# Direct Instantaneous Torque Control of SRM Based on a Novel Multilevel Converter for Low Torque Ripple

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## Abstract

**:**

## 1. Introduction

## 2. Conventional DITC for SRM

#### 2.1. Asymmetrical Half-Bridge Converter

#### 2.2. Conventional DITC System and Control Method for SRM

_{on_b}) of phase B (following phase) and the maximum inductance (θ

_{a}) of phase A (preceding phase), where the inductances of both phases A and B are rising, and two phases together produce positive torque required by the motor. The single-phase conduction region is between the θ

_{a}and the turn-on angle (θ

_{on_c}) of phase C. In this region, phase A enters the falling inductance region, and phase B remains in the rising inductance region, hence phase B alone provides positive torque.

_{H}, −T

_{L}, 0, T

_{L}, and T

_{H}) are defined based on its value The solid and dashed arrows represent the transfer direction of the torque error. During the operation of the DITC system, the torque hysteresis controller selects different operating states to adjust each phase torque based on rotor position, torque error, and transfer direction of torque error in order to make synthesized torque follow the reference torque.

_{k}is phase torque, i

_{k}is phase current, and L

_{k}is phase inductance. Based on the torque expression, since the current and inductance of each phase winding in the commutation region constantly change, it is difficult to maintain a constant synthesized torque using a single control strategy.

_{H}. At the end of commutation, the following phase experiences an increase in the change rate of inductance; at this point, the inductance of the preceding phase is still increasing, which leads to excess output torque due to its slow current decrease, causing the torque error to exceed −T

_{H}significantly. In addition, the current tailing of the preceding phase enters the falling inductance region, resulting in the generation of negative torque; since the negative torque needs to be compensated by the positive torque in the single-phase conduction region, the efficiency of the motor is reduced.

## 3. Novel Multilevel Converter

_{DC}+ U

_{C2}) equals the sum of the C2 voltage and DC voltage. The bus connected to the positive terminal of the power supply is called the DC bus.

_{A1}is off, S

_{A2}and S

_{A3}are on, and the winding operates in the +1 state; compared with the +2 state, the current is increased slowly, and the conduction path is shown in Figure 7b. When S

_{A1}and S

_{A2}are off, S

_{A3}is on, the winding operates in the 0 state, and the conduction path is shown in Figure 7c. When all switching devices in the A-phase bridge arm are off, the winding operates in the −2 state, and the current can be decreased more quickly. The conduction path is shown in Figure 7d.

## 4. DITC for SRMs with the Novel Multilevel Converter

_{on}, θ

_{off}, and θ

_{h}. ΔT is the error in T

_{ref}and T

_{est}; T

_{ref}is gained from the speed controller, and T

_{est}is determined by using a lookup table in the torque calculation unit. θ is the rotor position, θ

_{on}is the turn-on angle, and θ

_{off}is the turn-off angle. θ

_{h}is defined as the control angle that maintains the voltage stability of the high-voltage bus, and [θ

_{on}, θ

_{h}] is defined as the region where +2 is used. For the three-phase 12/8 SRM, θ

_{h}is located between [θ

_{on}, θ

_{on}+ 15°] and is determined by the boost voltage controller according to U

_{C2}, V

_{ref}, θ

_{on}, and θ. U

_{C2}is the instantaneous voltage of C2, and V

_{ref}is the reference voltage of C2. During the operation of the novel DITC system, the torque hysteresis controller determines the operating state for each phase winding based on θ

_{on}, θ

_{off}, θ

_{h}, ΔT, and θ. Then, the switch table generates the drive signal for the converter, and the converter operates to realize the DITC for the SRM.

#### 4.1. Torque Hysteresis Control Strategy with the Novel Multilevel Converter

_{h}. θ

_{h}is between [θ

_{on_b}, θ

_{on_c}], +n is +2 within [θ

_{on_b}, θ

_{h}], and +n is +1 within [θ

_{h}, θ

_{on_c}], as shown in Figure 12 from the implementation waveform of the novel control strategy.

_{L}). Since phase A has a higher torque output capacity per ampere of current and the total electromagnetic torque is primarily available from phase A, this is conducive to improving the torque response speed and electromechanical conversion efficiency of the system. Phase B increases current preferentially in the +2 state, which allows the current in the following phase of the commutation region to build up more quickly than with the AHBC. When the output torque needs to be further reduced, i.e., ΔT decreases to −T

_{L}along the negative horizontal axis, phase B enters the 0 state and reduces the output torque together with phase A. If ΔT continues to decrease along the horizontal axis to −T

_{H}, phase A enters the −2 state and rapidly reduces the output torque. While ΔT returns to zero along the positive horizontal axis, phase B returns to the excitation state.

_{L}). Since phase B has a higher torque output capacity per ampere of current and the total electromagnetic torque is primarily available from phase B, this is conducive to improving the torque response speed and electromechanical conversion efficiency of the system. When ΔT decreases to −T

_{H}along the negative horizontal axis, phase B is in the −2 state to rapidly reduce the output torque. Phase A enters the −2 state in Region II to reduce the current tailing and avoid generating negative torque, which allows the current in the preceding phase of the commutation region to decrease to zero more quickly than with the AHBC.

_{L}↔ T

_{L}). If ΔT decreases to −T

_{H}along the negative horizontal axis, phase B is in the −2 state to rapidly reduce the output torque.

#### 4.2. Stability Control of the High-Voltage Bus Voltage

_{C2}and U

_{DC}. Under the condition that U

_{DC}remains stable and its ripple is small, the stability of the high-voltage bus voltage mainly depends on the stability of U

_{C2}. In this article, the stable control of the high-voltage bus voltage is realized by the boost voltage controller, and its structure is presented in Figure 13. The U

_{C2}is collected by the voltage transducer (VT) and is calculated by the average voltage calculation unit based on θ

_{on}and θ to obtain V

_{av}; as shown in Figure 12, V

_{av}is the average voltage of C2 in T

_{t}. Additionally, the controller adjusts the error between V

_{av}and V

_{ref}by PI, limits the amplitude, and outputs θ

_{h}. The balance between discharging and charging of C2 in T

_{t}is controlled to achieve stable control of the high-voltage bus voltage.

#### 4.3. Optimization of Control Parameters

_{K}and W

_{E}are the weighting factors for torque ripple and drive efficiency, respectively. At each torque-speed point (ω, T

_{ref}), K

_{min}is the minimum torque ripple, and E

_{max}is the maximum drive efficiency. K is represented by the following formula:

_{max}is the maximum torque, T

_{min}is the minimum torque, and T

_{av}is the average torque. E is represented by the following formula:

_{in}, P

_{out}, ω, U

_{DC}, and I

_{av}are the input power, output power, rotor angular velocity, DC voltage, and average current, respectively.

_{on}and θ

_{off}, as shown in the following formula:

_{off}is set to 15° (θ

_{off}(min)). The following phase should be turned on before the preceding phase turns off, so there is a minimum conduction angle of 15° (θ

_{c}(min)). The current of the preceding phase enters the falling inductance region after 22.5° and produces negative torque, so the maximum θ

_{off}should be set and maintained at a certain margin. In this analysis, the maximum θ

_{off}is set at 21° (θ

_{off}(max)). In addition, the minimum and maximum values of θ

_{on}are set to −5° (θ

_{on}(min)) and 5° (θ

_{on}(max)), the minimum and maximum values of T

_{ref}are set to 1 N·m (T

_{ref}(min)) and 5 N·m (T

_{ref}(max)), and the minimum and maximum values of ω are set to 250 r/min (ω (min)) and 1750 r/min (ω (max)). At the end of the search for each operating point, K

_{min}and E

_{max}are found in the output results, and then the optimal θ

_{on}and θ

_{off}are gained by calculating the objective function. In this article, torque ripple suppression is the primary objective, and improving the system efficiency is the secondary objective. Thus, W

_{K}is 0.6 and W

_{E}is 0.4. Figure 15 shows the optimized results for θ

_{on}and θ

_{off}gained by the search algorithm, which is used to establish a lookup table for optimal control of the SRM.

## 5. Simulation Analysis

## 6. Experimental Verification

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Conventional torque hysteresis control strategy: (

**a**) control strategy in the commutation region; (

**b**) control strategy in the single-phase conduction region.

**Figure 11.**Novel torque hysteresis control strategy in each region: (

**a**) Region Ⅰ; (

**b**) Region Ⅱ; (

**c**) Region Ⅲ.

**Figure 12.**Implementation waveforms with the novel torque hysteresis control strategy in one-third of the electrical cycle.

**Figure 15.**Optimization results for θ

_{on}and θ

_{off}: (

**a**) optimized θ

_{on}; (

**b**) optimized θ

_{off}.

Motor Parameters | Values |
---|---|

Number of stator/rotor poles | 12/8 |

Rated voltage | 295 V |

Rated power | 1.1 kW |

Rated speed | 2000 r/min |

Rated load | 5.25 N·m |

Speed (r/min) | Load (N·m) | K (Conventional DITC) (%) | K (Novel DITC) (%) |
---|---|---|---|

250 | 2 | 23.3 | 23.2 |

500 | 2 | 24.1 | 23.2 |

750 | 2 | 27.6 | 23.4 |

1000 | 2 | 28.1 | 25.1 |

1250 | 2 | 29.3 | 25.5 |

1500 | 2 | 31.6 | 25 |

1750 | 2 | 47 | 26.2 |

Speed (r/min) | Load (N·m) | K (Conventional DITC) (%) | K (Novel DITC) (%) |
---|---|---|---|

250 | 5 | 22.6 | 20.4 |

500 | 5 | 27.6 | 22 |

750 | 5 | 30.3 | 23.2 |

1000 | 5 | 32.7 | 23.7 |

1250 | 5 | 34.4 | 25.6 |

1500 | 5 | 42.8 | 27.8 |

1750 | 5 | 73.7 | 36.3 |

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## Share and Cite

**MDPI and ACS Style**

Cai, Y.; Dong, Z.; Liu, H.; Liu, Y.; Wu, Y.
Direct Instantaneous Torque Control of SRM Based on a Novel Multilevel Converter for Low Torque Ripple. *World Electr. Veh. J.* **2023**, *14*, 140.
https://doi.org/10.3390/wevj14060140

**AMA Style**

Cai Y, Dong Z, Liu H, Liu Y, Wu Y.
Direct Instantaneous Torque Control of SRM Based on a Novel Multilevel Converter for Low Torque Ripple. *World Electric Vehicle Journal*. 2023; 14(6):140.
https://doi.org/10.3390/wevj14060140

**Chicago/Turabian Style**

Cai, Yan, Zhongshan Dong, Hui Liu, Yunhu Liu, and Yuhang Wu.
2023. "Direct Instantaneous Torque Control of SRM Based on a Novel Multilevel Converter for Low Torque Ripple" *World Electric Vehicle Journal* 14, no. 6: 140.
https://doi.org/10.3390/wevj14060140