# Sensorless Control for DC–DC Boost Converter via Generalized Parameter Estimation-Based Observer

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## Abstract

**:**

## 1. Introduction

_{∞}control [16] and backstepping control [17]. It is noted that the abovementioned results focus on the full-information feedback control scheme. That is, it should be supposed that all of the states can be measured. However, the current sensors and their processing circuits cause extra hardware costs, delays and noise in the system. They can also harm the reliability of the power system. Therefore, current sensorless control techniques can provide cost-effective and reliable solutions for various boost converter applications.

- A PI-PBC is proposed to stabilize a DC–DC boost converter with exponential stability.
- A GPEBO is constructed to estimate the inductor current. It is noted that the FTC of this observer is ensured and a very weak persistence of excitation (PE) condition is needed. Moreover, this result can be easily extended to a large class of converters.
- The experimental results are given to assess the performance of the proposed sensorless control law.

## 2. System Model and Problem Formation

#### 2.1. Model of DC–DC Boost Converter with CPL

**Remark**

**1.**

#### 2.2. Problem Formulation

- F1.
- The estimate of the state i can converge to its real value with the FTC. That is,$$\begin{array}{c}\hfill \widehat{i}\left(t\right)=i\left(t\right),\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall t>{t}_{c}\end{array}$$
- F2.
- $({i}_{\star},{v}_{\star})$ is an exponentially stable equilibrium of the closed-loop system. Namely, for all initial conditions, the following claim is achieved with the estimate $\widehat{i}$.$$\underset{\infty}{lim}v\left(t\right)={v}_{\star},$$

## 3. Sensorless Controller Design

- It is supposed that the state i is measured. The full-information PI-PBC is designed.
- A GPEBO is devised to estimate the current with FTC.
- By combining the PI-PBC and GPEBO, a sensorless control scheme is achieved.

#### 3.1. PI-PBC Design

**Proposition**

**1.**

**Proof.**

**Remark**

**2.**

#### 3.2. GPEBO Design

**Assumption**

**1.**

**Proposition**

**2.**

**Proof.**

#### 3.3. Observer-Based PI-PBC

**Proposition**

**3.**

**Proof.**

**Remark**

**3.**

## 4. Simulation Results

#### 4.1. Scenario 1: Tracking Performance Test

#### 4.2. Scenario 2: GPEBO Performance Test

#### 4.3. Scenario 3: Robustness Performance Test

#### 4.4. Scenario 4: Phase Portrait

## 5. Experimental Result

## 6. Conclusions and Future Work

- Although the proposed controller is insensitive to the perturbations of the circuit parameters including $L,C,E$, the implementation of the designed GPEBO depends on the exact knowledge of these parameters.
- In this paper, a full-order GPEBO is proposed to estimate two states. In fact, the state ${x}_{2}$ can be measured. Hence, to avoid the heavy computation task in digital signal processors, a reduced-order observer is desired to only reconstruct the state ${x}_{1}$. This does not mean that the full-order GPEBO is useless. Indeed, the estimate ${\widehat{x}}_{2}$ can be used to view the performance of the power system. An alternative method is still needed to suit different application scenarios.
- The proposed method can deal with the sensorless control problem of boost converters with resistance load. However, the constant power load (CPL) exists in many practical applications.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The application cases of a boost converter in a power system. (

**a**) Battery-power system, (

**b**) wound rotor asynchronous motor system, (

**c**) wind generator system, (

**d**) solar cell system.

**Figure 4.**Boost converter transient under the proposed sensorless controller. (

**a**) Output voltage v, (

**b**) estimated current $\widehat{i}$, (

**c**) duty ratio d.

**Figure 5.**Response curves of boost converter under the proposed sensorless controller with different references. (

**a**) Output voltage v, (

**b**) estimated current $\widehat{i}$, (

**c**) duty ratio d.

**Figure 6.**Transient of GPEBO with different $\gamma $. (

**a**) estimated current $\widehat{i}$, (

**b**) estimation error.

**Figure 7.**Response curves of boost converter with a step change in R. (

**a**) Output voltage v, (

**b**) estimated current $\widehat{i}$, (

**c**) estimation error.

**Figure 8.**The phase portrait of closed-loop system. The black point is the equilibrium. The red lines are the state trajectories.

**Figure 10.**Response curves of boost converter under the proposed sensorless controller (experiment). (

**a**) Output voltage v, (

**b**) estimated current i, (

**c**) duty ratio d.

Parameter | Symbol (Unit) | Value |
---|---|---|

Input voltage | $E\phantom{\rule{3.33333pt}{0ex}}\left(\mathrm{V}\right)$ | 6 |

Reference output voltage | ${x}_{2\star}\left(\mathrm{V}\right)$ | 12 |

Gain | ${x}_{2\star}/E$ | 2 |

Resistance | $R\phantom{\rule{3.33333pt}{0ex}}\left(\mathsf{\Omega}\right)$ | 100 |

Inductance | $L\phantom{\rule{3.33333pt}{0ex}}\left(\mathrm{mH}\right)$ | 5 |

Capacitance | $C\phantom{\rule{3.33333pt}{0ex}}\left(\mathsf{\mu}\mathrm{F}\right)$ | 680 |

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**MDPI and ACS Style**

Zhang, X.; Martinez-Lopez, M.; He, W.; Shang, Y.; Jiang, C.; Moreno-Valenzuela, J. Sensorless Control for DC–DC Boost Converter via Generalized Parameter Estimation-Based Observer. *Appl. Sci.* **2021**, *11*, 7761.
https://doi.org/10.3390/app11167761

**AMA Style**

Zhang X, Martinez-Lopez M, He W, Shang Y, Jiang C, Moreno-Valenzuela J. Sensorless Control for DC–DC Boost Converter via Generalized Parameter Estimation-Based Observer. *Applied Sciences*. 2021; 11(16):7761.
https://doi.org/10.3390/app11167761

**Chicago/Turabian Style**

Zhang, Xiaoyu, Mizraim Martinez-Lopez, Wei He, Yukai Shang, Chen Jiang, and Javier Moreno-Valenzuela. 2021. "Sensorless Control for DC–DC Boost Converter via Generalized Parameter Estimation-Based Observer" *Applied Sciences* 11, no. 16: 7761.
https://doi.org/10.3390/app11167761