# Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation

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## Abstract

**:**

## 1. Introduction

## 2. Background of the Proposed Solution

## 3. Proposed Sliding-Mode Controller

#### 3.1. Converter Model and Sliding Function Expressions

#### 3.2. Transversality Condition

- Stand-by stage (${i}_{b}=0$): since L and ${v}_{dc}$ are positive quantities, the parameter ${k}_{b}$ must be set as a positive quantity, as reported in (13).$$\begin{array}{c}\hfill \frac{d}{du}\left(\right)open="("\; close=")">\frac{d\mathrm{\Psi}}{dt}=\frac{{k}_{b}\xb7{v}_{dc}}{L}0\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}\left(\right)open="\{"\; close>\begin{array}{c}{i}_{b}=0\hfill \\ {k}_{b}0\hfill \end{array}\end{array}$$
- Charging stage (${i}_{b}<0$): since L, C, ${v}_{dc}$ and ${k}_{b}$ are positive quantities, the parameter ${k}_{p}$ must be set as a negative quantity, as reported in (14).$$\begin{array}{c}\hfill \frac{d}{du}\left(\right)open="("\; close=")">\frac{d\mathrm{\Psi}}{dt}=\frac{{k}_{b}\xb7{v}_{dc}}{L}+\frac{{k}_{p}\xb7{i}_{b}}{C}0\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}\left(\right)open="\{"\; close>\begin{array}{c}{i}_{b}0\hfill \\ {k}_{b}0\hfill \\ {k}_{p}0\hfill \end{array}\end{array}$$
- Discharging stage (${i}_{b}>0$): since L, C, ${v}_{dc}$ and ${k}_{b}$ are positive quantities, the parameter ${k}_{p}$ must fulfill the constraint presented in (15) to ensure the positive sign of the transversality.$$\begin{array}{c}\hfill \frac{d}{du}\left(\right)open="("\; close=")">\frac{d\mathrm{\Psi}}{dt}0\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}\left(\right)open="\{"\; close>\begin{array}{c}{i}_{b}0\hfill \\ {k}_{b}0\hfill \\ {k}_{p}-\frac{C}{L}\xb7\frac{{v}_{b}}{{i}_{b}}\hfill \end{array}\end{array}$$

#### 3.3. Reachability Conditions

#### 3.4. Equivalent Control

#### 3.5. Summary

## 4. Design of the Sliding-Mode Dynamics

#### 4.1. Selection of the Type of Dynamic Response

#### 4.2. Design of the Maximum Overshoot

#### 4.3. Design of the Settling Time

#### 4.4. Calculation of Parameters ${k}_{p}$ and ${k}_{i}$

#### 4.5. Summary

- Based on the load voltage requirements, define the maximum overshoot $\Delta {v}_{dc}$ and settling time ${t}_{s}$ (also specify the settling time band $\u03f5$).
- The parameter ${k}_{b}$ must be adapted continuously based on (32).
- Calculate the pole ${P}_{1}$ by solving (48) to provide the desired settling time ${t}_{s}$ for the band $\u03f5$.

## 5. Implementation and Operation Analysis

#### 5.1. Control Law and Switching Circuit

#### 5.2. Synthesis of the Sliding Function

#### 5.3. Speed Limitation under Perturbations

## 6. Design Example and Simulation Results

- Bus current step from 0 A to 1 A (5 ms): the bus voltage deviation produced under the control of the new solution is only $16\%$ of the deviation produced under the control of the solution in [15].
- Bus current step from 1 A to 0 A (10 ms): the bus voltage deviation produced under the control of the new solution is only $6\%$ of the deviation produced under the control of the solution in [15].
- Bus current step from 0 A to $-1$ A (15 ms): the bus voltage deviation produced under the control of the new solution is only $5\%$ of the deviation produced under the control of the solution in [15].
- Bus current step from $-1$ A to 2 A (20 ms): the bus voltage deviation produced under the control of the new solution is only $33\%$ of the deviation produced under the control of the solution in [15].

## 7. Experimental Validation

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Simulation of the controller presented in [15].

**Figure 5.**Proposed structure of a sliding-mode controller with improved disturbance rejection for the charger/discharger.

**Figure 8.**Simulation of ${G}_{dc}\left(s\right)$ for $m=0.0765$ to ensure that $\Delta {v}_{dc}=5\%$.

**Figure 10.**Simulation of ${G}_{dc}\left(s\right)$ with values of ${P}_{1}$ to ensure that ${t}_{s}=3$ ms for a settling time band $\u03f5=2\%$.

**Figure 11.**Switching circuit implementing the control law in (51).

**Figure 17.**Simulation of both the proposed SMC and the SMC without measuring ${i}_{dc}$ presented in [15].

**Figure 19.**Experimental platform. (

**a**) Schematic diagram of the experimental platform; (

**b**) Experimental devices.

**Figure 20.**Experimental results for 1 A steps in the bus current. (

**a**) DC bus voltage regulation with the SMC reported in [15]; (

**b**) DC bus voltage regulation with the proposed SMC.

$\mathbf{\Delta}{\mathit{v}}_{\mathit{dc}}$ | m | ${\mathit{P}}_{\mathbf{1}}$ | ${\mathit{P}}_{\mathbf{2}}$ |
---|---|---|---|

$5\%$ | 13.0719 | $473.7$ rad/s | $6192.2$ rad/s |

$7\%$ | 7.8128 | $664.4$ rad/s | $5190.8$ rad/s |

$9\%$ | 4.9373 | $847.1$ rad/s | $4182.4$ rad/s |

$11\%$ | 3.0858 | $1057.6$ rad/s | $3263.5$ rad/s |

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**MDPI and ACS Style**

Serna-Garcés, S.I.; González Montoya, D.; Ramos-Paja, C.A.
Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation. *Energies* **2018**, *11*, 594.
https://doi.org/10.3390/en11030594

**AMA Style**

Serna-Garcés SI, González Montoya D, Ramos-Paja CA.
Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation. *Energies*. 2018; 11(3):594.
https://doi.org/10.3390/en11030594

**Chicago/Turabian Style**

Serna-Garcés, Sergio Ignacio, Daniel González Montoya, and Carlos Andrés Ramos-Paja.
2018. "Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation" *Energies* 11, no. 3: 594.
https://doi.org/10.3390/en11030594