# Research on Linear Active Disturbance Rejection Control in DC/DC Boost Converter

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## Abstract

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## 1. Introduction

## 2. Modeling of DC/DC Boost Converter

_{i}is the input voltage, I

_{L}is the inductive current, U

_{o}is the output voltage, L is the inductance, C is the capacitance, and R is the resistive load.

_{sw}is 10 kHz in this paper, where T =1/f

_{sw}is the switching period, d is the duty cycle, 0 < d < 1 and n = 0, 1, 2…

_{i}charges the inductor L, and the charging current is kept substantially constant. At the same time, the voltage of capacitor C supplies power to load R.

_{i}and the inductor L together charge the capacitor C and supply power to the load resistor.

## 3. Control Method Design

#### 3.1. Cascade Control

_{L}(∞) and U

_{o}(∞) are the steady state values of I

_{L}and U

_{o}, respectively.

_{Lref}and U

_{oref}are reference values of the inductor current and the output voltage, respectively.

_{Lref}is calculated from U

_{oref}, and there are two problems: (1) The relationship between the inductor current and the output voltage is based on the stability of the system. Therefore, it is difficult to ensure the dynamic performance of the output voltage. (2) Since the input voltage U

_{i}and the load resistance R of the DC/DC boost converter are uncertain, the U

_{oref}cannot be obtained directly from the I

_{Lref}. To solve the above problem, a cascade control system is formed by designing an output voltage controller in the front stage of the current controller. The output voltage controller produces an I

_{Lref}by the error between the desired value of the output voltage and output voltage observation.

#### 3.2. Linear Active Disturbance Rejection Control

_{0}is the controlled quantity; ω is external disturbance of the system; G

_{p}is the controlled object; y is the system output; $\widehat{y}$ is the estimated value of system output; $\widehat{f}$ is the estimated value of the total disturbance; k

_{p}is the controller parameter; and b

_{0}is the system gain.

_{1}= y, x

_{2}= f, then

_{o}of the LESO and K

_{p}of the LSEF are designed. By introducing the concept of bandwidth, the setting of L

_{o}and K

_{p}is converted into the observer’s bandwidth ω

_{o}and the controller’s bandwidth ω

_{c}, which simplifies the parameter tuning process.

_{o}, then

_{o}is the bandwidth of observer.

_{c}, where ω

_{c}is the controller bandwidth.

## 4. Controller Design

#### 4.1. Design of Current Controller

_{L}= y

_{1}, d = u

_{1}, then

_{1}is the system output, u

_{1}is the system input, and ${f}_{1}=\frac{{U}_{i}}{L}-\frac{{U}_{o}}{L}=\frac{{U}_{i}-{U}_{o}}{L}$ is the total disturbance of the system.

_{1}= y

_{1}, x

_{2}= f

_{1}, then

_{o1}and K

_{1}is converted to the tuning of the observer bandwidth ω

_{o1}and the controller bandwidth ω

_{c1}. All poles of the observer are configured to −ω

_{o1}, and all poles of the controller are configured to −ω

_{c1}.

#### 4.2. Design of Voltage Controller

_{o}= y

_{2}, I

_{L}= u

_{2}, then

_{2}is the system output, u

_{2}is the system input, and ${f}_{2}=-\frac{{y}_{2}}{RC}$ is the total disturbance of the system.

_{1}= y

_{2}, x

_{2}= f

_{2}, then

_{o2}and K

_{2}tuning is converted to the tuning of the observer bandwidth ω

_{o2}and the controller bandwidth ω

_{c2}. All poles of the observer are configured to −ω

_{o2}, and all poles of the controller are configured to −ω

_{c2}.

#### 4.3. System Stability Analysis

_{p}(s) is shown in Figure 5.

_{p}(s) is −16.3 deg and the amplitude margin is −33.6 dB. According to the stability criterion of closed-loop control system, the system is unstable.

_{ref}is the reference voltage of the voltage loop, $\Delta $I

_{ref}is the reference current of the current loop, and $\Delta $U

_{o}is the output voltage. The LADRC voltage outer loop is composed of H

_{1}(s) and G

_{c1}(s), and the LADRC current inner loop is composed of H

_{2}(s) and G

_{c2}(s). G

_{p1}(s) is the transfer function of the controlled quantity to the output voltage, and G

_{p2}(s) is the transfer function of the controlled quantity to the inductor current.

_{p1}(s) and G

_{p2}(s) transfer functions are obtained by the DC/DC boost circuit small signal model.

_{o}is

_{L}is

_{p}(s) is 53.7 deg and the amplitude margin is 38 dB. According to the stability criterion of the closed-loop control system, the closed-loop control system satisfies the stability characteristic, and the stability margin of system is excellent.

## 5. Simulation Results

**Case 1:**The converter input voltage was changed to examine the stabilization performance. At the beginning, the output voltage was regulated at 24 V with a 50 Ω resistance load. At 0.6 s, the input voltage of the converter was reduced from 12 V to 10 V. The voltage response is shown in Figure 8; the converter is controlled by LADRC cascade, the output voltage drops from 24 V at 23.6 V and reaches the desired value after 0.05 s. In contrast, the converter is controlled by PI cascade, the output voltage drops from 24 V to 23.3 V, and it takes 0.25 s to reach the desired value. The converter controlled by the proposed method can respond immediately and achieve the desired effect. At the same time, a longer response time and a large voltage deviation can be observed under the PI controller. The current response is shown in Figure 9; by further observing the change of the inductor current, both the LADRC control and the PI control can quickly reach the desired value, but the current shock of the PI control is larger than proposed method.

**Case 2:**To further validate the proposed control method, the changes of the input voltage were doubled. The basic setting was identical with the Case 1. Firstly, the output voltage was regulated at 24 V, and a 50 Ω resistance was connected to the DC bus. At 0.6 s, the input voltage of the converter was reduced from 12 V to 8 V. The output voltage response is shown in Figure 10; the converter is controlled by LADRC cascade, the output voltage drops from 24 V at 23.2 V and reaches the desired value after 0.07 s. In contrast, the converter is controlled by PI cascade, the output voltage drops from 24 V to 22.6 V, and it takes 0.28 s to reach the desired value. The current response is shown in Figure 11; the verification results are consistent with the results of Case 1.

**Case 3:**For load changes, the proposed control method was verified by Case 3. Initially, the output voltage was stable at 24 V and a 50 Ω resistance is connected. Then, the resistance decreased to 25 Ω in 0.6 s. The output voltage response is shown in Figure 12. With the same load change, the voltage deviation of PI control is 2.6 V and the recovery process is 0.35 s. The recovery process of the proposed control algorithm is 0.1 s, which is shorter than the recovery process of PI control by 0.25 s. Simulation results show that the proposed control algorithm has good dynamic performance. In addition, the output current response is shown in Figure 13; by observing changes of the inductor current, LADRC control can quickly reach the desired value, while PI control takes a long time to reach the desired value.

## 6. Hardware Experiment

_{c1}, ω

_{o1}, ω

_{c2}, ω

_{o2}, k

_{p1}, k

_{i1}, k

_{p2}and k

_{i2}were redesigned as 33, 160, 300, 900, 0.03, 1, 0.05 and 2.

## 7. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Symbols | Description |

DC | direct current |

AC | alternating current |

LADRC | linear active disturbance rejection control |

LSEF | linear state error feedback |

LESO | linear extended state observer |

ADRC | active disturbance rejection control |

NLSEF | nonlinear state error feedback |

ESO | extended state observer |

TD | tracking differentiator |

PD | proportional-derivative |

PWM | pulse width modulation |

U_{i} | input voltage of DCDC boost converter |

U_{o} | output voltage of DCDC boost converter |

I_{L} | inductor current |

L | inductance value |

C | capacitance value |

R | resistive load |

f_{sw} | switching frequency |

T | switching period |

d | duty cycle |

μ(t) | pulse function |

U_{o}(∞) | the steady state values of U_{o} |

I_{L}(∞) | the steady state values of I_{L} |

U_{oref} | reference value of output voltage |

I_{Lref} | reference value of inductor current |

r | first-order LADRC input reference |

u_{0} | controlled quantity |

ω | external disturbance of the system |

G_{p} | controlled object |

y | system output |

$\widehat{y}$ | estimated value of system output |

f | total disturbance of the system |

$\widehat{f}$ | estimated value of the total disturbance |

b_{0} | system gain |

K_{p} | gain of LSEF |

L_{o} | gain of LESO |

ω_{o} | observer’s bandwidth |

ω_{c} | controller’s bandwidth |

D | 1-d |

G_{p}(s) | transfer function of the DC/DC boost converter |

$\Delta $U_{ref} | reference voltage of the voltage loop |

$\Delta $I_{ref} | reference current of the current loop |

$\Delta $U_{o} | output voltage |

H_{1}(s), G_{c1}(s) | transfer function of LADRC voltage outer loop |

H_{2}(s), G_{c2}(s) | transfer function of LADRC current inner loop |

G_{p1}(s) | transfer function of the $\Delta $d to $\Delta $U_{o} |

G_{p2}(s) | transfer function of the $\Delta $d(t) to the $\Delta $I_{L} |

G_{1}(s) | transfer function of the inner loop current loop |

G_{0}(s) | system open loop transfer function |

ω_{c1}, ω_{o1}, b_{1} | LADRC parameters of current control loop |

ω_{c2}, ω_{o2}, b_{2} | LADRC parameters of voltage control loop |

k_{p1}, k_{i1} | PI parameters of voltage control loop |

k_{p2}, k_{i2} | PI parameters of current control loop |

## References

- Dragicevic, T.; Lu, X.; Vasquez, J.; Guerrero, J. DC Microgrids–Part I: A Review of Control Strategies and Stabilization Techniques. IEEE Trans. Power Electron.
**2016**, 31, 4876–4891. [Google Scholar] [CrossRef] - El-Shahat, A.; Sumaiya, S. DC-Microgrid System Design, Control, and Analysis. Electronics
**2019**, 8, 124. [Google Scholar] [CrossRef] - Baranwal, M.; Askarian, A.; Salapaka, S.; Salapaka, M. Distributed Architecture for Robust and Optimal Control of DC Microgrids. IEEE Trans. Ind. Electron.
**2018**. [Google Scholar] [CrossRef] - Kakigano, H.; Nishino, A.; Ise, T. Distribution Voltage Control for DC Microgrids Using Fuzzy Control and Gain-Scheduling Technique. IEEE Trans. Power Electron.
**2013**, 28, 2246–2258. [Google Scholar] [CrossRef] - Shenai, K.; Shah, K. Smart DC micro-grid for efficient utilization of distributed renewable energy. In Proceedings of the Energytech, Cleveland, OH, USA, 25–26 May 2011. [Google Scholar]
- Dragicevic, T.; Vasquez, J.C.; Guerrero, J.M.; Skrlec, D. Advanced LVDC Electrical Power Architectures and Microgrids: A step toward a new generation of power distribution networks. IEEE Elect. Mag.
**2014**, 2, 54–65. [Google Scholar] [CrossRef] - Boujelben, N.; Masmoudi, F.; Djemel, M.; Derbel, N. Design and comparison of quadratic boost and double cascade boost converters with boost converter. In Proceedings of the 14th International Multi-Conference on Systems, Signals Devices (SSD), Marrakech, Morocco, 28–31 March 2017; pp. 245–252. [Google Scholar]
- Jou, H.; Huang, J.; Wu, J.; Wu, K. Novel Isolated Multilevel DC–DC Power Converter. IEEE Trans. Power Electron.
**2016**, 31, 2690–2694. [Google Scholar] [CrossRef] - Zhang, C.; Gao, Z.; Chen, T.; Yang, J. Isolated DC/DC converter with three-level high-frequency link and bidirectional power flow ability for electric vehicles. IET Power Electron.
**2019**, 12, 1742–1751. [Google Scholar] [CrossRef] - Leyva-Ramos, J.; Ortiz-Lopez, M.G.; Diaz-Saldierna, L.H.; Morales-Saldana, J.A. Switching regulator using a quadratic boost converter for wide DC conversion ratios. Power Electron. IET
**2009**, 2, 605–613. [Google Scholar] [CrossRef] - Wang, Y.; Qiu, Y.; Bian, Q.; Guan, Y.; Xu, D. A Single Switch Quadratic Boost High Step up DC-DC Converter. IEEE Trans. Ind. Electron.
**2018**, 66, 4387–4397. [Google Scholar] [CrossRef] - Wu, G.; Ruan, X.; Ye, Z. Non-isolated High Step-up DC-DC Converters Adopting Switched-capacitor Cell. Ind. Electron. IEEE Trans.
**2015**, 62, 383–393. [Google Scholar] [CrossRef] - Chen, F.; Cai, X.S. Design of feedback control laws for switching regulators based on the bilinear large signal model. Power Electron. IEEE Trans.
**1989**, 5, 236–240. [Google Scholar] [CrossRef] - Zhang, C.; Wang, X.; Lin, P.; Liu, P.X.; Yan, Y.; Yang, J. Finite-Time Feedforward Decoupling and Precise Decentralized Control for DC Microgrids Towards Large-Signal Stability. IEEE Trans. Smart Grid
**2019**. [Google Scholar] [CrossRef] - Lee, T.S. Input-output linearization and zero-dynamics control of three-phase AC/DC voltage-source converters. Power Electron. IEEE Trans.
**2003**, 18, 11–22. [Google Scholar] - Viswanathan, K.; Oruganti, R.; Srinivasan, D. Dual mode control of tri-state boost converter for improved performance. In Proceedings of the IEEE Power Electronics Specialist Conference, Acapulco, Mexico, 15–19 June 2003. [Google Scholar]
- Sastry, J.; Ojo, O.; Wu, Z. High performance control of a boost AC-DC PWM rectifier-induction generator system. In Proceedings of the Industry Applications Conference, Hong Kong, China, 2–6 October 2005. [Google Scholar]
- Wei, X.; Tsang, K.M.; Chan, W.L. DC/DC Buck Converter Using Internal Model Control. Electr. Mach. Power Syst.
**2009**, 37, 320–330. [Google Scholar] [CrossRef] - Shuai, D.; Xie, Y.; Wang, X. The Research of Input-Output Linearization and Stabilization Analysis of Internal Dynamics on the CCM Boost Converter. In Proceedings of the International Conference on Electrical Machines Systems, Wuhan, China, 17–20 October 2008. [Google Scholar]
- Sira-Ramírez, H.; Silva-Ortigoza, R. Control Design Techniques in Power Electronics Devices; Springer: London, UK, 2006; pp. 235–355. [Google Scholar]
- Han, J. From PID to Active Disturbance Rejection Control. IEEE Trans. Ind. Electron.
**2009**, 56, 900–906.22. [Google Scholar] [CrossRef] - Han, J. The auto-disturbance-rejection controller (ADRC) and its application. Control Decis.
**1998**, 1, 19–23. [Google Scholar] - Gao, Z. Scaling and bandwidth-parameterization based controller tuning. In Proceedings of the American Control Conference, Denver, CO, USA, 4–6 June 2003; pp. 4989–4996. [Google Scholar]
- Gao, Z. Active Disturbance Rejection Control: A paradigm shift in feedback control system design. In Proceedings of the American Control Conference, Minneapolis, MN, USA, 14–16 June 2006. [Google Scholar]
- Gang, T.; Gao, Z. Benchmark tests of Active Disturbance Rejection Control on an industrial motion control platform. In Proceedings of the 2009 American Control Conference, St. Louis, MO, USA, 10–12 June 2009; pp. 5552–5557. [Google Scholar]
- Huang, Y.; Xue, W.; Gao, Z.; Sira-Ramirez, H.; Sun, M. Active Disturbance Rejection Control: Methodology, Practice and Analysis. In Proceedings of the Control Conference, Hilton, Portland, 4–6 June 2014. [Google Scholar]
- Song, C.; Wei, C.; Yang, F.; Cui, N. High-Order Sliding Mode-Based Fixed-Time Active Disturbance Rejection Control for Quadrotor Attitude System. Electronics
**2018**, 7, 357. [Google Scholar] [CrossRef] - Li, H.; Qu, Y. A Composite Strategy for Harmonic Compensation in Standalone Inverter Based on Linear Active Disturbance Rejection Control. Energies
**2019**, 12, 2618. [Google Scholar] [CrossRef] - Zuo, Y.; Zhu, X.; Li, Q.; Chao, Z.; Yi, D.; Xiang, Z. Active Disturbance Rejection Controller for Speed Control of Electrical Drives Using Phase-locking Loop Observer. IEEE Trans. Ind. Electron.
**2019**, 66, 1748–1759. [Google Scholar] [CrossRef] - Zheng, Q.; Dong, L.; Lee, D.H.; Gao, Z. Active disturbance rejection control for MEMS gyroscopes. In Proceedings of the American Control Conference, St. Louis, MO, USA, 10–12 June 2009. [Google Scholar]
- You, J.; Fan, W.; Yu, L.; Fu, B.; Liao, M. Disturbance Rejection Control Method of Double-Switch Buck-Boost Converter. Energies
**2019**, 12, 278. [Google Scholar] [CrossRef]

**Figure 7.**(

**a**) Current loop open loop transfer function; and (

**b**) open-loop bode diagram of systems with Controller.

**Figure 15.**(

**a**) LADRC controller: experimental comparison responses with Case 1; and (

**b**) PI controller: experimental comparison responses with Case 1.

**Figure 16.**(

**a**) LADRC controller: experimental comparison responses with Case 2; and (

**b**) PI controller: experimental comparison responses with case 2.

**Figure 17.**(

**a**) LADRC controller: experimental comparison responses with Case 3; and (

**b**) PI controller: experimental comparison responses with Case 3.

Parameters | Description | Value |
---|---|---|

U_{oref} | Reference value of output voltage | 24 V |

L | inductance value | 1 mH |

C | capacitance value | 920 μF |

f_{sw} | switching frequency | 10 KHz |

ω_{c1}, ω_{o1,}b_{1} | LADRC parameters of current control loop | 165, 270, 543.5 |

ω_{c2}, ω_{o2,}b_{2} | LADRC parameters of voltage control loop | 1600, 8800, 24,000 |

k_{p1}, k_{i1} | PI parameters of voltage control loop | 0.3, 7 |

k_{p2}, k_{i2} | PI parameters of current control loop | 0.25, 30 |

Case | Input Voltage | Load |
---|---|---|

1 | 12 V→10 V | 50 Ω |

2 | 12 V→8 V | 50 Ω |

3 | 12 V | 50 Ω→25 Ω |

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**MDPI and ACS Style**

Li, H.; Liu, X.; Lu, J.
Research on Linear Active Disturbance Rejection Control in DC/DC Boost Converter. *Electronics* **2019**, *8*, 1249.
https://doi.org/10.3390/electronics8111249

**AMA Style**

Li H, Liu X, Lu J.
Research on Linear Active Disturbance Rejection Control in DC/DC Boost Converter. *Electronics*. 2019; 8(11):1249.
https://doi.org/10.3390/electronics8111249

**Chicago/Turabian Style**

Li, Hui, Xinxiu Liu, and Junwei Lu.
2019. "Research on Linear Active Disturbance Rejection Control in DC/DC Boost Converter" *Electronics* 8, no. 11: 1249.
https://doi.org/10.3390/electronics8111249