# Electromechanical Actuator Servo Control Technology Based on Active Disturbance Rejection Control

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Control of PMSM

#### 2.1.1. Mathematical Model of PMSM

- 1.
- Stator voltage equationThe stator voltage equation in $dq$ coordinate system is$$\left\{\begin{array}{l}{u}_{d}={R}_{s}{i}_{d}+\frac{d{\psi}_{d}}{dt}-{\omega}_{e}{\psi}_{q}\\ {u}_{q}={R}_{s}{i}_{q}+\frac{d{\psi}_{q}}{dt}+{\omega}_{e}{\psi}_{d}\end{array}\right.$$

- 2.
- Stator flux linkage equationThe stator flux linkage equation in $dq$ coordinate system is$$\left\{\begin{array}{l}{\psi}_{d}={\psi}_{f}+{L}_{d}{i}_{d}\\ {\psi}_{q}={L}_{q}{i}_{q}\end{array}\right.$$

- 3.
- Electromagnetic torque equationThe electromagnetic torque equation in $dq$ coordinate system is$${T}_{e}=1.5{n}_{p}({\psi}_{d}{i}_{q}-{\psi}_{q}{i}_{d})$$

- 4.
- Motion equilibrium equationThe equation of motion in $dq$ coordinate system remains unchanged, which is$${T}_{e}=\frac{J}{{n}_{p}}\frac{d{\omega}_{e}}{dt}+{T}_{l}$$

#### 2.1.2. Vector Control Technology

^{−1}to obtain the voltage value ${u}_{\alpha}$ and ${u}_{\beta}$ in a two-phase stationary ($\alpha \beta $) coordinate system. The PWM waveform is generated through the space vector pulse width modulation (SVPWM) technology, and the voltage vector of the motor is controlled by the inverter to complete the position vector control of PMSM.

#### 2.1.3. Three Closed-Loop Controller Design

- 1.
- Current loop design

- 2.
- Speed loop design

- 3.
- Position loop design

#### 2.2. Linear ADRC

#### 2.2.1. Improved ESO

#### 2.2.2. Linear Error Feedback Control Law

#### 2.3. Design of Linear Active Disturbance Rejection Controller for PMSM

#### 2.3.1. Design of Active Disturbance Rejection Controller for the Speed Loop

#### 2.3.2. Design of the Position Loop ADRC

#### 2.3.3. Stability Analysis of ADRC

#### 2.4. Simulation of the Linear ADRC System for PMSM

## 3. Results

^{2}, the torque constant is 5.2 N·m/A and the back electromotive force constant is 0.01 V/rpm. The lead of the PRSM is 0.2 inches. The motor controller is the AKD-P00606 drive controller of Kollmorgen, with continuous output power up to 2 kW.

#### 3.1. Load Step Test

#### 3.2. Load Disturbance Test

## 4. Discussion

- In the aspect of mathematical modeling, the nonlinear factors such as the clearance and friction of the mechanical system are simplified, and the model is not accurate enough, which needs further improvement;
- In terms of the calculation method, the discretization method adopted is the Euler method. The approximate accuracy is not high enough, and it is easy to produce a high-frequency tremor. A better discretization method can be adopted;
- In the system test, the output of the sensor is analog, which is easily affected by noise. The digital sensor can be used to improve the measurement accuracy. The loading mode of the load also needs to be improved.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Fang, Q.; Zhou, Y.; Ma, S.; Zhang, C.; Wang, Y.; Huangfu, H.
Electromechanical Actuator Servo Control Technology Based on Active Disturbance Rejection Control. *Electronics* **2023**, *12*, 1934.
https://doi.org/10.3390/electronics12081934

**AMA Style**

Fang Q, Zhou Y, Ma S, Zhang C, Wang Y, Huangfu H.
Electromechanical Actuator Servo Control Technology Based on Active Disturbance Rejection Control. *Electronics*. 2023; 12(8):1934.
https://doi.org/10.3390/electronics12081934

**Chicago/Turabian Style**

Fang, Qian, Yong Zhou, Shangjun Ma, Chao Zhang, Ye Wang, and Haibin Huangfu.
2023. "Electromechanical Actuator Servo Control Technology Based on Active Disturbance Rejection Control" *Electronics* 12, no. 8: 1934.
https://doi.org/10.3390/electronics12081934