Magic Formula Research Articles

A Computationally Efficient Path-Following Control Strategy of Autonomous Electric Vehicles With Yaw Motion Stabilization

This article proposes a computationally efficient path-following control strategy of autonomous electric vehicles (AEVs) with yaw motion stabilization. First, the nonlinear control-oriented model, including path-following model, single-track vehicle model, and magic formula tire model, is constructed. To handle the stability constraints with ease, the nonlinear model predictive control (NMPC) technique is applied for path-following issue. Here, NMPC control problem is reasonably established with the constraints of vehicle sideslip angle, yaw rate, steering angle, lateral position error, and Lyapunov stability. To mitigate the online calculation burden, the continuation/generalized minimal residual (C/GMRES) algorithm is adopted. The dead-zone penalty functions are employed for handling the inequality constraints and holding the smoothness of solution. Moreover, the varying predictive duration is utilized in this article to gain the good initial solution fast by numerical algorithm. Finally, the simulation validations are carried out, which yields that the proposed strategy can achieve desirable path following and vehicle stability efficacy, while greatly reducing the computational burden compared with the NMPC controllers by active set algorithm or interior point algorithm.

Genetic PI based model and path tracking control of four traction electrical vehicle

Modeling and control of four-wheel electric vehicles are difficult due to their dynamic parameters and variable road conditions. In this paper, a robust and adaptive electric vehicle model and position control that can be adapted to state variables using a dynamic lateral and longitudinal model of a four-wheel electric vehicle have been proposed. The longitudinal and lateral forces have been modeled according to Newton’s second law, depending on the parameters such as the vehicle’s size, width, height, weight and slope angle by using dynamic equations of the vehicle. In this paper, a permanent magnet synchronous hub motor has been used for each wheel of the electric vehicle. The magic formula wheel model has been used to determine the relationship between the slip and the friction of the designed vehicle. Using the slip system, the relationship between the speed of the electric vehicle itself and the wheel speeds have been defined. The proportional controller at the position loop and proportional + integral controller at the speed loop of the designed system have been used. In the path tracking control system, position controls have been made in the X and Y coordinate planes. A P position controller and a PI speed controller have been used for each plane. Thus, there are 6 controller coefficients in total. Because of the complicated structure of the system, it is difficult to determine the most suitable controller coefficients by analytical methods. Therefore, the genetic algorithm which is one of the heuristic algorithms has been used in determining these coefficients. Simulation studies have been conducted with a different path and position references to see the effectiveness of the proposed electric vehicle model and position control. The obtained results show that the proposed model and control system are robust, effective and reliable.

Determinants of hospital efficiency: A literature review

Background: Inefficiency is a pervasive problem in health systems. The World Health Organization estimates that on average, 20%-40% of the global total health expenditure is wasted. The proportion of total health expenditure attributed to hospitals is high, which implies that improving the efficiency of hospitals will lead to more efficient health systems. This study aims to synthetize the major determinants of hospital inefficiency and to develop a framework to identify causes of inefficiency and develop multi-factor interventions to address inefficiencies.Methods: The study is based on survey of the literature on the determinants of hospital efficiency. The studies include those that employ ratio methods of efficiency analysis, data envelopment analysis and stochastic frontier models and econometric models such as the Tobit regression to assess determinants of technical efficiency. Data was extracted in a table format categorized as those that are within the hospital, outside the hospital but within the health system and those that are outside the hospital and health system in the broader macroeconomic system and analyzed.Results: Hospital efficiency is influenced by factors that may be internal to the hospital or external and thus could be wholly or partially out of the control of the hospital. Hospital-level characteristics that influence efficiency include ownership, size, specialization/scope economies, teaching status, membership of multihospital system and other factors such as case-mix and ratio of outpatients to inpatients. However, the effects of these variables are not definitive and consistent; all depends on the context. Factors out of the direct control of the hospital include geographic location, competition and reimbursement systems. The findings further elucidate that no single factor is effective in addressing hospital inefficiencies in isolation from others.Conclusion: There is no one single magic formula or intervention that can be adopted by different hospitals to improve hospital efficiencies. Multiple factors influence the efficiency of hospitals. To address hospital inefficiency multi-intervention packages focusing on the hospital and its environment should be developed.

A Real-Time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin's minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts.

Characterization and Modelling of Various Sized Mountain Bike Tires and the Effects of Tire Tread Knobs and Inflation Pressure

Mountain bikes continue to be the largest segment of U.S. bicycle sales, totaling some USD 577.5 million in 2017 alone. One of the distinguishing features of the mountain bike is relatively wide tires with thick, knobby treads. Although some work has been done on characterizing street and commuter bicycle tires, little or no data have been published on off-road bicycle tires. This work presents laboratory measurements of inflated tire profiles, tire contact patch footprints, and force and moment data, as well as static lateral and radial stiffness for various modern mountain bike tire sizes including plus size and fat bike tires. Pacejka’s Motorcycle Magic Formula tire model was applied and used to compare results. A basic model of tire lateral stiffness incorporating individual tread knobs as springs in parallel with the overall tread and the inflated carcass as springs in series was derived. Finally, the influence of inflation pressure was also examined. Results demonstrated appreciable differences in tire performance between 29 × 2.3”, 27.5 × 2.8”, 29 × 3”, and 26 × 4” knobby tires. The proposed simple model to combine tread knob and carcass stiffness offered a good approximation, whereas inflation pressure had a strong effect on mountain bike tire behavior.

Nonlinear Model Predictive Control of Autonomous Vehicles Considering Dynamic Stability Constraints

<div class="section abstract"><div class="htmlview paragraph">Autonomous vehicle performance is increasingly highlighted in many highway driving scenarios, which leads to more priorities to vehicle stability as well as tracking accuracy. In this paper, a nonlinear model predictive controller for autonomous vehicle trajectory tracking is designed and verified through a real-time simulation bench of a virtual test track. The dynamic stability constraints of nonlinear model predictive control (NLMPC) are obtained by a novel quadrilateral stability region criterion instead of the conventional phase plane method using the double-line region. First, a typical lane change scene of overtaking is selected and a new composited trajectory model is proposed as a reference path that combines smoothness of sine wave and comfort of linear functional path. Reference lateral velocity, azimuth angle, yaw rate, and front wheel steering angle are subsequently taken into account. Then, by establishing a nonlinear vehicle dynamics model where Magic Formula of nonlinear tire model is adapted, the quadrilateral vehicle stability region is defined in consideration of designed velocity, road adhesion coefficient, and front wheel steering angle. Working condition-variant constraints determined by the boundaries of the quadrilateral region are subsequently obtained to guarantee the stability and vehicle performance. Finally, a nonlinear motion state space model with measured and unmeasured disturbance for NLMPC tracking maneuver is proposed, Meanwhile, a multi-objective cost function based on track error, ride comfort, and the smoothness of control derivative is established. Laguerre functions are applied to design optimal control trajectory and Hildreth’s quadratic programming procedure is introduced to find converged solutions meeting constraints derived from previously investigated quadrilateral stability region for sake of lightening computation load and finding better numerically conditioned solutions of control when NLMPC is implemented online. The configuration of a real-time virtual test track is explained and the NLMPC algorithm is validated. The simulation and experiment results are illustrated to show the effectiveness of the designed nonlinear model predictive control scheme under the test of the overtaking scene compared with the conventional driver control. This work may provide a useful basis for researches of autonomous vehicle lane change in terms of track accuracy, ride comfort as well as stability.</div></div>

Selection of Optimal Tire and Design Optimisation of Steering System for a Formula Student Race Car through Tire Data Treatment

Selection of tires plays a crucial role in Vehicle Dynamics, which is important to design the steering and suspension system. An attempt is made to select the most optimum tire for lateral performance by using the tire data acquired from Tire Testing Consortium. Parameters including the tire’s lateral grip, cornering stiffness, cornering stiffness coefficient, camber stiffness, and lateral frictional coefficient have aided this selection. The tire is modelled using the Pacejka Magic Formula where the lateral and aligning coefficients are found, and used to get pneumatic trail, a parameter not provided in the raw data. The novelty of the work is seen when the selected tire is analysed to set the camber, pressure, and caster using the Design of Experiments method, without the need for building and testing a car. Making the best use of the tires’ forces and moments, the steering geometry is designed for a target range of radii by operating the tire slip angles at its optimum value. Further the influence of the change in toe angle on the Ackermann percentage is examined. Steering moment, calculated using the aligning moment curves of the tire, is applied to the steering column to conduct finite element analysis.

Simulation of curvilinear motion of automobile with the use of two-degree-of-freedom flat model

Development of active safety systems of automobiles is nowadays based not only on road tests, but also on computer simulation of vehicle's curvilinear motion. To properly perform simulation, all required model parameters have to be properly estimated. The less complicated model is, the less parameters it requires. So that, it makes no sense to apply too complicated models, if we are not able to estimate parameters with relatively low error. One of the most popular is two- degree-of-freedom flat model to describe curvilinear motion of automobile. It is widely used in design and improvement of active safety systems. The article discusses the application of simple two- degree-of-freedom flat model of automobile, which requires only several parameters. These parameters are: mass of a vehicle, location of center of gravity of a vehicle, yaw mass moment of inertia of a vehicle, side-slip characteristics. Furthermore, to be able to compare simulation and measurement results, it is necessary to know some input signals such as steering wheel angle and velocity of a vehicle, recorded during road tests. In this article signal of steering wheel angle was taken from Controller Area Network (CAN) bus. In case of model of a vehicle, the Authors decided to compare the results of simulation using two different side slip characteristics known as the dependence between lateral reaction force and side slip angle: linear characteristic (constant cornering stiffness) and the characteristic represented by Pacejka’s Magic Formula in steady-state version.

Analysis and Prediction of Tire Cornering Properties for Different Inflation Pressures Based on Deflection Control

ABSTRACT The variation of inflation pressure has an important effect on the mechanical characteristics of tires that can affect vehicle performance, so the influence of inflation pressure should be taken into account in high-precision tire models. Much research has focused on tire mechanical characteristics under different inflation pressures and modeling methods, such as the Improved Magic Formula/Swift Tire model developed by Schmeitz et al. that takes inflation pressure into account. Based on a large number of tire testing data under different inflation pressures, an empirical model can be obtained, but numerous tire tests are expensive and cannot reveal the mechanism. In previous studies, most tire tests were based on load control, wherein the load is constant while the footprint, carcass, and belt stiffness can change with the variation of inflation pressure, making the cornering characteristics much more complicated. Herein, a method of deflection control is used and the contact patch is well maintained. The effect of tire inflation pressure is simplified to be the change of structure stiffness and averaged contact pressure. The effect of inflation pressure on cornering properties under deflection control is systematically observed under different tire deflection values. In addition, a prediction model extended from the Magic Formula model is proposed. The model of Schmeitz et al. [1,2] needs test data from at least three inflation pressures; the model proposed herein requires tests at only two inflation pressures. The validation shows that this prediction method has good accuracy, almost the same as that of the model of Schmeitz et al. The error index of the lateral force is at most 2%, and the error index of the self-aligning torque is 4% at the maximum.

Influence of Tire Inflation Pressure on Vehicle Dynamics and Compensation Control on FWID Electric Vehicles

AbstractThis paper presents a comprehensive study revealing the influences of tire pressure variations and their distribution among four tires on vehicle dynamics performance and driver's steering workload for a four wheel independent drive electric vehicle (FWID EV). Then a direct yaw-moment control (DYC) strategy employing an unbiased adaptive model predictive control (MPC) algorithm is proposed to compensate for the influences. An unbiased estimation strategy is developed to update the time-variant prediction model for the adaptive MPC system. An extended magic formula (MF) tire model and a modified Unitire model involving tire inflation pressure are employed to describe the tire longitudinal and lateral forces, respectively. Various tire pressure variations are simulated in CarSim to exhibit the influences of tire inflation pressure, including all four tires at same and different pressures. The unbiased estimation results and compensation effects of the DYC strategy are also verified through simulations. A vehicle dynamics and lateral motion stability index, and driver's steering workload are proposed to quantify the influence of tire pressure variations and distributions. Analyses on the simulation results indicate that: pressure reduction on a front tire and rear tire induces a large steering angle and a large vehicle sideslip angle, respectively; all-tire inflation pressure decrease will increase driver's steering workload. The proposed DYC strategy can achieve satisfactory compensation effects through significantly decreasing the vehicle sideslip angle, steering wheel angle and reducing driver's steering workload by up to 90%.

Creativity, Experience, and Reflection: One Magic Formula to Develop Preventive Water Competences

Preventive water competences that children should learn to be safe in the water have been discussed and revised. Methodology to promote these wáter competences has not had the same amount of examination and discussion so far. From an ecological perspective, we share some key points derived from the objectives of the research-into-action program called “The development of preventive water competences in 5th and 6th grade school students” as conducted in Junior Lifeguard programs in Uruguay. It involved six groups of 10 to 12-year-old Estate School students studied in two cycles. The whole process conveyed how our methodology changed from experiences and assessment results.

Finite-Gap CMV Matrices: Periodic Coordinates and a Magic Formula

Abstract We prove a bijective unitary correspondence between (1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum ${\textsf{E}}$ and (2) special periodic block-CMV matrices satisfying a Magic Formula. This latter class arises as ${\textsf{E}}$-dependent operator Möbius transforms of certain generating CMV matrices that are periodic up to a rotational phase; for this reason we call them “MCMV.” Such matrices are related to a choice of orthogonal rational functions on the unit circle, and their correspondence to the isospectral torus follows from a functional model in analog to that of GMP matrices. As a corollary of our construction we resolve a conjecture of Simon; namely, that Caratheodory functions associated to such CMV matrices arise as quadratic irrationalities.

Integrated Control of Differential Braking and Active Aerodynamic Control for Improving High Speed Stability of Vehicles

In this paper, an integrated control strategy (ICS) is proposed to improve high speed dynamics stability of the vehicle by the integration of active aerodynamic control (AAC) and differential braking control (DBC). Two aerodynamic surfaces are attached to the roof of the vehicle and servo-controlled separately in real-time. A hierarchical control structure is used to design the proposed scheme, which is composed of an upper and a lower controller. In the upper controller, the additional yaw moment required for stability control is determined by sliding mode control with the consideration of driver inputs, vehicle dynamic and the limitation of road adhesion. In the lower controller, a control strategy is designed to coordinate differential brake and active aerodynamic control, and an optimal control allocation algorithm is adopted to distribute the brake pressure of each wheel. A simplified magic formula tire model is used to describe the nonlinearity of the tires. Two double lane change tests on dry and wet road performed to study the effectiveness of the control algorithm in CarSim/Simulink Co-simulation. The results show the proposed control strategy can effectively improve the vehicle dynamics stability and tire workload usage.

Vehicle Shimmy Modeling With Pacejka's Magic Formula and the Delayed Tire Model

Abstract This paper investigates a three-degrees-of-freedom (DoF) shimmy model of vehicle front wheels with steering system and dependent suspension. The contact models of rigid ground and elastic tire are analyzed from the viewpoint of predicting shimmy. Pacejka's magic formula and the delayed tire model are compared by means of stability charts in various parameter domains. Conclusions are obtained regarding the advantages and disadvantages of the use of the delayed tire model.

Five Simple and Low Maintenance Investing Strategies: Seeking an Automated Investing System

The purpose of the paper is to examine five different investment strategies which are known to be easily implemented by ordinary investors: (1) SP Fed funds rate; Greenblatt’s magic formula; Sector rotation, Warren Buffett stock market indicator DOI : 10.7176/RJFA/11-2-01 Publication date: January 31 st 2020

BEHAVIORAL FINANCE: EMPIRICAL EVIDENCE USING MAGIC FORMULA IN THE BRAZILIAN STOCK MARKET

ABSTRACT Purpose: Explain the causes of inefficiencies in asset pricing on the Brazilian stock exchange through the behavioral finance hypothesis. Originality/value: Research made in the stock market over the last decades suggests that there is evidence of obtaining returns above the market average, through the purchase of undervalued assets, that is, when it has a low relation between the price and the fundamentals of the company. However, there is a notable discrepancy regarding the interpretation of causes among academics. The efficient markets hypothesis was presented, which is based on the premise of the strict rationality of economic agents. On the other hand, the behavioral finance theory was also discussed, which presents different assumptions. Design/methodology/approach: Using the historical quotes of the shares traded on B3, extracted from economática(r)'s database, the present work used the Magic Formula methodology to investigate the behavioral effect through the inefficiencies found in the pricing of these assets. Findings: The results suggest that the Brazilian stock market, in conformity with works of the same nature performed in markets in other countries, has inefficiencies in the pricing of assets, so that it is possible to obtain advantages from economic agents. The interpretation for the causes of such inefficiencies is based on the premises of behavioral finance, and points to the existence of a limitation in the rationalization of these agents.

A Brush-Type Tire Model with Nonsmooth Representation

This paper proposes a brush-type tire model with a new mathematical representation. The presented model can be seen as a generic model that describes the distributed viscoelastic force and Coulomb-like friction force, which are balancing each other at each point, in the contact patch. The model is described as a partial differential algebraic inclusion (PDAI), which involves the set-valuedness to represent the static friction. A numerical integration algorithm for this PDAI is derived through the implicit Euler discretization along both space and time. Some numerical comparisons with Magic Formula and a LuGre-based tire model are presented. The results show that, with appropriate choice of parameters, the proposed model is capable of producing steady-state characteristics similar to those of Magic Formula. It is also shown that the proposed model realizes a proper static friction state, which is not realized with a LuGre-based tire model.

Tire Model with Temperature Effects for Formula SAE Vehicle

Formula Society of Automotive Engineers (SAE) (FSAE) is a student design competition organized by SAE International (previously known as the Society of Automotive Engineers, SAE). Commonly, the student team performs a lap simulation as a point mass, bicycle or planar model of vehicle dynamics allow for the design of a top-level concept of the FSAE vehicle. However, to design different FSAE components, a full vehicle simulation is required including a comprehensive tire model. In the proposed study, the different tires of a FSAE vehicle were tested at a track to parametrize the tire based on the empirical approach commonly known as the magic formula. A thermal tire model was proposed to describe the tread, carcass, and inflation gas temperatures. The magic formula was modified to incorporate the temperature effect on the force capability of a FSAE tire to achieve higher accuracy in the simulation environment. Considering the model validation, the several maneuvers, typical for FSAE competitions, were performed. A skidpad and full lap maneuvers were chosen to simulate steady-state and transient behavior of the FSAE vehicle. The full vehicle simulation results demonstrated a high correlation to the measurement data for steady-state maneuvers and limited accuracy in highly dynamic driving. In addition, the results show that neglecting temperature in the tire model results in higher root mean square error (RMSE) of lateral acceleration and yaw rate.

A study of Hangul jeonjeok(典籍) in the Hwaseong Municipal Folk Museum

본 논문은 화성시 향토박물관에 소장된 한글 전적 19종을 소개하고 그 가치를 논의한 것이다. 한글 전적 19종은 화성 지역에 세거한 양반가에서 기증된 것으로, 본고는 19종의 형태사항과 내용을 개관하였다. 그 결과 간행본이 3종, 필사본이 16종인 점, 문학 작품이 5종인데 비해 14종은 대개 교육적 또는 실용적 성격을 띤 자료임을 밝혔다. 14종 가운데 가장 큰 비중을 차지하는 것은 당대 이념과 윤리 교육을 위한 자료로, 7종이 이에 해당한다. 나머지 7종 중 3종은 진언(眞言) 또는 점복(占卜)에 관한 것으로, 이러한 진언류 전적은 실제 생활에서 활용하기 위한 실용서로 파악했다. 이로 미루어 화성 지역 양반가는 당대 윤리와 이념 교육적 성격이 강한 한글 전적을 주로 향유하였으며 그런 가운데 진언류 전적도 중시했다고 보았다. 다음으로 본고는 한글 전적 19종 가운데 더 중요한 가치를 지닌 것으로 판단되는 3종의 자료를 장을 달리하여 검토하였다. 『列女傳』은 여성 필사자의 존재를 고증하고 필사본 규범서를 연구하는데 일조할 수 있는 자료라는 점에서 중요하다. 『대왕대비전 언교』는 관련 계통 자료들 가운데 원본에 가까운 것으로 판단되므로 남다른 가치를 지닌다. 『精所』는 순 한글로 이루어진 필사본 진언집으로, 조선 후기 진언의 대중화 양상은 물론 한글 소설에 관습적으로 등장하는 진언의 사회, 문화적 배경을 규명하는데 유용한 자료임이 분명하다.This paper is study of Hangul jeonjeok(典籍) in the Hwaseong Municipal Folk Museum. This Hangul jeonjeok(典籍) donated from four noble families who lived from generation to generation in Hwaseong. This paper examined the form and content of these materials. As s result. Noble families in Hwaseong mainly enjoyed books that contained ethical content. and valued the book with the contents of the magic formula. Next. this article discussed more important material separately. Yeolnyeojeon(『列女傳』) can help confirm the existence of female transcriber and study the written ethics book. Daewangdaebijoen Unkyo(『대왕대비전 언교』) is worth the original. Jeongso(『精所』) is the magic book of the Hangul manuscript. This material is useful in identifying the popularization of magic in the late Joseon Dynasty.

Nigella sativa Oil Mouth Rinse Improves Chemotherapy-Induced Oral Mucositis in Patients with Acute Myeloid Leukemia

Objective The present study aims at evaluating the beneficial effect of Nigella sativa (NS) oil mouth rinse in the management of chemotherapy- (CT-) induced oral mucositis (OM) in patients with acute myeloid leukemia (AML). Methods Fifty-four AML patients were participated in this study and randomly allocated to either the test group or a control group. The patients of the test group received NS oil mouth rinse during 28-day CT, while the participants of the control group received a “magic mouthwash” formula. The primary outcome of this study was the incidence and severity of CT-induced OM in terms of erythema and ulcer. The secondary outcomes were the pain severity score, swallowing function, and the salivary concentrations of interleukin-6 (IL-6) and tumor necrosis factor-alpha (TNF-α). Results NS oil mouth rinse attenuated the progression of CT-induced OM compared with the control formula (AUC = 5.9 vs. 38.4, P < 0.05) and significantly decreased the erythema and ulceration scores (AUC of total OMAS = 11.4 vs. 85.9, P < 0.001) compared with the magic mouthwash formula. It also reduced the pain score and enabled all the participants of this group to consume normal food during treatment. It significantly decreased salivary IL-6 (AUC = 7376 vs. 16599, P < 0.001), while the changes of TNF-α levels were not significant (AUC = 676.9 vs. 885.2, P > 0.05). Conclusions NS oil mouth rinse is effective in attenuating the severity of CT-induced OM and improves the pain and swallowing function in AML patients.