrow> </semantics></math> and a standard deviation of <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.3</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> <mo>Ω</mo> </mrow> </semantics></math>.</p>
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<p>Influence of different measurement errors at all measurement points on resistance estimation.</p>
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<p>Estimation of EPS wiring harness path resistance <math display="inline"><semantics> <msub> <mi>R</mi> <mi>EPS</mi> </msub> </semantics></math> in vehicle. (<b>a</b>) Measurement input from PDM and EPS. (<b>b</b>) Resistance estimation by using the diagnostic approach.</p>
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7 pages, 827 KiB  
Proceeding Paper
Enhancing Safety-Critical Brake System Testing with Vector SIL over Complex Vector HIL
by János Májer, Dénes Fodor, Péter Panyi, Félix Tivadar Nagy and Balázs István Németh
Eng. Proc. 2024, 79(1), 34; https://doi.org/10.3390/engproc2024079034 - 5 Nov 2024
Viewed by 428
Abstract
Advanced vehicle technologies that substitute or assist the driver are crucial and safety-critical elements, including independently acting electronic control units. A key element of vehicle road safety is its behavior on the road, influenced by various factors such as adhesion and physical forces. [...] Read more.
Advanced vehicle technologies that substitute or assist the driver are crucial and safety-critical elements, including independently acting electronic control units. A key element of vehicle road safety is its behavior on the road, influenced by various factors such as adhesion and physical forces. Self-activating brake systems, including related sensors and processing units, are vital for modern autonomous vehicles. The complexity of software in vehicle electronic control units (ECUs) has significantly increased, making traditional testing methods inadequate. This paper explores the use of Software-in-the-Loop (SIL) and Hardware-in-the-Loop (HIL) testing methods in an automated test environment to enhance software development and testing processes. It can be demonstrated that there is interoperability between the HIL and SIL systems using the same test case implementation in the Vector CANoe simulation environment. As a result, it can be demonstrated that in the case of a safety-critical function, such as an ABS (anti-lock brake system) control intervention, the ECU control software behaves the same in both the HIL and SIL simulation environments. Full article
(This article belongs to the Proceedings of The Sustainable Mobility and Transportation Symposium 2024)
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<p>Simplified representation of (<b>a</b>) Hardware-in-the-Loop and (<b>b</b>) Software-in-the-Loop simulation concepts.</p>
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<p>(<b>a</b>) ABS measurement results from HIL test and (<b>b</b>) SIL test.</p>
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<p>(<b>a</b>) ABS measurement results from HIL test and (<b>b</b>) SIL test.</p>
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21 pages, 11384 KiB  
Article
Hardware-in-the-Loop Simulations and Experiments of Anti-Lock Braking System for Cornering Motorcycles
by Jie-An Hsu, Chih-Keng Chen and Xiao-Dong Zhang
Electronics 2024, 13(21), 4171; https://doi.org/10.3390/electronics13214171 - 24 Oct 2024
Viewed by 861
Abstract
This study focuses on developing an advanced anti-lock braking system (ABS) for motorcycles, specifically targeting the challenges associated with cornering. Significant roll angles during motorcycle turns can often lead to slipping and the loss of control, increasing the risk of accidents. Existing ABSs [...] Read more.
This study focuses on developing an advanced anti-lock braking system (ABS) for motorcycles, specifically targeting the challenges associated with cornering. Significant roll angles during motorcycle turns can often lead to slipping and the loss of control, increasing the risk of accidents. Existing ABSs primarily address longitudinal dynamics and fail to provide optimal braking control during cornering. To address this gap, this study utilizes BikeSim and MATLAB/Simulink for simulations and experiments to design an ABS that adapts to varying roll angles by analyzing motorcycle dynamics during cornering. A tire model is constructed using the Magic Formula to examine both longitudinal and lateral characteristics under different conditions, which helps determine the current tire slip set-point. The controller, designed with a finite-state machine combined with bang-off-bang control, uses tire slip as the control variable. It adjusts the slip set-point based on changes in roll angle and sends control signals to the hydraulic actuator to regulate braking pressure, ensuring optimal braking performance without the loss of control. Finally, hardware-in-the-loop experiments are conducted, with real-time control commands sent to the hardware platform’s actuator via BikeSim RT. These experiments validate the effectiveness of the designed controller, significantly enhancing braking stability during cornering and improving safety for motorcycle riders. Full article
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<p>Vehicle coordinates and parameters.</p>
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<p>Bicycle model.</p>
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<p>The dynamics of a cornering motorcycle.</p>
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<p>Camber and roll angle relationship during motorcycle turning.</p>
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<p>Tire forces as function of slip ratio λ under various slip angles α. (<b>a</b>) longitudinal force; (<b>b</b>) lateral force.</p>
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<p>Tire friction ellipse with side-slip curves.</p>
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<p>A block diagram of the cornering ABS.</p>
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<p>Longitudinal friction coefficient as function of slip ratio for different road friction coefficients.</p>
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<p>Longitudinal force as function of slip ratio for various vertical forces at <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> .</p>
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<p>Slip set-point look-up table.</p>
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<p>Front and rear wheel slip set-points <math display="inline"><semantics> <mrow> <mover> <mi>λ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math> for different road surfaces.</p>
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<p>Controller flow chart.</p>
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<p>Finite-state machine in ABS controller.</p>
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<p>Bang-off-bang control flow chart.</p>
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<p>Motorcycle hardware-in-the-loop (HIL) braking experimental platform.</p>
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<p>Hardware-in-the-loop (HIL) braking experiment architecture diagram.</p>
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<p>(<b>a</b>) Host and (<b>b</b>) Target PC.</p>
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<p>(<b>a</b>) Kvaser PCIEcan 4xHS interface card and (<b>b</b>) National Instruments PCI-6024E data acquisition card.</p>
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<p>(<b>a</b>) Electro-hydraulic braking module and (<b>b</b>) JPT-131 pressure sensor.</p>
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<p>Comparison scenario of cornering braking with and without cornering ABS.</p>
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<p>Cornering braking experiment results of high-friction road (<math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.85</mn> </mrow> </semantics></math>).</p>
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<p>Cornering braking experiment results of low-friction road (<math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>).</p>
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<p>Comparison of cornering braking experiment with cornering ABS and without ABS control (on high-friction road).</p>
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<p>Comparison of cornering braking experiment with cornering ABS and fixed-slip ABS control (on high-friction road).</p>
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22 pages, 3449 KiB  
Article
fBrake, a Method to Simulate the Brake Efficiency of Laden Light Passenger Vehicles in PTIs While Measuring the Braking Forces of Their Unladen Configurations
by Víctor Romero-Gómez and José Luis San Román
Sensors 2024, 24(20), 6602; https://doi.org/10.3390/s24206602 - 13 Oct 2024
Viewed by 902
Abstract
This study introduces fBrake, a novel simulation method now designed for use in periodic technical inspections of M1 and N1 vehicle categories, addressing challenges posed by Directive 2014/45/EU. The directive mandates that braking efficiency must be measured relative to the vehicle’s [...] Read more.
This study introduces fBrake, a novel simulation method now designed for use in periodic technical inspections of M1 and N1 vehicle categories, addressing challenges posed by Directive 2014/45/EU. The directive mandates that braking efficiency must be measured relative to the vehicle’s maximum mass, which often results in underperformance during inspections due to vehicles typically being unladen. This discrepancy arises because the maximum braking forces are proportional to the vertical load on the wheels, causing empty vehicles to lock their wheels prematurely compared to laden ones. fBrake simulates the braking forces of unladen vehicles to reflect a laden state by employing an optimal brake-force distribution curve that aligns with the vehicle’s inherent braking behavior, whether through proportioning valves or through electronic brake distribution systems in anti-lock-braking-system-equipped vehicles. Our methodology, previously applied to heavy vehicles, involved extensive experimentation with a roller brake tester, comparing the actual braking performances of dozens of vehicles to those of their simulated counterparts using fBrake. The results demonstrate that fBrake reliably replicates the braking efficiency of laden vehicles, validating its use as an accurate and effective tool for braking system assessments in periodic inspections, irrespective of the vehicle’s load condition during the test. This approach ensures compliance with regulatory requirements while enhancing the reliability and safety of vehicle inspections. Full article
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<p>fBrake simulation workflow.</p>
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<p>Diagram of forces involved in a dynamic longitudinal test.</p>
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<p>Ideal brake-force distribution curves of a 2-axle vehicle. Units for both axes: daN.</p>
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<p>(<b>a</b>) Correlation between vehicle total height and <span class="html-italic">CG<sub>h</sub></span>; (<b>b</b>) Correlation between vehicle track width and <span class="html-italic">CG<sub>h</sub></span>; (<b>c</b>) Correlation between vehicle wheelbase and <span class="html-italic">CG<sub>h</sub></span>.</p>
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<p><span class="html-italic">CG<sub>h</sub></span> and pitch inertia measuring facility modeled in SOLIDWORKS. (<b>a</b>) Modeled facility without a dummy vehicle on it; (<b>b</b>) Modeled facility with a dummy vehicle on it; (<b>c</b>) Side blueprint of the assembly.</p>
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<p>Probability distribution representation of the bootstrapped data for both unladen and close-to-laden tests (X-axis data in N).</p>
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<p>(<b>a</b>) fBrake simulation results for Scenario 1; (<b>b</b>) fBrake simulation results for Scenario 2. X-axis shows <span class="html-italic">F<sub>xf</sub></span> (N). Y-axis shows <span class="html-italic">F<sub>xr</sub></span> (N).</p>
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<p>(<b>a</b>) GPS data logged by MATLAB Mobile and represented on the map. (<b>b</b>) GPS speed.</p>
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<p>(<b>a</b>) Total longitudinal force (N) vs. time (s); (<b>b</b>) Closeup view of the highest longitudinal forces.</p>
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<p>CarSim dimensions and inertial data window, prior to simulation.</p>
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<p>CarSim simulation animation.</p>
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<p>CarSim simulation results: Individual longitudinal braking forces (N) vs. time (s).</p>
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<p>Angle of oscillation (°) over time (s) for the vehicle–platform assembly.</p>
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<p>Relative angle of oscillation (°) over time (s) for the vehicle–platform assembly.</p>
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31 pages, 10592 KiB  
Article
Detecting Wheel Slip to Suppress Self-Excited Oscillations in Braking Mode
by Aleksander V. Klimov, Baurzhan K. Ospanbekov, Akop V. Antonyan, Viktor R. Anisimov, Egor A. Dvoeglazov, Danila A. Novogorodov, Andrey V. Keller, Sergey S. Shadrin, Daria A. Makarova, Vladimir S. Ershov and Yury M. Furletov
World Electr. Veh. J. 2024, 15(8), 340; https://doi.org/10.3390/wevj15080340 - 28 Jul 2024
Viewed by 776
Abstract
The wheels of decelerating vehicles in braking mode roll with increased slip, up to complete lock-up, which is a negative phenomenon. This is effectively managed by the anti-lock braking system (ABS). However, in the course of braking, especially before the system activation, self-excited [...] Read more.
The wheels of decelerating vehicles in braking mode roll with increased slip, up to complete lock-up, which is a negative phenomenon. This is effectively managed by the anti-lock braking system (ABS). However, in the course of braking, especially before the system activation, self-excited oscillatory processes with high amplitudes may occur, causing increased dynamic loads on the drive system. The paper studies the braking processes of a vehicle with an electromechanical individual traction drive in both electrodynamic regenerative and combined braking modes, utilizing the drive and the primary braking system. The theoretical framework is provided for identifying the self-excited oscillation onset conditions and developing a technique to detect wheel slips during braking to suppress these oscillations. To check the functionality of the wheel-slip observer in braking mode, the performance of the self-excited oscillation pulse suppression algorithm was studied in the MATLAB Simulink 2018b software package. The study results can be used to develop control systems equipped with the function of suppressing self-excited oscillations by vehicle motion. Full article
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<p>Drive scheme (<b>a</b>) and elastic-tire–solid-support-base interaction scheme (<b>b</b>): 1—mass M of the cushioned vehicle parts attributed to the wheel; 2—the wheel mass m; 3—rollers; 4—spring; 5—support base; 6—rolling wheel; 7—traction motor (TM); <span class="html-italic">c</span>—spring stiffness; <span class="html-italic">x</span><sub>1</sub>, <span class="html-italic">x</span><sub>2</sub>—longitudinal displacements of masses 1 and 2, respectively; <span class="html-italic">F</span>(<span class="html-italic">V</span><sub>2<span class="html-italic">sk</span></sub>)—friction force depending on the wheel slip speed <span class="html-italic">V</span><sub>2<span class="html-italic">sk</span></sub> relative to the support base; <span class="html-italic">ω</span><sub>K</sub>—angular wheel speed; <span class="html-italic">r</span><sub>K</sub>—distance from the wheel center to the support base; <span class="html-italic">M<sub>t</sub></span>—braking torque developed by the TM; <span class="html-italic">c<sub>m</sub></span>—angular ‘electromagnetic stiffness’ of the synchronous TM with permanent magnets; <span class="html-italic">J<sub>m</sub></span>—inertia moment of the motor’s rotating parts, referred to the rotor; <span class="html-italic">M</span><sub>K</sub>—braking torque developed by the wheel brake mechanism.</p>
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<p>Kistler RoaDyn strain gauge wheels.</p>
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<p>Window of programs for data analysis: (<b>a</b>) Vector CANoe; (<b>b</b>) MatLab Simulink.</p>
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<p>Changes in TM torques, wheel and rotor angular speeds, and TM currents over time during acceleration to 20 km/h and subsequent combined braking. Reprinted from Ref. [<a href="#B32-wevj-15-00340" class="html-bibr">32</a>].</p>
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<p>Plane design scheme of a two-axle vehicle: <span class="html-italic">l</span><sub>1</sub>, <span class="html-italic">l</span><sub>2</sub>—distances from the center of mass to the front and rear axles; <span class="html-italic">L</span>—wheelbase; <span class="html-italic">j<sub>x</sub></span>, <span class="html-italic">j<sub>y</sub></span>—projections of the linear acceleration of the center of mass on the vehicle body-related coordinate system axes; <span class="html-italic">ω<sub>z</sub></span>—angular speed of rotation around the vertical axis; Θ<sub>1</sub>—wheelbase steering angle; <span class="html-italic">V</span><sub>1</sub>, <span class="html-italic">V</span><sub>2</sub>—speed vectors of the front and rear axle centers; <span class="html-italic">V<sub>c</sub></span>—speed vector of the center of mass.</p>
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<p>Design scheme for determining the current linear speed of the vehicle’s wheel centers during braking.</p>
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<p>Relay function diagram of the slip and self-excited oscillation prevention system.</p>
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<p>Control algorithm (block diagram).</p>
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<p>Block diagram for implementing the self-oscillation suppression algorithm in MATLAB: Condition 1: abs (PD_SpeedRearAxleLeftWheel_mps) &gt; Vagv &amp;&amp; Vagv ~= 0; Condition 2: abs (PD_SpeedRearAxleRightWheel_mps) &gt; abs(Vavg) &amp;&amp; Vavg ~= 0.</p>
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<p>Implementation of the self-oscillation suppression algorithm in MATLAB Simulink: PD_SpeedFrontAxleLeftWheel_mps—signal about the value of the linear speed of the front left wheel, m/s; PD_SpeedFrontAxleRightWheel_mps—signal about the value of the linear speed of the front right wheel, m/s; PD_SpeedRearAxleLeftWheel_mps—signal about the value of the linear speed of the rear left wheel, m/s; PD_SpeedRearAxleRightWheel_mps—signal about the value of the linear speed of the rear right wheel, m/s.</p>
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<p>Simulation mathematical model of motion in MATLAB Simulink.</p>
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<p>Simulation mathematical model of the slip observer with the wheel oscillation suppression function in MATLAB Simulink.</p>
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<p>Trajectories of vehicle movement when braking and turning on ice and snow: (<b>a</b>) conventional ABS; (<b>b</b>) ABS with the self-excited oscillation suppression function.</p>
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<p>Realizations of the electric bus driving wheel angular speeds during braking with turning on ice with snow: (<b>a</b>) conventional ABS; (<b>b</b>) ABS with the self-excited oscillation suppression function (1 is left drive wheel, line 2 is right drive wheel).</p>
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<p>Realizations of the total braking torques on the electric bus driving wheels during braking with turning on ice with snow: (<b>a</b>) conventional ABS; (<b>b</b>) ABS with the self-excited oscillation suppression function (1—left drive wheel, 2—right drive wheel).</p>
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<p>Realization of angular velocities of the driving wheels of an electric bus when braking and turning on asphalt: (<b>a</b>) conventional ABS; (<b>b</b>) ABS with the self-excited oscillation suppression function.</p>
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<p>Realizations of the electric bus driving wheel angular speeds during braking with turning on asphalt: (<b>a</b>) conventional ABS; (<b>b</b>) ABS with the self-excited oscillation suppression function (1 is left drive wheel, 2 is right drive wheel).</p>
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<p>Realizations of the total braking torques on the electric bus driving wheels during braking with turning on asphalt: (<b>a</b>) conventional ABS; (<b>b</b>) ABS with the self-excited oscillation suppression function (1—left drive wheel, 2—right drive wheel).</p>
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<p>Support base (wet basalt).</p>
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<p>Torque on the wheel with the vibration suppression system deactivated, run No. 1: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel rotation speed with the auto-oscillation suppression system deactivated, run No. 1: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Torque on the wheel with the vibration suppression system deactivated, run No. 2: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel rotation speed with the vibration suppression system deactivated, run No. 1: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Torque on the wheel with the vibration suppression system deactivated, run No. 3: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel rotation speed with the vibration suppression system deactivated, run No. 3: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel torque with the vibration suppression system activated, run No. 1: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel rotation speed with the vibration suppression system activated, run No. 1: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel torque with the vibration suppression system activated, run No. 2: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel rotation speed with the vibration suppression system activated, run No. 2: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel torque with the vibration suppression system activated, run No. 3: (<b>a</b>) left; (<b>b</b>) right.</p>
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<p>Wheel rotation speed with the vibration suppression system activated, run No. 3: (<b>a</b>) left; (<b>b</b>) right.</p>
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30 pages, 31803 KiB  
Article
An NMPC-Based Integrated Longitudinal and Lateral Vehicle Stability Control Based on the Double-Layer Torque Distribution
by Xu Bai, Yinhang Wang, Mingchen Jia, Xinchen Tan, Liqing Zhou, Liang Chu and Di Zhao
Sensors 2024, 24(13), 4137; https://doi.org/10.3390/s24134137 - 26 Jun 2024
Viewed by 1487
Abstract
With the ongoing promotion and adoption of electric vehicles, intelligent and connected technologies have been continuously advancing. Electrical control systems implemented in electric vehicles have emerged as a critical research direction. Various drive-by-wire chassis systems, including drive-by-wire driving and braking systems and steer-by-wire [...] Read more.
With the ongoing promotion and adoption of electric vehicles, intelligent and connected technologies have been continuously advancing. Electrical control systems implemented in electric vehicles have emerged as a critical research direction. Various drive-by-wire chassis systems, including drive-by-wire driving and braking systems and steer-by-wire systems, are extensively employed in vehicles. Concurrently, unavoidable issues such as conflicting control system objectives and execution system interference emerge, positioning integrated chassis control as an effective solution to these challenges. This paper proposes a model predictive control-based longitudinal dynamics integrated chassis control system for pure electric commercial vehicles equipped with electro–mechanical brake (EMB) systems, centralized drive, and distributed braking. This system integrates acceleration slip regulation (ASR), a braking force distribution system, an anti-lock braking system (ABS), and a direct yaw moment control system (DYC). This paper first analyzes and models the key components of the vehicle. Then, based on model predictive control (MPC), it develops a controller model for integrated stability with double-layer torque distribution. The required driving and braking torque for each wheel are calculated according to the actual and desired motion states of the vehicle and applied to the corresponding actuators. Finally, the effectiveness of this strategy is verified through simulation results from Matlab/Simulink. The simulation shows that the braking deceleration of the braking condition is increased by 32% on average, and the braking distance is reduced by 15%. The driving condition can enter the smooth driving faster, and the time is reduced by 1.5 s~5 s. The lateral stability parameters are also very much improved compared with the uncontrolled vehicles. Full article
(This article belongs to the Special Issue Integrated Control and Sensing Technology for Electric Vehicles)
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<p>Automotive electronic control system architecture.</p>
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<p>EMB Response Characteristics.</p>
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<p>Integrated control system architecture.</p>
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<p>Friction coefficient as a function of slip ratio for different surfaces.</p>
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<p>High-adhesion braking test: vehicle speed and wheel speed. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>High-adhesion braking test: slip ratio. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>High-adhesion braking test: deceleration. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>High-adhesion braking test: braking torque. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 80 km/h): vehicle speed and wheel speed. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 80 km/h): slip ratio. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 80 km/h): deceleration. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 80 km/h): braking torque. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 60 km/h): vehicle speed and wheel speed. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 60 km/h): slip ratio. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 60 km/h): deceleration. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Low-adhesion braking test (initial speed: 60 km/h): braking torque. (<b>a</b>) Integrated control (<b>b</b>) Rule-based ABS strategy.</p>
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<p>High-adhesion driving test: vehicle speed and wheel speed.</p>
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<p>High-adhesion driving test: slip ratio.</p>
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<p>High-adhesion driving test: motor driving torque.</p>
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<p>Low-adhesion driving test: vehicle speed and wheel speed.</p>
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<p>Low-adhesion driving test: slip ratio.</p>
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<p>Low-adhesion driving test: motor driving torque.</p>
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<p>Steering wheel angle under double-lane change conditions high-adhesion and low-adhesion.</p>
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<p>High-adhesion double-lane change test: path-tracking.</p>
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<p>High-adhesion double-lane change test: yaw rate.</p>
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<p>High-adhesion double-lane change test: slip angle.</p>
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<p>High-adhesion double-lane change test: slip ratio.</p>
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<p>High-adhesion double-lane change test: braking torque.</p>
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<p>Low-adhesion double-lane change test: path-tracking.</p>
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<p>Low-adhesion double-lane change test: yaw rate.</p>
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<p>Low-adhesion double-lane change test: slip angle.</p>
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<p>Low-adhesion double-lane change test: slip ratio.</p>
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<p>Low-adhesion double-lane change test: braking torque.</p>
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27 pages, 7949 KiB  
Article
RBS and ABS Coordinated Control Strategy Based on Explicit Model Predictive Control
by Liang Chu, Jinwei Li, Zhiqi Guo, Zewei Jiang, Shibo Li, Weiming Du, Yilin Wang and Chong Guo
Sensors 2024, 24(10), 3076; https://doi.org/10.3390/s24103076 - 12 May 2024
Viewed by 1597
Abstract
During the braking process of electric vehicles, both the regenerative braking system (RBS) and anti-lock braking system (ABS) modulate the hydraulic braking force, leading to control conflict that impacts the effectiveness and real-time capability of coordinated control. Aiming to enhance the coordinated control [...] Read more.
During the braking process of electric vehicles, both the regenerative braking system (RBS) and anti-lock braking system (ABS) modulate the hydraulic braking force, leading to control conflict that impacts the effectiveness and real-time capability of coordinated control. Aiming to enhance the coordinated control effectiveness of RBS and ABS within the electro-hydraulic composite braking system, this paper proposes a coordinated control strategy based on explicit model predictive control (eMPC-CCS). Initially, a comprehensive braking control framework is established, combining offline adaptive control law generation, online optimized control law application, and state compensation to effectively coordinate braking force through the electro-hydraulic system. During offline processing, eMPC generates a real-time-oriented state feedback control law based on real-world micro trip segments, improving the adaptiveness of the braking strategy across different driving conditions. In the online implementation, the developed three-dimensional eMPC control laws, corresponding to current driving conditions, are invoked, thereby enhancing the potential for real-time braking strategy implementation. Moreover, the state error compensator is integrated into eMPC-CCS, yielding a state gain matrix that optimizes the vehicle braking status and ensures robustness across diverse braking conditions. Lastly, simulation evaluation and hardware-in-the-loop (HIL) testing manifest that the proposed eMPC-CCS effectively coordinates the regenerative and hydraulic braking systems, outperforming other CCSs in terms of braking energy recovery and real-time capability. Full article
(This article belongs to the Special Issue Integrated Control and Sensing Technology for Electric Vehicles)
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<p>The configuration of a four-wheel hub drive electric vehicle.</p>
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<p>Motor efficiency map.</p>
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<p>The illustration of the offline control law generation of the eMPC-CCS.</p>
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<p>The illustration of the online control law transplantation and state error compensation of the eMPC-CCS.</p>
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<p>The Generation of state feedback control laws in the basic empc controller.</p>
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<p>The illustration of the online implementation of the eMPC-CCS.</p>
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<p>The illustration of the three-dimensional eMPC control law generation method.</p>
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<p>The architecture of the improved eMPC.</p>
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<p>Simulation results of four coordinated control strategies for high-adhesion-coefficient road.</p>
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<p>Simulation results of four coordinated control strategies for low-adhesion-coefficient road.</p>
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<p>Comparison of four coordinated control strategies on high- and low-adhesion-coefficient roads.</p>
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<p>Simulation results of four coordinated control strategies for the joint road.</p>
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<p>Simulation results of four coordinated control strategies for the bisectional road.</p>
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<p>Comparison of four coordinated control strategies on the joint road and the bisectional road.</p>
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<p>HIL test platform.</p>
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<p>Slip ratio curves by different CCSs.</p>
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31 pages, 1531 KiB  
Article
A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy
by Yinhang Wang, Liqing Zhou, Liang Chu, Di Zhao, Zhiqi Guo and Zewei Jiang
Energies 2024, 17(9), 2032; https://doi.org/10.3390/en17092032 - 25 Apr 2024
Cited by 2 | Viewed by 1084
Abstract
Advancements in electric vehicle technology have promoted the development trend of smart and low-carbon environmental protection. The design and optimization of electric vehicle braking systems faces multiple challenges, including the reasonable allocation and control of braking torque to improve energy economy and braking [...] Read more.
Advancements in electric vehicle technology have promoted the development trend of smart and low-carbon environmental protection. The design and optimization of electric vehicle braking systems faces multiple challenges, including the reasonable allocation and control of braking torque to improve energy economy and braking performance. In this paper, a multi-source braking force system and its control strategy are proposed with the aim of enhancing braking strength, safety, and energy economy during the braking process. Firstly, an ENMPC (explicit nonlinear model predictive control)-based braking force control strategy is proposed to replace the traditional ABS strategy in order to improve braking strength and safety while providing a foundation for the participation of the drive motor in ABS (anti-lock braking system) regulation. Secondly, a grey wolf algorithm is used to rationally allocate mechanical and electrical braking forces, with power consumption as the fitness function, to obtain the optimal allocation method and provide potential for EMB (electro–mechanical brake) optimization. Finally, simulation tests verify that the proposed method can improve braking strength, safety, and energy economy for different road conditions, and compared to other methods, it shows good performance. Full article
(This article belongs to the Special Issue Energy Management Control of Hybrid Electric Vehicles)
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<p>Braking torque from different sources.</p>
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<p>Vehicle electronic control system architecture.</p>
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<p>EMB response characteristics.</p>
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<p>The motor’s external characteristics.</p>
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<p>Braking force control strategy process.</p>
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<p>The relationship between motor torque and speed.</p>
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<p>The relationship between deceleration and brake torque.</p>
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<p>The relationship between deceleration and brake torque for different adhesion coefficients.</p>
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<p>Nonlinear model predictive control process.</p>
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<p>Explicit process.</p>
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<p>Different parts divided by velocity and brake torque.</p>
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<p>The grey wolf algorithm process.</p>
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<p>Mass estimate results: (<b>a</b>) No load. (<b>b</b>) Full load.</p>
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<p>Adhesion coefficient estimates: (<b>a</b>) High adhesion. (<b>b</b>) Low adhesion.</p>
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<p>Vertical tire forces for no load: (<b>a</b>) Front axle. (<b>b</b>) Rear axle.</p>
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<p>Vertical tire forces for full load: (<b>a</b>) Front axle. (<b>b</b>) Rear axle.</p>
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<p>Vehicle and wheel speed for high adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Brake torque for high adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Slip ratio for high adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Deceleration for high adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Vehicle and wheel speed for low adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Brake torque for low adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Slip ratio for low adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Deceleration for low adhesion: (<b>a</b>) ENMPC strategy. (<b>b</b>) Rule-based ABS strategy.</p>
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<p>Brake torque from each sources: (<b>a</b>) Grey wolf strategy. (<b>b</b>) Rule-based distribution strategy.</p>
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<p>Energy obtained: (<b>a</b>) Grey wolf strategy. (<b>b</b>) Rule-based distribution strategy.</p>
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20 pages, 4370 KiB  
Article
Exploring the Benefits of a Simulator-Based Emergency Braking Exercise with Novice Teen Drivers
by Rakesh Gangadharaiah, Johnell O. Brooks, Lauren Mims, Patrick J. Rosopa, Mark Dempsey, Robert Cooper and Donnie Isley
Safety 2024, 10(1), 14; https://doi.org/10.3390/safety10010014 - 24 Jan 2024
Viewed by 2132
Abstract
This exploratory study investigated whether using the Pedals Emergency Stop© interactive driving simulator exercise improved the understanding and performance of emergency braking among novice teen drivers. Seventy-one high school driver education students (aged 15–19) participated. All of the teens completed the Pedals Emergency [...] Read more.
This exploratory study investigated whether using the Pedals Emergency Stop© interactive driving simulator exercise improved the understanding and performance of emergency braking among novice teen drivers. Seventy-one high school driver education students (aged 15–19) participated. All of the teens completed the Pedals Emergency Stop© interactive exercise driving simulator task and then an on-road ABS exercise in a driver’s education vehicle; there was no control group. Students’ ability to complete the simulator-based emergency braking task increased from an initial passing rate of only 18.3% to a maximum of 81.7% by the end of the simulation exercise. A positive trend was observed over successive simulator trials, with the linear effect explaining 51.1% of the variance in emergency stopping “pass” rates using the simulator task. In addition, participants who passed more trials during the Pedals Emergency Stop© simulator exercise were 12.3% more likely to fully activate the ABS during the on-road emergency stop activity using the driver’s education vehicle. Post-study surveys revealed that 95% of the participants improved their understanding of ABS as a result of the simulation-based training, and 98% felt there was a positive impact from the driving simulation exercise on their real-world emergency braking capabilities. Participants highly endorsed the Pedals Emergency Stop© exercise for ABS education and refresher training, with a rating of 4.7 out of 5. This study emphasizes the potential benefits of incorporating simulator-based exercises into driver education and training, with the long-term goal of promoting safe driving behaviors and outcomes. Full article
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<p>The study simulator with the haptic feedback device is in red. The yellow circle indicates how the haptic feedback was mounted to the pedal assembly.</p>
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<p>Pedals Static© Level 1, Level 2, and Level 3 target zone sizes, reproduced from Brooks et al. [<a href="#B26-safety-10-00014" class="html-bibr">26</a>]. The right, gas pedal uses a green target zone and indicator, while the left, brake pedal uses red.</p>
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<p>Pedals Chase© Level 2. The up and down arrow shows the target zone moves vertically on the pedal.</p>
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<p>Pedals Emergency Stop© dynamic gas target (<b>left</b>) and static brake target (<b>right</b>).</p>
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<p>Example illustrates the results obtained after the Pedals Emergency Stop© interactive exercise. In trials where participants did not achieve a pass, advice was provided.</p>
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<p>Participants’ performance in percentage to pass Pedals Emergency Stop© exercise.</p>
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<p>ABS on-road exercise performance. (<b>a</b>) The top figure shows the participants’ performance ratings of the ABS exercise. (<b>b</b>) The instructor’s justifications for rating the participants who did not pass ABS activation for both Run 1 and Run 2.</p>
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<p>ABS on-road exercise performance. (<b>a</b>) The top figure shows the participants’ performance ratings of the ABS exercise. (<b>b</b>) The instructor’s justifications for rating the participants who did not pass ABS activation for both Run 1 and Run 2.</p>
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14 pages, 2197 KiB  
Article
Voltage-Based Braking Controls for Electric Vehicles Considering Weather Condition and Road Slope
by Jonghoek Kim
Appl. Sci. 2023, 13(24), 13311; https://doi.org/10.3390/app132413311 - 16 Dec 2023
Viewed by 1348
Abstract
This article addresses the braking controls for an electric vehicle with DC motors such that the voltage in the motors is used for controlling the wheel angular velocity. Other papers on the anti-lock braking system (ABS) handled how to derive the braking torque [...] Read more.
This article addresses the braking controls for an electric vehicle with DC motors such that the voltage in the motors is used for controlling the wheel angular velocity. Other papers on the anti-lock braking system (ABS) handled how to derive the braking torque (or braking pressure) for controlling the wheel angular velocity. However, heavy or prolonged braking can cause brake fade or wear. According to EURO 7 regulations, brake fade or wear is not desirable, since the regulations refer to the reduction in particles emitted from brake pads. For avoiding heavy or prolonged braking, this paper does not use a brake unit, such as electro-mechanical brake units or hydraulic brake units, for vehicle stop. Instead, the motor voltage is used for controlling the wheel angular velocity. While a vehicle moves, the goal of this paper is to provide automatic braking controls in real time, so that the vehicle stops safely and smoothly without slippage before colliding with an obstacle. In practice, road conditions can change depending on weather conditions, such as rain or snow. Moreover, road slope can have an effect on the braking distance for the vehicle. Thus, this article introduces automatic braking controls, while considering both road slope and road conditions. This article is unique in presenting automatic braking controls for the smooth stop of electric vehicles with DC motors, while considering both road slope and road conditions. In addition, this article is unique in controlling the motor voltage for controlling the wheel angular velocity, while not requiring any brake units. Full article
(This article belongs to the Section Mechanical Engineering)
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<p>According to [<a href="#B19-applsci-13-13311" class="html-bibr">19</a>], <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> </semantics></math> in wet or dry road conditions is plotted.</p>
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<p>Algorithm 1 runs by considering the vehicle which moves on a flat dry road. (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time goes on; (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time elapses; (<b>c</b>) plots <span class="html-italic">w</span> and <math display="inline"><semantics> <msup> <mi>w</mi> <mi>o</mi> </msup> </semantics></math> as time goes on; and (<b>d</b>) plots the road slope measured via the IMU of the vehicle.</p>
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<p>Algorithm 1 runs considering the vehicle which moves on a flat dry road. We present the optimal case where <math display="inline"><semantics> <mrow> <mi>w</mi> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> <mo>=</mo> <msup> <mi>w</mi> <mi>o</mi> </msup> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </mrow> </semantics></math> for all time steps <span class="html-italic">k</span>. (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time goes on. (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time goes on. (<b>c</b>) plots <span class="html-italic">w</span> and <math display="inline"><semantics> <msup> <mi>w</mi> <mi>o</mi> </msup> </semantics></math> as time elapses. (<b>d</b>) plots the road slope measured via the IMU.</p>
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<p>Algorithm 1 runs considering the vehicle which moves on a flat dry road. We handle the case where <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> (V). (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time goes on. (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time elapses. (<b>c</b>) plots <span class="html-italic">w</span> as time goes on. (<b>d</b>) plots the road slope measured via the vehicle’s IMU.</p>
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<p>Algorithm 1 runs considering the vehicle which moves on a slanted dry road. (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time goes on. (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time goes on. (<b>c</b>) plots <span class="html-italic">w</span> and <math display="inline"><semantics> <msup> <mi>w</mi> <mi>o</mi> </msup> </semantics></math> as time elapses. (<b>d</b>) plots the road slope measured via the IMU.</p>
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<p>Algorithm 1 runs considering the vehicle which moves on a slanted dry road. We present the optimal case where <math display="inline"><semantics> <mrow> <mi>w</mi> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> <mo>=</mo> <msup> <mi>w</mi> <mi>o</mi> </msup> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </mrow> </semantics></math> for all time steps <span class="html-italic">k</span>. (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time goes on. (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time goes on. (<b>c</b>) plots <span class="html-italic">w</span> and <math display="inline"><semantics> <msup> <mi>w</mi> <mi>o</mi> </msup> </semantics></math> as time goes on. (<b>d</b>) plots the road slope measured via the IMU.</p>
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<p>Algorithm 1 runs considering the vehicle which moves on a slanted wet road. (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time elapses. (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time goes on. (<b>c</b>) plots <span class="html-italic">w</span> as time goes on. Compared to <a href="#applsci-13-13311-f005" class="html-fig">Figure 5</a>, the braking distance <span class="html-italic">d</span> increased due to the wet road condition. (<b>d</b>) plots the road slope measured via the IMU.</p>
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<p>Algorithm 1 runs considering the vehicle which moves on a slanted wet road. We present the optimal case where <math display="inline"><semantics> <mrow> <mi>w</mi> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> <mo>=</mo> <msup> <mi>w</mi> <mi>o</mi> </msup> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </mrow> </semantics></math> for all time steps <span class="html-italic">k</span>. (<b>a</b>) plots the vehicle speed <span class="html-italic">v</span> as time elapses. (<b>b</b>) plots the braking distance <span class="html-italic">d</span> as time goes on. (<b>c</b>) plots <span class="html-italic">w</span> and <math display="inline"><semantics> <msup> <mi>w</mi> <mi>o</mi> </msup> </semantics></math> as time goes on. (<b>d</b>) plots the road slope measured via the IMU.</p>
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27 pages, 5869 KiB  
Article
On the Benefits of Active Aerodynamics on Energy Recuperation in Hybrid and Fully Electric Vehicles
by Petar Georgiev, Giovanni De Filippis, Patrick Gruber and Aldo Sorniotti
Energies 2023, 16(15), 5843; https://doi.org/10.3390/en16155843 - 7 Aug 2023
Cited by 2 | Viewed by 2892
Abstract
In track-oriented road cars with electric powertrains, the ability to recuperate energy during track driving is significantly affected by the frequent interventions of the antilock braking system (ABS), which usually severely limits the regenerative torque level because of functional safety considerations. In high-performance [...] Read more.
In track-oriented road cars with electric powertrains, the ability to recuperate energy during track driving is significantly affected by the frequent interventions of the antilock braking system (ABS), which usually severely limits the regenerative torque level because of functional safety considerations. In high-performance vehicles, when controlling an active rear wing to maximize brake regeneration, it is unclear whether it is preferable to maximize drag by positioning the wing into its stall position, to maximize downforce, or to impose an intermediate aerodynamic setup. To maximize energy recuperation during braking from high speeds, this paper presents a novel integrated open-loop strategy to control: (i) the orientation of an active rear wing; (ii) the front-to-total brake force distribution; and (iii) the blending between regenerative and friction braking. For the case study wing and vehicle setup, the results show that the optimal wing positions for maximum regeneration and maximum deceleration coincide for most of the vehicle operating envelope. In fact, the wing position that maximizes drag by causing stall brings up to 37% increased energy recuperation over a passive wing during a braking maneuver from 300 km/h to 50 km/h by preventing the ABS intervention, despite achieving higher deceleration and a 2% shorter stopping distance. Furthermore, the maximum drag position also reduces the longitudinal tire slip power losses, which, for example, results in a 0.4% recuperated energy increase when braking from 300 km/h to 50 km/h in high tire–road friction conditions at a deceleration close to the limit of the vehicle with passive aerodynamics, i.e., without ABS interventions. Full article
(This article belongs to the Section E: Electric Vehicles)
Show Figures

Figure 1

Figure 1
<p>Schematic of the powertrain configuration of the case study HEV. The two front on-board EMs are mechanically independent, and each is connected to a gearbox; the rear motor is installed between the ICE and the rear transmission, including a gearbox and a differential.</p>
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<p>(<b>a</b>) Lift and (<b>b</b>) drag coefficients, <math display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>z</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>r</mi></mrow></msub></mrow></semantics></math> and <math display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>x</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>r</mi></mrow></msub></mrow></semantics></math>, of the rear wing as a function of the angle of attack, <math display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>r</mi></msub></mrow></semantics></math>.</p>
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<p>(<b>a</b>) Schematic of the test rig setup at the University of Surrey, including electric machines emulating the road load (Dyno motors); power supplies for the test piece and test rig inverters; inverters of the electric axle (eAxle); eAxle components, namely gearboxes (Gbx) and EMs, where the notations ‘fl’ and ‘fr’ refer to the front left and front right powertrains; and (<b>b</b>) test rig with test piece installation.</p>
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<p>(<b>a</b>) Torque loss (<math display="inline"><semantics><mrow><msub><mi>T</mi><mrow><mi>l</mi><mi>o</mi><mi>s</mi><mi>s</mi><mo>,</mo><mi>f</mi></mrow></msub></mrow></semantics></math>) map of each front gearbox, referred to at the EM shaft level, as a function of EM torque (<math display="inline"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow></semantics></math>) and speed (<math display="inline"><semantics><mrow><msub><mi>ω</mi><mi>m</mi></msub></mrow></semantics></math>); and (<b>b</b>) power loss map (<math display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>l</mi><mi>o</mi><mi>s</mi><mi>s</mi><mo>,</mo><mi>m</mi></mrow></msub></mrow></semantics></math>) of the individual inverter and EM.</p>
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<p>Schematic of the 3-DoF vehicle model with indications of the main variables and their sign conventions. The black arrows refer to accelerations, the red arrows refer to forces, and the orange arrows refer to moments.</p>
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<p>(<b>a</b>) Front and rear axle lift coefficients, <math display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>z</mi><mo>,</mo><mi>a</mi><mi>e</mi><mi>r</mi><mo>,</mo><mi>f</mi></mrow></msub></mrow></semantics></math> and <math display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>z</mi><mo>,</mo><mi>a</mi><mi>e</mi><mi>r</mi><mo>,</mo><mi>r</mi></mrow></msub></mrow></semantics></math>, as a function of <math display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>r</mi></msub></mrow></semantics></math>; and (<b>b</b>) drag coefficient at the vehicle level, <math display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>x</mi><mo>,</mo><mi>a</mi><mi>e</mi><mi>r</mi></mrow></msub></mrow></semantics></math>, as a function of <math display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>r</mi></msub></mrow></semantics></math>.</p>
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<p>Simplified block diagram of the time domain simulation architecture.</p>
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<p>Workflow diagram from the quasi-static optimizations to the time domain feedforward control block.</p>
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<p>Results of the Problem 1 optimization: maximum deceleration, <math display="inline"><semantics><mrow><msub><mi>a</mi><mrow><mi>x</mi><mo>,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></semantics></math>, as a function of <math display="inline"><semantics><mi>V</mi></semantics></math> for the Passive and Active configurations.</p>
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<p><math display="inline"><semantics><mrow><msub><mi>a</mi><mrow><mi>x</mi><mo>,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></semantics></math> as a function of <math display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>r</mi></msub></mrow></semantics></math> for different values of <math display="inline"><semantics><mi>μ</mi></semantics></math>, for (<b>a</b>) the airfoil used in the target vehicle of this study (see <a href="#energies-16-05843-f002" class="html-fig">Figure 2</a>) and (<b>b</b>) an airfoil similar to the one in [<a href="#B25-energies-16-05843" class="html-bibr">25</a>].</p>
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<p>(<b>a</b>) Contour plot of the percentage increase in regenerative power, <math display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>P</mi><mrow><mi>m</mi><mo>,</mo><mi>t</mi><mi>o</mi><mi>t</mi></mrow></msub></mrow></semantics></math>, as a function of <math display="inline"><semantics><mi>V</mi></semantics></math> and <math display="inline"><semantics><mrow><msub><mi>a</mi><mi>x</mi></msub></mrow></semantics></math>. The dashed and continuous lines are the maximum decelerations for Passive and Active. (<b>b</b>) Equivalent decelerations—see (41)–(44)—corresponding to the EM limits (‘Motor Limit’), regeneration functional safety limit (‘Safety Limit’), battery limit (‘Battery Limit’), actual front EM regenerative level (‘Front Actual’), and actual deceleration associated with the regenerative braking effect (‘Total Actual’), for <math display="inline"><semantics><mrow><msub><mi>a</mi><mi>x</mi></msub><mo>=</mo></mrow></semantics></math> −11 m/s<sup>2</sup>.</p>
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<p>Contour plots of (<b>a</b>) optimal front-to-total brake force distribution ratio, <math display="inline"><semantics><mrow><msub><mi>b</mi><mrow><mi>f</mi><mi>t</mi></mrow></msub></mrow></semantics></math> (expressed in percentage), for Active and (<b>b</b>) optimal <math display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>r</mi></msub></mrow></semantics></math> for Active.</p>
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<p>Contour plot of the ratio of the friction brake force to the total braking force, <math display="inline"><semantics><mrow><msub><mi>b</mi><mrow><mi>f</mi><mi>r</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></msub></mrow></semantics></math> (expressed in percentage), for Active.</p>
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<p>Spider chart showing the benefit (braking distance reduction, peak deceleration increase, and regenerated energy increase) of Active w.r.t. Passive for Tests 1–5.</p>
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<p>Comparison of the Passive and Active vehicle configurations along Test 5. Time profiles of (<b>a</b>) <math display="inline"><semantics><mrow><msub><mi>a</mi><mi>x</mi></msub></mrow></semantics></math>; and (<b>b</b>) total regenerative power, <math display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>r</mi><mi>e</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo>,</mo><mi>t</mi><mi>o</mi><mi>t</mi></mrow></msub></mrow></semantics></math>.</p>
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<p>Time profiles of the total braking force contributions, <math display="inline"><semantics><mrow><msub><mi>F</mi><mrow><mi>x</mi><mo>,</mo><mi>c</mi><mi>t</mi><mi>r</mi><mi>l</mi><mo>,</mo><mi>t</mi><mi>o</mi><mi>t</mi></mrow></msub></mrow></semantics></math>, from the EMs (‘Motors’), and the combination of EMs and friction brakes (‘Motors + Friction Brakes’), for (<b>a</b>) Passive and (<b>b</b>) Active.</p>
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<p>Time profiles of the front and rear slip ratios, <math display="inline"><semantics><mrow><msub><mi>σ</mi><mi>i</mi></msub></mrow></semantics></math>, for (<b>a</b>) the front (‘f’) and rear (‘r’) corners of Passive and (<b>b</b>) the front and rear corners of Active.</p>
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<p>Time profile of <math display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>r</mi></msub></mrow></semantics></math>.</p>
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<p>Time profiles of the equivalent regeneration force limits, <math display="inline"><semantics><mrow><msub><mi>F</mi><mrow><mi>x</mi><mo>,</mo><mi>h</mi><mi>s</mi><mo>,</mo><mi>c</mi><mi>t</mi><mi>r</mi><mi>l</mi><mo>,</mo><mi>l</mi><mi>i</mi><mi>m</mi></mrow></msub></mrow></semantics></math>, related to the EM torque characteristics (‘Motor’); the feedforward (‘FF’) output from the map resulting from the Problem 2 optimization; and the feedforward output with the feedback correction (‘FF + FB’) induced by the ABS intervention with variable <math display="inline"><semantics><mrow><msub><mi>a</mi><mrow><mi>x</mi><mo>,</mo><mi>e</mi><mi>q</mi><mo>,</mo><mi>l</mi><mi>i</mi><mi>m</mi><mo>,</mo><mi>s</mi><mi>a</mi><mi>f</mi></mrow></msub></mrow></semantics></math>.</p>
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17 pages, 6121 KiB  
Article
Design and Verification of Offline Robust Model Predictive Controller for Wheel Slip Control in ABS Brakes
by Jaffar Seyyed Esmaeili, Abdullah Başçi and Arash Farnam
Machines 2023, 11(8), 803; https://doi.org/10.3390/machines11080803 - 4 Aug 2023
Cited by 3 | Viewed by 1767
Abstract
Wheel slip control is a critical aspect of vehicle safety systems, notably the antilock braking system (ABS). Designing a robust controller for the ABS faces the challenge of accommodating its strong nonlinear behavior across varying road conditions and parameters. To ensure optimal performance [...] Read more.
Wheel slip control is a critical aspect of vehicle safety systems, notably the antilock braking system (ABS). Designing a robust controller for the ABS faces the challenge of accommodating its strong nonlinear behavior across varying road conditions and parameters. To ensure optimal performance during braking and prevent skidding or lock-up, the ideal wheel slip value can be determined from the peak of the tire–road friction curve and maintained throughout the braking process. Among various control approaches, model predictive control (MPC) demonstrates superior performance and robustness. However, online MPC implementation encounters significant computational burdens and real-time limitations, particularly when dealing with larger problem sizes. To address these issues, this study introduces an offline robust model predictive control (RMPC) methodology. The proposed approach is based on the robust asymptotically stable invariant ellipsoid methodology, which employs linear matrix inequalities (LMIs) to calculate a collection of invariant state feedback laws associated with a sequence of nested invariant stable ellipsoids. Simulation results indicate a significant reduction in computational burden with the offline RMPC approach compared to online implementation, while effectively tracking the desired wheel slip reference values and system constraints. Moreover, the offline RMPC design aligns well with the online MPC design and verifies its effectiveness in practice. Full article
(This article belongs to the Special Issue Adaptive and Optimal Control of Vehicles)
Show Figures

Figure 1

Figure 1
<p>Single-wheel model.</p>
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<p>Burckhardt tire–road friction curves for different road conditions.</p>
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<p>Block diagram of online model predictive control system.</p>
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<p>The overall structure of the proposed offline robust model predictive control system.</p>
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<p>Nested ellipsoids defined by <math display="inline"><semantics><mrow><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></mrow></semantics></math> for 10 state sequences of dry road.</p>
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<p>Closed-loop response of the linear system: dashed lines with (+), online MPC; solid lines, offline RMPC. (<b>a</b>) State response of the ABS; (<b>b</b>) control input signal.</p>
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<p>Closed-loop response of the nonlinear ABS controller for a dry asphalt road. (<b>a</b>) Wheel slip: dashed line, online RMPC; solid line, offline RMPC. (<b>b</b>) Offline estimation error. (<b>c</b>) Control input signal (Nm). (<b>d</b>) Vehicle and wheel velocities.</p>
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<p>Comparison of CPU times for the computational burden of online and offline RMPC controllers for ABS in dry asphalt road conditions using a box–whisker plot.</p>
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<p>Nested ellipsoids defined by <math display="inline"><semantics><mrow><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></mrow></semantics></math> for seven state sequences of wet road.</p>
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<p>Closed-loop response of the nonlinear ABS controller for wet asphalt road. (<b>a</b>) Wheel slip: dashed line, online RMPC; solid line, offline RMPC. (<b>b</b>) Offline estimation error. (<b>c</b>) Control input signal (Nm). (<b>d</b>) Vehicle and wheel velocities.</p>
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<p>Comparison of CPU times for the computational burden of online and offline RMPC controllers for ABS in wet asphalt road conditions using a box–whisker plot.</p>
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<p>Nested ellipsoids defined by <math display="inline"><semantics><mrow><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></mrow></semantics></math> for seven state sequences of a snowy road.</p>
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<p>Closed-loop response of the nonlinear ABS controller for a snowy asphalt road. (<b>a</b>) Wheel slip: dashed line, online RMPC; solid line offline, RMPC. (<b>b</b>) Offline estimation error. (<b>c</b>) Control input signal (Nm). (<b>d</b>) Vehicle and wheel velocities.</p>
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<p>Comparison of CPU times for the computational burden of online and offline RMPC controllers for ABS in snowy asphalt road conditions using a box–whisker plot.</p>
Full article ">
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