Constant Torque Research Articles

Features of Nonlinear Calculation of Bending Rods Partially Supported on Elastic Foundation

The paper investigates the results of solving spatial contact problems on the free support of bending rods (hereinafter referred to as beams) on elastic quarter-space and octant of space. The objectives of the study include determining the stress state of contact pads, obtaining a picture of the distribution of contact stresses over them, and studying the features that arise when solving these contact problems. The main solution method is the method of B. N. Zhemochkin, based on the discretization of contact areas by replacing a continuous contact with a point one. This approach allows us to reduce the contact problem to the calculation of a statically indeterminate system using well-developed methods of structural mechanics. The mathematical model of the contact problems to be solved is built on the assumption of linear elastic (geometric and physical linearity) work of both the bending element and the elastic foundation. Since in the process of deformation the end sections of the beam element can break away from the support areas, the contact problems to be solved belong to the group of contact problems with a previously unknown contact area. The design schemes of such problems are constructively nonlinear, and their calculation is carried out by iterative methods. Based on the results of solving the considered contact problems, it has been found that with a geometrically symmetrical support of the beam element on the left and right on elastic quarter-spaces (space octants) with equal support areas, but different mechanical characteristics, as well as symmetrical loading, the values of support reactions, considering them as resultants of contact stresses on the left and right contact pads, and the coordinates of the points of their application are not equal to each other. The solution of the contact problem leads to a similar result in the case of a bending beam element resting on the elastic quarter-space on one side, and on the edge of the space octant on the other. In addition, a constant torque appears along the entire length of the beam element, indicating that the beam element is in a torsional transverse bending condition.

Three-phase PMSM vector control using decoupled flux and speed controller

Described in this paper is a control method for a permanent magnet synchronous motor (PMSM) based on a decoupled speed and flux control technique where the speed and the flux of the PMSM are controlled separately. The actual torque and the feedback flux of the PMSM are directly calculated from the stator currents, while the speed and the angular position are read from the motor. Therefore, no flux/torque or speed/position estimators are required. A separate flux controller is used to generate the d-axis current error. The speed controller is used to generate the reference torque, while the q-axis current error is generated by the constant torque relation. The performance of the overall control system is examined using the Matlab/Simulink environment. The experimental work is tested using dSPACE DS1104. The performance of the motor is presented with reference speed step change. The simulation and the hardware results prove the effectiveness of the proposed method in controlling the speed and flux of a three-phase PMSM.

Design and Implementation of Predictive Controllers for a 36-Slot 12-Pole Outer-Rotor SPMSM/SPMSG System with Energy Recovery

This paper investigates a drive system with energy recovery which uses a 3-phase 1-kW 36-slot 12-pole distributed winding outer-rotor surface-mounted permanent-magnet synchronous motor (SPMSM) and surface-mounted permanent-magnet synchronous generator (SPMSG), which can be used in indoor exercise bicycles. In order to extend drive system operating speed range, the constant torque control, flux-weakening control, and maximum torque/voltage control are used to extend its operation speed up to 1.75 times rated speed. In addition, a predictive speed controller and a predictive current controller are proposed to improve transient responses, load disturbance responses, and tracking responses. A digital signal processor, type TMS-320F-28035, manufactured by Texas Instruments, is used as a control center for the proposed SPMSM/SPMSG drive system. Experimental results validate the feasibility and correctness of the proposed methods.

Mathematical substantiation of mine locomotive braking efficiency under pulsiting braking torque

Purpose. Determination of braking torque parameters that provide high braking performance of a mine locomotive by mathematical modeling of the braking of a mine locomotive by a disc brake that creates a pulsating braking torque. The methods. Forced vibrations of the elements of the wheel-motor unit (WMU) of a mine locomotive in the process of braking with a disc brake are studied by the methods of differential calculus and mathematical modeling. Integration of the system of differential equations is performed by the Runge-Kutt method. Findings. A comparative analysis of a mine locomotive braking by a disc brake, which creates a constant and pulsating sinusoidal braking torque with a different number of sinusoid periods per revolution of the wheel pair, is carried out. It has been proved that the pulsating sinusoidal braking moment generated on the axle of the wheel pair equal to the sum of the constant component and the amplitude of the oscillations of the variable component multiplied by the sine of the product of the number of sinusoid periods per revolution of the wheel pair by its angular coordinate provides higher braking characteristics than the constant braking moment. It is shown that pulsating braking torque reduces the braking time and braking distance of the mine locomotive. The values of the amplitude of oscillations, which depend on the average value of the braking torque, and the number of periods of the sinusoid per one revolution of the wheelset, at which the greatest effect is achieved, are determined. The originality. For the first time, a mathematical model has been developed for braking a mine locomotive by a disc brake, which creates a pulsating braking torque on the axle of the wheel pair, depending on its angular coordinate, taking into account the nonlinear dependence of the adhesion coefficient on relative slip, on the basis of which the efficiency of a disc brake with a multi-sector disc is shown in comparison with a disc brake with a homogeneous disk under various conditions of the rail track. Practical implementation. The research results make it possible to determine the parameters of a disc brake with a multi-sector disc located on the wheelset axle and on the engine shaft, which provide the highest braking efficiency.

Dynamic Control of Traction Motor for EV Fed via Dual Source Inverter with a Two Battery System

An electric vehicle uses multiple energy-storage systems to power the traction motor. Dual-source inverters (DSIs) are used for single-stage power conversion by skipping the dc/dc boost converter stage; therefore, eliminating the passive magnetic storing element which improves the overall efficiency of the drive; moreover, multiple energy-storage systems improve the power density of the system. This article discusses the fine control of a traction motor from zero speed to rated speed supplied through a dual-source inverter. Field-oriented control with space vector modulation technique is applied to achieve closed-loop control. Two dc sources are used, one having a higher-voltage battery and one a lower-voltage battery. The higher-voltage battery is the main battery which supplies power to the traction motor, whereas the lower-voltage battery supplies power to supplementary loads of the EV. This article presents improved dynamic behaviour of an induction-motor-driven EV fed from a dual-source inverter using modified closed-loop field-oriented control with space vector modulation. The improvement includes reduced control complexity due to space vector modulation and achieving the option of EV operation in an emergent situation using the same converter and control system. The simulated performance of the presented system is obtained in MATLAB/Simulink. A step-down experimental prototype is used for verification of effective control of the induction motor as the EV is under constant torque variable speed operation with real-time parameters such as power, power factor, current harmonics, and voltage/current stresses across the switch using two batteries individually.

Experimental study of floating wind turbine control on a TetraSub floater with tower velocity feedback gain

We present an experimental study of floating wind turbine control with inclusion of tower motion feedback. The study is conducted for a 1:60 scaled-model of the DTU 10MW reference wind turbine on a design variant of the TetraSub floater. A review of control methods for floating wind turbines is provided, covering both de-tune and tower motion feedback methods. We next detail the implementation in the experimental setup that includes real-time integration and low-pass filtering of the measured tower-top acceleration. We demonstrate how the tower feedback loop is able to stabilize an otherwise unstable land-based controller. The results further show that the stability is maintained for increasing values of the feedback gain until a certain limit. For the chosen control parameters and the lab-generated wind field, which had limited low-frequency energy, we observe that the variations in rotor speed, blade pitch and platform motion are generally larger for the tower loop controller. This finding is not generalizable due to the special inflow conditions and because controller optimization is not performed. For the tower loop controller, a substantial response at the floater roll frequency is identified. This is caused by the influence of blade pitch on the aerodynamic torque in combination with the constant generator torque. Mitigation through generator torque control is proposed.

Torque Analytical Calculation of Formed Winding Permanent Magnet Motor

The development of electrification has put forward higher requirements for the efficiency and power density of permanent magnet motors. The combination of formed flat wire windings and open slots with rectangular cross-sections has been applied in permanent magnet motors, which makes the motor torque fluctuate significantly, and the vibration and noise caused by it seriously influence the stability of operation. Therefore, it is essential to study the torque characteristics for permanent magnet motors with formed windings. The open slot brings rich tooth harmonics to the air-gap magnetomotive force. In this study, an analytical model of the motor magnetic field was established based on magnetic potential and relative permeance theory. According to the Lorentz force law, an analytical model of the instantaneous torque of the permanent magnet motor with a formed winding is derived. The model points out that under the modulation of the relative permeance function, the constant torque and torque fluctuation are generated after the interaction of the stator magnetomotive force and rotor magnetic potential that meet the corresponding harmonic order relationship, and the order of the torque fluctuation is a multiple of 6. According to the analytical model, different torque components of the permanent magnet motor with formed windings are calculated and verified by the finite element method.

3-D Analytical Model of Axial-Flux Permanent Magnet Machine With Segmented Multipole-Halbach Array

This paper presents a 3-D analytical model of an axial-flux permanent magnet (AFPM) machine with a segmented multipole-Halbach PM array. Closed-form solutions are self-consistently derived in terms of modified Bessel functions of the first- and the second-kind by solving analytically Laplace and Poisson equations by the method of magnetic scalar potential subject to the appropriate boundary conditions. In the preceding studies, their formulations are based on a 2-D or quasi 3-D geometry, and their discussions are often limited to the magnetic fields with low-poles of the regular PM. The proposed model successfully provides more rigorous and widely applicable expressions for magnetic fields, back-electromotive force, Lorentz torque and torque constant without limitations on the number of poles and the arrangements of the PM. Behavior of the torque constant is then shown against the number of poles ranging widely from low-poles to high-poles of the regular PM, the standard-Halbach PM and the multipole-Halbach PM for changeable geometrical parameters. The obtained results are of much use in understanding intrinsically the performance characteristics of the AFPM.

Speed Regulation Characteristics of Variable Conductivity-Based Barrel-Type Permanent Magnet Eddy Current Governor

In this study, a conductivity-regulated barrel-type permanent magnet eddy current governor is proposed, and a conductor barrel structure scheme consisting of four sections of materials with different conductivities is presented. The torque equation of the barrel-type permanent magnet eddy current governor with the equivalent conductivity as the covariate was established using the separation variable method based on the subdomain model, and the equivalent conductivity function was established to obtain the speed regulation characteristics of the governor under a constant torque load. The influence of the conductivity parameters of the conductor barrel on the speed regulation characteristics was studied by numerical simulation, the influence of the conductivity values of each section of the material on the conductivity function was investigated, and the torque equation and conductivity function were verified by three-dimensional electromagnetic finite element simulation. The results show that the structural scheme of the four-segment combined conductor barrel can realize a continuous change in conductivity with the displacement of the magnet disk, thus realizing continuous speed regulation of the constant torque load, and the speed regulation characteristic of the governor is segmented linearly. Compared with the air gap-regulated disk-type permanent magnet eddy current governor, the conductivity-regulated barrel-type permanent magnet eddy current governor has a wider speed regulation range, a lower unloading torque after overload protection, and can start with its maximum torque, thus enabling heavy-load starting of constant torque loads, speed regulation operation, and unloading overload protection of equipment.

Transport of closed ring containing chiral active particles under transversal temperature difference

Active matter is a new and challenging field of physics. Chiral active particle experiences a constant torque and performs circular motion due to the self-propulsion force not aligning with the propulsion direction. Recently, most of studies of the active particle systems focused on constant temperature, but did not take into consideration the constraints by the barriers. In our work, the rectification of a ring containing chiral active particles with transversal temperature difference is numerically investigated in a two-dimensional periodic channel. It is found that the ring powered by chiral active particles can be rectified by the transversal temperature difference and the direction of the transport is determined by the chirality of active particles. The average velocity is a peaked function of angular velocity, the temperature of the lower wall or temperature difference. The transport behaviors of the ring containing one chiral active particle is qualitatively different from those of the ring containing several particles. Especially, the ring radius can strongly affect the transport behaviors. For the ring containing one chiral active particle, the interaction between the particle and the ring facilitates the rectification of the ring when the circular trajectory radius of the chiral particle is large. The average velocity decreases with the increase of the ring radius because the propelling force to the ring by the particle is small. When the circular trajectory radius is small, the interaction between the particle and the ring suppresses the transport. The speed increases as the ring radius increases because the directional transport comes from the difference in temperature between the upper wall and the lower wall. For the ring containing several particles, the interaction between particles reduces the rectification of the ring. The average velocity increases with the increase of the ring radius due to the interaction between particles decreasing. Remarkably, the velocity of the ring decreases as the particle number increases when the ring radius is small, but is a peaked function when the ring radius is not small. Our results offer new possibilities for manipulating an active particle flow on a microscale, and can be applied practically to propelling carriers and motors by a bath of bacteria or artificial microswimmers, such as hybrid micro-device engineering, drug delivery, micro-fluidics, and lab-on-chip technology.

Fully Integrated Multilevel Power Converter for SRM Drive With Charging Capabilities (G2V) for Electric Vehicle Application

This article presents a fully integrated multilevel power converter topology (IML-PCT) with integrated battery charging capability for a switched reluctance motor (SRM) drive. The battery charger is integrated within the IML-PCT, which eliminates the requirement of any additional module for charging purposes. The proposed IML-PCT applies higher energization and de-energization voltages during the driving mode, which leads to an enhanced constant torque region for SRM drive. For the battery charging mode, the proposed IML-PCT exhibits the characteristics of an onboard charger (OBC) capable of charging the battery energy storage system directly via a standard ac outlet. The OBC functionality is realized by reconfiguring the proposed IML-PCT into an interleaved bridgeless boost power factor correction circuit (IBB-PFCC). The charging inductors for IBB-PFCC are realized by reutilizing/reconfiguring all the windings of the four-phase SRM. Also, with the proposed IBB-PFCC configuration, the charging current in the windings leads to an average zero torque production. Thus, the rotor is kept stationary during battery charging mode without any external braking mechanism. Detailed simulation and experimental studies on a 1.1-kW laboratory prototype four-phase SRM demonstrate ac level-1 (120 V/240 V) charging performance of the proposed IML-PCT.

EVOLUTION OF ROTATIONAL MOTIONS IN A RESISTIVE MEDIUM OF A NEARLY DYNAMICALLY SPHERICAL GYROSTAT SUBJECTED TO CONSTANT BODY-FIXED TORQUES

A satellite or a spacecraft in its motion about the center of mass is affected by the torques of forces of various physical nature. It is influenced by the gravitational, aerodynamic torques, the torques due to the light pressure, and the torques due to the motions of masses inside the body. These motions may have various causes, for example, the presence of fluid in the cavities in the body (for example, liquid fuel or oxidizer in the tanks of a rocket). Therefore, there is a necessity to study the problems of the dynamics of bodies with cavities containing a viscous fluid, to calculate the motion of spacecrafts about the center of mass, as well as their orientation and stabilization. The mentioned torques, acting on the body, are often relatively small and can be considered as perturbations. It is natural to use the methods of small parameter to analyze the dynamics of rigid body under the action of applied torques. The method applied in this paper is the Krylov-Bogolubov asymptotic averaging method. The studies of F. L. Chernousko showed that solving the problems of dynamics of a rigid body with a viscous fluid can be subdivided into two parts – the hydrodynamic and dynamic ones – which can greatly simplify the initial problem. We investigated the motion about its center of mass in a resistive medium of a nearly dynamically spherical rigid body with a cavity filled with a viscous fluid at small Reynolds numbers, subjected to constant body-fixed torque which is described by the system of differential equations, considering the asymptotic approximation of the moments of the viscous fluid in the cavity. The determination of the motions of forces acting on the body from side of the viscous fluid in the cavity was proposed in the works of F. L. Chernousko. We obtained the system of equations of motion in the standard form which refined in square-approximation by small parameter. The Cauchy problem for a system determined after averaging was analyzed. The evolution of the motion of a rigid body under the action of small internal and external torques of forces is described by the solutions which obtained as a result of asymptotic, analytical and numerical calculations over an infinite time interval.

A control technique for hybrid floating offshore wind turbines using oscillating water columns for generated power fluctuation reduction

Abstract The inherent oscillating dynamics of floating offshore wind turbines (FOWTs) might result in undesirable oscillatory behavior in both the system states and the generated power outputs, leading to unwanted effects on critical, extreme, and fatigue loads, and finally to a premature failure of the facility. Therefore, this kind of system should be capable of lessening such undesired effects. In this article, four oscillating water columns (OWC) have been installed within a FOWT barge-type platform. A novel switching control technique has been developed in order to reduce oscillations of the system created by both wind and wave, as well as the fluctuations in the generated power, by adequately regulating the airflow control valves. While the impact of the coupled wind-wave loads has been considered, a set of representative case studies have been taken into account for a range of regular waves and wind speeds. The study relies on the use of response amplitude operators (RAO) that have been pre-processed and evaluated in order to apply the switching control technique. In this sense, the starting time of the switching for below-rated, rated, and above-rated wind speeds have been calculated using the platform’s corresponding pitch RAO. Additionally, the blades’ pitch and generator torque have also been regulated by means of a constant torque variable speed controller to capture maximum energy for below-rated wind speed conditions and to match the rated generator power for rated and above-rated wind speed conditions, respectively. In order to peruse the feasibility and performance of the proposed strategy, a comparison has been carried out between the uncontrolled traditional barge-type platform and the controlled OWCs-based barge FOWT. The results demonstrate that the proposed control approach can effectively and successfully decrease both the oscillations in the system’s modes and the fluctuations in the generated power.

Numerical Investigations on Operation Modes and Transients of IPM Machines with Dual Windings

This paper investigates the flux-weakening characteristics and transient response of a dual winding interior permanent magnet (DWIPM) machine designed using the 2010 Toyota Prius IPM Machine specifications. In order to thoroughly adjust the main flux, dual windings are fed by separate identical inverters. Thus, significantly high-torque for high-speed requirements can be simply achieved by making one of the inverters open-circuited. Transient response of the DWIPM machine, including torque and current pulsations, occurring during normal drive or deactivation of one of the inverters has also been investigated for different operation modes. The flux-weakening performance characteristics of the proposed DWIPM machine have been compared with those of its single-fed counterpart in order to highlight the benefits and drawbacks of the dual-winding topology. The steady-state performance characteristics, torque/speed and power/speed curves, efficiency maps, machine transient response, different machine design options with various numbers of turns per phase and current amplitudes, and the importance of the electromagnetic coupling between dual windings have all been addressed. For transient and steady-state analyses, 2D, nonlinear, time-stepping finite element method (FEM) has been employed. It has been revealed that the proposed DWIPM machine exhibit significantly improved flux-weakening characteristics, particularly high-power at constant power region and high efficiency at constant torque region, and quite low current and torque pulsations occurring during operation mode change.

Design of a non‐ferromagnetic spoke array Vernier permanent magnet generator with iron‐bar based on enhanced equivalent magnetic network model

AbstractThe spoke‐type arrangement of permanent magnets (PMs) in rotor of Vernier PM (VPM) machines was first introduced in a dual‐stator topology to overcome low‐power drawback of VPM machines. However, this structure is mostly applicable for high‐power motor drives. A non‐ferromagnetic spoke array VPM generator with a special rotor structure for small‐scale wind turbine generator is presented. The leakage flux lines tend to be aligned with the main flux routes due to a special design of flux barriers in end portion of PM housings. High torque‐density, low weight, torque‐speed curve with a wide constant torque region, promising efficiency, and power factor are the advantages of the proposed machine. An Equivalent‐Magnetic‐Network (EMN) model is established for predicting the complex behaviour of flux lines and operating quantities of the proposed structure with reasonable accuracy. The contribution of the modelling method includes a special mesh cell for the air‐gap permeance network to more accurately capture the flux routes, continuous positioning method for omitting spikes on post‐processing waveforms due to numerical errors, and a stable solving flowchart with a high convergence rate. The validity of the EMN model is validated by comparing the operating waveforms of the machine with the corresponding waveforms obtained by the finite element and experiments.The cover image is based on the Research Article Design of a non‐ferromagnetic spoke array Vernier permanent magnet generator with iron‐bar based on enhanced equivalent magnetic network model by Mehrage Ghods et al., https://doi.org/10.1049/elp2.12272.

Stress distribution of the nonwoven fabric package during winding

During winding, the defects of wrinkles and buckling are prone to occur in the material package. This problem increases in larger packaging sizes, and it is related to the uneven distribution of internal stress. In order to study the internal stress distribution law of the wound package, it is necessary to analyze and discuss the mechanical behavior of the winding process. In this paper, a winding model based on thick-cylinder theory was established to deduce the internal stress distribution and change law of the wound package. Polypropylene melt-blown nonwoven fabric was used as the test material; it showed no deformation residue after the stretching test, which was the allowable stretching conditions of the nonwoven fabric from the low-strain stretching experiment. Based on the material mechanical properties, three tension control strategies (namely constant tension, constant torque, and taper tension winding) of the winding tension were analyzed and the variation law of winding stress was described. The internal stress of the ideal packaging was premised, which was determined as the winding tension control curve under even internal tension and can be called equal internal tension winding. The results showed that the properties of materials have a significant impact on packaging quality, and equal internal tension winding can effectively improve packaging quality and size. The research results can provide some reference for tension control in the winding process of nonwoven fabric or other textile materials.

Closed-Loop Voltage Control for Maximizing Inverter Output Voltage in the Field Weakening Region of Induction Machines

It is desirable in induction motors drives to maximize the inverter output voltage to increase the output torque and power in the field weakening (FW) region. Existing FW control methods produce high torque ripples and show high step reductions of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis current during the transient period from constant torque (CT) to FW. In addition, many proposed controllers are difficult to tune and require specific control algorithms to deal with parameter sensitivities. In this article, a closed-loop voltage control method is developed based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis reference current to maximize the voltage extraction from dc-link voltage while minimizing the above disadvantages. This is achieved by applying the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis current, which compensates the difference between the hexagonal reference voltage and stator voltage for corresponding stator voltage vector position. Therefore, the output torque and power of the induction machine (IM) are maximized in the FW region. The proposed method is first presented analytically, and then, simulation and experimental results are included to verify the control method.

A comparative braking scheme in auto-electric drive systems with permanent magnet synchronous machine

&lt;span lang="EN-US"&gt;Permanent magnet synchronous machines (PMSMs) are gaining popularity due to renewable energy and the electrification of transportation. Permanent magnet synchronous machines are receiving interest because to their great dependability, low maintenance costs, and high-power density. This research compares surface mounted permanent magnet (SMPM) with interior permanent magnet (IPM) synchronous machines using MATLAB. Mathematical models and simulation analyses of two permanent magnet synchronous machines under regenerative braking are presented. Maximum regeneration power point (MRPP) and torque (MRPP-torque) for two machine types were simulated at variable electrical speed and q-axis current. Simulation results showed IPMSM produced more output power due to saliency than SMPM at varying speed and current with higher MRPP and MRPP-Torque. Simulation was used to compare the dynamic impacts of constant and variable braking torques on an auto-electric drive's speed and produced torque on a plain surface and a sloppy driving plane. 81.68% and 74.95% braking efficiency were measured on level ground and a sloppy plane, respectively. Simulations indicated that lithium-ion battery state of charge varied linearly with constant braking torque and exponentially with varying braking torque, reflecting efficiency values. All simulations were in MATLAB/Simulink 2014.&lt;/span&gt;

Detection of Permanent Magnet Damage of PMSM Drive Based on Direct Analysis of the Stator Phase Currents Using Convolutional Neural Network

Permanent magnet synchronous motors (PMSMs) due to their numerous advantages, such as simple and compact design, easy production and high power-to-weight ratio, high power factor in the range of constant torque, low inertia, and more precise control compared to other electric motors, are increasingly used in various applications, such as electric vehicles, wind power, home, and industrial appliances. However, PMSMs, such as other electrical machines, may subject to various types of damage during the operation. Due to their use in devices of a critical nature (e.g., transport applications), the detection of these damages at their initial stage constitutes an extremely important issue. In this article, we investigate the possibility of the permanent magnets (PMs) faults detection of PMSM using a convolutional neural network (CNN) based on the raw stator current data. The article aims to show the possibility of detecting the PM demagnetization using the information obtained directly from the measured current signal as well as indicate the influence of simultaneous incipient interturn short circuits and the operating condition of the drive on the accuracy of the developed diagnostic system. The results of the experimental research carried out on a specially designed PMSM show the impressive capability of the developed CNN-based diagnostic system to precisely detect the initial phase of PMs damage.

Optimizing Torque Delivery for an Energy-Limited Electric Race Car Using Model Predictive Control

This paper presents a torque controller for the energy optimization of the powertrain of an electric Formula Student race car. Limited battery capacity within electric race car designs requires energy management solutions to minimize lap time while simultaneously controlling and managing the overall energy consumption to finish the race. The energy-managing torque control algorithm developed in this work optimizes the finite onboard energy from the battery pack to reduce lap time and energy consumption when energy deficits occur. The longitudinal dynamics of the vehicle were represented by a linearized first-principles model and validated against a parameterized electric Formula Student race car model in commercial lap time simulation software. A Simulink-based model predictive controller (MPC) architecture was created to balance energy use requirements with optimum lap time. This controller was tested against a hardware-limited and torque-limited system in a constant torque request and a varying torque request scenario. The controller decreased the elapsed time to complete a 150 m straight-line acceleration by 11.4% over the torque-limited solution and 13.5% in a 150 m Formula Student manoeuvre.