# Linear Active Disturbance Rejection Control-Based Diagonal Recurrent Neural Network for Radar Position Servo Systems with Dead Zone and Friction

^{*}

## Abstract

**:**

## 1. Introduction

- A.
- Literature Review

- B.
- Contributions Statement

- C.
- Paper Organization

## 2. Radar Position Servo System Modeling

## 3. Compound Controller DRNN-LADRC Design

#### 3.1. Preliminary to LADRC

**Assumption**

**1.**

**Assumption**

**2.**

#### 3.2. Proposed Adaptive Tracking Differentiator Design

**Remark**

**1.**

#### 3.3. Proposed Improved LADRC Design

**Remark**

**2.**

**Lemma**

**1**

**Theory**

**1.**

**Lemma**

**2.**

**Theory**

**2.**

**Definition**

**1.**

**Remark**

**3.**

## 4. Case Study

#### 4.1. Case Study 1: Performance Comparison between ATD and TD

#### 4.2. Case Study 2: Regular Controller Performances

#### 4.3. Case Study 3: Performance Comparison between DRNN-LADRC and BPNN-LADRC

#### 4.4. Case Study 4: Robust Performance Verification

#### 4.5. Case Study 5: Step Response via the LADRC by Introducing ATD

#### 4.6. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Tracking outputs of TD while $\kappa =1.5$, ${h}_{0}=0.002$. (

**a**) Tracking the given signal, (

**b**) Tracking the derivative signal.

**Figure 6.**Tracking outputs of TD while $\kappa =15$, ${h}_{0}=0.002$. (

**a**) Tracking the given signal, (

**b**) Tracking the derivative signal.

**Figure 7.**Tracking outputs of TD while $\kappa =15$, ${h}_{0}=0.2$. (

**a**) Tracking the given signal, (

**b**) Tracking the derivative signal.

**Figure 8.**Tracking outputs of the ATD. (

**a**) Tracking the given signal, (

**b**) Tracking the derivative signal.

**Figure 9.**The adaptive adjustment curves of the speed factor $\kappa (k)$ and filter factor ${h}_{0}(k)$.

**Figure 12.**Responses of the ATD. (

**a**) Tracking signals of ${v}_{1}$ and ${v}_{2}$, (

**b**) Adaptive adjustment curves of $\kappa (k)$ and ${h}_{0}(k)$.

**Figure 15.**Curves of the internal nonlinear disturbances. (

**a**) The friction nonlinearity, (

**b**) The dead zone.

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**MDPI and ACS Style**

Cui, S.; Zhu, G.; Zhao, T.
Linear Active Disturbance Rejection Control-Based Diagonal Recurrent Neural Network for Radar Position Servo Systems with Dead Zone and Friction. *Appl. Sci.* **2022**, *12*, 12839.
https://doi.org/10.3390/app122412839

**AMA Style**

Cui S, Zhu G, Zhao T.
Linear Active Disturbance Rejection Control-Based Diagonal Recurrent Neural Network for Radar Position Servo Systems with Dead Zone and Friction. *Applied Sciences*. 2022; 12(24):12839.
https://doi.org/10.3390/app122412839

**Chicago/Turabian Style**

Cui, Shuai, Guixin Zhu, and Tong Zhao.
2022. "Linear Active Disturbance Rejection Control-Based Diagonal Recurrent Neural Network for Radar Position Servo Systems with Dead Zone and Friction" *Applied Sciences* 12, no. 24: 12839.
https://doi.org/10.3390/app122412839