# A New Hyperloop Transportation System: Design and Practical Integration

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## Abstract

**:**

## 1. Introduction

## 2. LSM Model and Controller Design

#### 2.1. Modeling of the Linear Synchronous Motor

_{abc}is the stator a, b, and c phase self-mutual inductance matrix. This is shown in (2).

_{Mabc}is the stator a, b, and c phase flux linkages due to the permanent magnets and damper windings on the rotor. This is shown in (3).

#### 2.2. Permanent Magnet Configuration

#### 2.3. Field Oriented Control

_{a}, i

_{b}, and i

_{c}) readings to convert it to qd0 form. Additionally, for the transformation, the rotor position of the PMSM is required. This can be obtained by first reading the speed sensor value to obtain the angular velocity.

_{r}). These four inputs provide the quadrature, direct, and zero currents (i

_{q}, i

_{d}, i

_{0}). These are the measured values. The reference Id current is set to zero. This allows the control of q-axis current (torque). The reference iq is obtained by first calculating the error signal of the speed (measure the difference) then place the error signal into a PI regulator (speed regulator). For the FOC of the PMSM design, the output of the regulator is the iq reference. The error signal of the reference iq and the measured iq is calculated. This is then placed into another regulator (current regulator). A similar process for the Id loop is done. Finally, the resultant signals are placed into an inverse transformation block (dq0 to abc). These signals are now the reference voltage for the PWM signals controlling the switching sequence of the inverter. Additionally, space vector pulse width modulation (SVPWM) technique was implemented for this study. It works by obtaining an optimal switching sequence for the inverter switches. This can be obtained by taking the signals into the alpha beta frame of reference [26]. The inverter output voltages are shown in (9).

#### 2.4. LSM Formulas to Generate Specifications

^{2}) is described by Equation (12). Where ‘p’ is the pole pairs, and L

_{i}is the armature stack length.

#### 2.5. Modeling of Battery and Bidirectional Converter

_{s}and K

_{p}are voltage and capacity derating factors which are set to 1.

## 3. Simulation Results

## 4. Experimental Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## Nomenclature

LIM | Linear Induction Motor |

LSM | Linear Synchronous Motor |

PMSM | Permanent Magnet Synchronous Motor |

EMS | Electromagnetic Suspension |

EDS | Electrodynamic Suspension |

POD | Referring to Hyperloop Capsule/Vehicle |

FOC | Field Oriented Control |

SVPWM | Space Vector Pulse Width Modulation |

u_{abc} | Stator a, b, c phase to neutral voltages |

R_{abc} | Stator a, b, c phase resistances |

i_{abc} | Stator a, b, c phase currents |

L_{abc} | Matrix of stator phase self and mutual inductances |

L_{aa}, L_{bb}, L_{cc} | Stator a, b, c phase self-inductances |

M_{ab}, M_{ac}, M_{ba}, M_{bc}, M_{ca}, M_{cb} | Mutual inductances of stator a, b, c phases |

Ψ_{Mabc} | Stator a, b, c phase flux linkages from PMSM |

T_{e} | Electromagnetic Torque |

SOC | State of Charge |

E_{rated} | Rated voltage of battery cell |

Q_{rated} | Rated capacity of battery cell |

R_{battery} | Internal resistance of the battery cell |

N_{p} | Number of cells in parallel of battery pack |

N_{p} | Number of cells in parallel of battery pack |

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**Figure 1.**Block diagram for LSM, adapted from [25].

Symbol | Quantity | Description |
---|---|---|

p | 8 | Poles |

R_{s} | 0.065 | Stator Resistance |

L_{d} | 0.001916 | d-axis inductance |

L_{q} | 0.005 | q-axis inductance |

P_{max} | 50,000 | Max motor power |

n_{max} | 5000 | Maximum rpm |

Parameters | Value | Units |
---|---|---|

Ns No. of cells in series | 70 | cells |

Np No. of cells in parallel | 60 | cells |

E_{rated} Rated voltage | 3.6 | V |

E_{cut} Discharge cut-off voltage | 2.5 | V |

Q_{rated} Rated capacity | 3.35 | Ah |

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**MDPI and ACS Style**

Bhuiya, M.; Aziz, M.M.; Mursheda, F.; Lum, R.; Brar, N.; Youssef, M.
A New Hyperloop Transportation System: Design and Practical Integration. *Robotics* **2022**, *11*, 23.
https://doi.org/10.3390/robotics11010023

**AMA Style**

Bhuiya M, Aziz MM, Mursheda F, Lum R, Brar N, Youssef M.
A New Hyperloop Transportation System: Design and Practical Integration. *Robotics*. 2022; 11(1):23.
https://doi.org/10.3390/robotics11010023

**Chicago/Turabian Style**

Bhuiya, Mohammad, Md Mohiminul Aziz, Fariha Mursheda, Ryan Lum, Navjeet Brar, and Mohamed Youssef.
2022. "A New Hyperloop Transportation System: Design and Practical Integration" *Robotics* 11, no. 1: 23.
https://doi.org/10.3390/robotics11010023