# An Intelligent Adaptive Neural Network Controller for a Direct Torque Controlled eCAR Propulsion System

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## Abstract

**:**

## 1. Introduction

## 2. Components of an eCAR Powertrain

#### 2.1. Battery Model

_{int}represents the internal resistance, V

_{oc}is the open circuit voltage of the battery, I is the current, E is the energy source and V

_{term}is the terminal voltage of the battery.

_{oc}is 690 Volts and R

_{int}is 0.1 Ohms. Equations (1a) and (1b) denote the power and power loss of the battery, respectively.

#### 2.2. Motor Model

#### 2.3. Glider Model

_{i}is the inertial mass that also accounts for the rotating inertia. Accordingly, m

_{i}, is faintly more than the actual (~4%). The force due to aerodynamic drag is computed by Equation (13):

_{d}is the air drag coefficient, A

_{f}is the frontal area and V represents velocity.

_{rr}is the rolling coefficient, m defines the mass and g represents the gravitational force.

_{1}, B

_{1}, C

_{1}are specific for each eCAR configuration and analogous to the standards originating in the Environmental Protection Agency (EPA). All of these forces sum up to the total tractive effort represented by Equation (18):

_{TR}is the tractive force. The expression for acceleration is obtained from Equations (12) and (18) as in Equation (19). The vehicle parameters are depicted in Table 2.

#### 2.4. Driver Model

_{p}, is 300 and the integral constant, k

_{i}, is 500.

## 3. Direct Torque Controlled eCAR

_{r}*, is compared with the actual angular speed, ω

_{r}, calculated with the help of an adaptive motor model block. The obtained speed error is given as an input to the speed controller or driver model, which produces reference torque magnitude, T

_{e}*. The reference torque is compared with the actual torque, T

_{e}, generated by the adaptive motor model and processed through the torque controller that produces the reference slip speed ω

_{sl}*.

_{e}*. The direct and quadrature axis reference voltages are calculated by the reference voltage vector calculator (RVVC) using Equation (20).

_{seq}

^{2}is the root mean square (RMS) value of stator flux ripple of a particular sequence and V

_{ref}is reference voltage vector at an angle α. Considering these two vectors as inputs, the magnitude and position of the reference voltage vector are calculated according to the set value of γ. The SVPWM block generates gating pulses to the inverter based on the space vector approach. The inverter voltage amplitude and frequency are varied in such a way as to achieve the desired speed [14,15].

## 4. ANN Controller

_{sl}and is shown in Figure 10. The MATLAB Simulink model of a developed ANN structure with two inputs, a hidden layer and one output is shown in Figure 11.

_{err}’ and the change in torque error ‘∆_Te

_{rr}’ data. The parameters of the ANN are tabulated in Table 3. The network output is used to tune the torque controller with the input layer and the hidden layer as a hyperbolic tangent sigmoid transfer function and the output layer as a pure line transfer function where weights and bias values are updated corresponding to the Levenberg–Marquardt optimization algorithm [17,18]. The ANN algorithm is elaborated in the following steps:

- Step 1: Firstly, torque error and the change in torque error are given as inputs to the network. The input vector matrix is given by [X] 2 × 1 with two inputs.
- Step 2: Subsequently, the targets are chosen in order to attain the desired variables of the network. The target vector matrix is given by [t] 1 × 1 with one output.
- Step 3: The weights and biases are then initialized and are updated corresponding to Levenberg–Marquardt optimization algorithm. The output vector matrix is given by [y] where [w]° and [b]° are the weights and biases row matrices, respectively.
- Step 4: The ANN is trained by using the data provided in Step 1 and Step 2, respectively, and by fixing the goal parameter to a minimum. The error data in the form of an error vector matrix (E) is generated to confirm that the desired convergence of the specified goal parameters or epochs during training has been met then training stops.$$\mathrm{E}=\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{t}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right)}^{2}}{\mathrm{I}}$$
- Step 5: After the training the network, the optimized value of the steady state error as the output is yielded.
- Step 6: The optimized steady state error output is applied as the input to the PI controller in order to produce the slip speed.

^{−7}which is accurate and is termed to be zero. The network is developed by typing “nntool” into the MATLAB command window. The Simulink model is generated using the command “genism(network)” and is shown in Figure 12 Subsystems of the neural network are shown in Figure 13, Figure 14 and Figure 15, respectively [19]. Table 5 depicts conventional and the ANN controller parameters.

## 5. Simulation Analysis of an eCAR

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 17.**The performance of an eCAR with a conventional torque controller and an ANN tuned PI controller under an ECE (R15) cycle.

**Figure 18.**The performance of an eCAR with a conventional torque controller and an ANN tuned PI controller under a HWFET cycle.

**Figure 19.**The performance of an eCAR with a conventional torque controller and an ANN tuned PI controller under an NYCC cycle.

3Ф, AC Induction Motor | |
---|---|

Motor Power, Pm | 90 kW |

Nominal Voltage, V_{n} | 380 V, RMS |

Current Rating, I_{n} | 200 A |

Variable Frequency, f_{s} | 0–400 Hz |

Constant Power | 90 kW @ 12,000 rpm |

Constant Torque | 120 N-m @ 7200 rpm |

Motor Inertia, J | 1.5 kg-m^{2} |

Stator Resistance, Rs | 0.021 Ohms |

Rotor Resistance, Rr | 0.016 Ohms |

Stator Reactance, Lls | 0.0164 Henry |

Rotor Reactance, Llr | 0.0167 Henry |

Mutual Inductance, Lm | 0.016 Henry |

Number of Poles, P | 4 |

Nominal Stator Flux, ψ_{s} | 0.98 Wb |

Vehicle Dynamics | |
---|---|

Mass of the vehicle, m | 1200 Kg |

Frontal area of the vehicle, A_{f} | 0.2 sq. mt |

Wheel radius, R_{w} | 0.2794 m |

Coefficient of rolling resistance, C_{rr} | 0.0015 |

Air density, $\rho $ | 1.225 Kg/m^{3} |

Air drag coefficient, C_{d} | 0.3 |

Gravitational constant, g | 9.81 Kg/m^{2} |

Transmission gear ratio, G | 6.842 |

Slope or gradient angle, α | 5° |

Constant A | 74.28 |

Constant B | 2.139 |

Constant C | 0.3922 |

Variables | Values |
---|---|

Number of neurons | 40 |

Hidden layer transfer function | Tansig |

Output layer transfer | Purlin |

Activation function | Net sum |

Gradient | 1.1045 × 10^{−6} |

Regression | 0.9897 |

Training sets | 100 |

Testing sets | 50 |

Training method | Levenberg–Marquardt back-propagation |

Optimization function | Mean square error (MSE) |

Learning method | Gradient descent weight and bias |

S. No | Input 1 | Input 2 | Output | Error | Target |
---|---|---|---|---|---|

1 | 0 | 0 | 282.9359 | −282.936 | 0 |

2 | 0.288448 | 9951.406 | 280.8798 | −272.321 | 8.558594 |

3 | −0.13429 | 9506.473 | 290.7358 | −275.806 | 14.9301 |

4 | −0.09254 | 9109.208 | 289.5684 | −270.595 | 18.97366 |

5 | −0.09145 | 8760.206 | 289.3706 | −267.585 | 21.78575 |

6 | 0.676865 | 8492.981 | 270.4763 | −247.518 | 22.95849 |

7 | −0.19752 | 8213.084 | 291.5531 | −266.385 | 25.16803 |

8 | −0.82494 | 7985.73 | 305.1781 | −278.464 | 26.7146 |

9 | −0.57358 | 7827.065 | 299.7575 | −272.655 | 27.10218 |

10 | 1.383714 | 7761.038 | 251.6016 | −226.022 | 25.57983 |

Torque Controller Constants | K_{p} | K_{i} |
---|---|---|

Conventional Controller | 0.2870 | 0.0167 |

ANN Controller | 0.2137 | 0.01 |

Drive Cycle | ECE (R15) | HWFET | NYCC | ||||
---|---|---|---|---|---|---|---|

Parameters | PI | ANN-PI | PI | ANN-PI | PI | ANN-PI | |

Avg torque ripple (Nm) | 28 | 4 | 12 | 2 | 10 | 2 | |

Avg flux ripple (wb) | 0.3 | 0.15 | 0.2 | 0.14 | 0.18 | 0.12 | |

Avg fuel consumption (J) | 120 | 102 | 3250 | 3133 | 250 | 176 | |

Avg output power (kW) | 50 | 48 | 120 | 90 | 145 | 115 |

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**MDPI and ACS Style**

Banda, G.; Kolli, S.G.
An Intelligent Adaptive Neural Network Controller for a Direct Torque Controlled eCAR Propulsion System. *World Electr. Veh. J.* **2021**, *12*, 44.
https://doi.org/10.3390/wevj12010044

**AMA Style**

Banda G, Kolli SG.
An Intelligent Adaptive Neural Network Controller for a Direct Torque Controlled eCAR Propulsion System. *World Electric Vehicle Journal*. 2021; 12(1):44.
https://doi.org/10.3390/wevj12010044

**Chicago/Turabian Style**

Banda, Gururaj, and Sri Gowri Kolli.
2021. "An Intelligent Adaptive Neural Network Controller for a Direct Torque Controlled eCAR Propulsion System" *World Electric Vehicle Journal* 12, no. 1: 44.
https://doi.org/10.3390/wevj12010044