#
Elimination of Chattering by Control Strategy Based on the Multiphase Sliding Model Control for Efficient Power Conversion in a DC-DC Circuit^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Sliding Mode Control

_{ref}is the reference current and I

_{L}is the Inductor current.

_{in}is the input voltage, V

_{c}is the capacitor voltage, and u is the control input.

- u is the system input and has a definition of –M sign($\mathsf{\sigma}$).
- $\sigma $ is the selected slide manifold of the system.
- M is the positive constant.

_{1}and s

_{2}are switching surfaces for each phase.

## 3. Simulation and Experimental Results

#### 3.1. Simulation

_{1}) and sign(s

_{2}) are different, the rising edge and falling edge of the hysteresis of s

_{2}will be formed. The velocity of the ramp signal based on the given the state–space equations of a two-phase boost converter above would be $\frac{{V}_{out}}{L}$, where s

_{n}is the n-th inductor current slide surface.

_{1}= i

_{L}

_{1}− i

_{Lref}/2

s

_{2}= i

_{L}

_{2}− i

_{Lref}/2

_{1}) and sign(s

_{2}) are identical, then the velocity of s

_{2}* would be zero.

_{1}equals the sign of s

_{2}.

_{1}) and sign(s

_{2}) are different, for example, sign(s

_{1}) equals +1, and sign(s

_{2}) equals −1, then;

_{1}) equals +1 and sign(s

_{2}) equals −1, then;

_{s}. The changes in the hysteresis of s

_{2}* could be easily seen.

_{L1}means the inductor current of the first switching phase.

#### 3.2. Experiment

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Proof of the convergence of the two-dimension control. The initial condition s

_{k}

_{−1}= 1, s

_{k}= 0. The control frequency = 10 kHz.

**Figure 11.**1/4 T

_{s}of the phase error of the inductor currents (upper) and s

_{2}* sliding surface (lower).

**Figure 13.**Forty-five percent of the phase error. Two inductor currents (upper) and s

_{2}* sliding surface (lower).

**Figure 14.**Forty-five percent of the phase error. Two gate signals (upper) and difference of the gate signals (lower).

Three-Phase Boost Mode | |
---|---|

Components | Parameters |

${V}_{in}$ | 10 V |

${V}_{out}$ | 20 V |

L | 1 mH |

${R}_{load}$ | 20 Ω |

${f}_{s}$ | 5 kHz |

M | 1 |

$\alpha $(3 phases) | 0.6667 |

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**MDPI and ACS Style**

Na, W.; Chen, P.; Kim, J.
Elimination of Chattering by Control Strategy Based on the Multiphase Sliding Model Control for Efficient Power Conversion in a DC-DC Circuit. *Energies* **2017**, *10*, 1389.
https://doi.org/10.3390/en10091389

**AMA Style**

Na W, Chen P, Kim J.
Elimination of Chattering by Control Strategy Based on the Multiphase Sliding Model Control for Efficient Power Conversion in a DC-DC Circuit. *Energies*. 2017; 10(9):1389.
https://doi.org/10.3390/en10091389

**Chicago/Turabian Style**

Na, Woonki, Pengyuan Chen, and Jonghoon Kim.
2017. "Elimination of Chattering by Control Strategy Based on the Multiphase Sliding Model Control for Efficient Power Conversion in a DC-DC Circuit" *Energies* 10, no. 9: 1389.
https://doi.org/10.3390/en10091389