【Advanced】Auto Disturbance Rejection Control (ADRC) MATLAB_Simulink Simulation Model

# 1. Active Disturbance Rejection Control (ADRC) Theoretical Foundation

Active Disturbance Rejection Control (ADRC) is a novel control method characterized by its strong robustness, good disturbance rejection capabilities, and high precision. The core idea of ADRC is to treat system disturbances as generalized states and estimate and compensate for them through the Extended State Observer (ESO).

The ADRC algorithm consists of three main modules: the Tracking Differentiator (TD), the Nonlinear State Error Feedback Controller (NLSEFC), and the Extended State Observer (ESO). The TD is used to estimate system states and disturbances, the NLSEFC generates control signals based on estimated states and disturbances, and the ESO is used to estimate the generalized states, including system states and disturbances.

# 2. Establishing MATLAB-Simulink Simulation Environment

### 2.1 Introduction to MATLAB Environment

MATLAB (Matrix Laboratory) is a high-level programming language and interactive environment for technical computing. It is widely used in the fields of science, engineering, finance, and industry. MATLAB has powerful capabilities in data analysis, visualization, and modeling, making it an ideal choice for establishing MATLAB-Simulink simulation environments.

### 2.2 Introduction to Simulink Simulation Platform

Simulink is a graphical simulation environment within MATLAB, used for modeling, simulating, and analyzing dynamic systems. It provides an intuitive drag-and-drop interface that allows users to create system models and simulate them. Simulink is tightly integrated with MATLAB, allowing users to combine MATLAB code with Simulink models, enabling more complex simulation functionalities.

#### Simulink Model Composition

Simulink models consist of the following basic elements:

- **Modules:** Represent components or functions within the system, such as gains, integrators, differentiators, etc.
- **Connections:** Link modules and represent signal flow.
- **Parameters:** Define the behavior of modules, such as gain values, integral time constants, etc.

#### Simulink Simulation Process

The Simulink simulation process includes the following steps:

1. **Model Creation:** Use modules and connections to create a system model.
2. **Parameter Settings:** Set appropriate parameters for the modules.
3. **Simulation:** Run the simulation; Simulink will calculate the system response based on the model.
4. **Result Analysis:** Analyze simulation results using MATLAB tools and graphical interfaces.

#### Code Block

% Creating a simple Simulink model
model = simulink.Model('SimpleModel');

% Adding a gain module
gain = model.addBlock('Simulink/Sources/Gain');

% Setting the gain value
gain.Gain = 10;

% Adding input and output ports
input = model.addInport('In');
output = model.addOutport('Out');

% Connecting modules
model.connect(input, gain, 1, 1);
model.connect(gain, output, 1, 1);

% Simulating the model
sim(model);

% Retrieving simulation results
out = model.get('Out');

% Plotting simulation results
plot(out);
xlabel('Time (s)');
ylabel('Output');
title('Simulink Simulation Result');

**Logical Analysis:**

This code creates a simple Simulink model with a gain module. The gain value is set to 10. The model has two ports: an input port and an output port. The input port receives the input signal, the gain module amplifies the input signal, and the output port outputs the amplified signal.

The code uses the `simulink.Model` class to create the model, the `addBlock` method to add a gain module, the `Gain` property to set the gain value, the `addInport` and `addOutport` methods to add input and output ports, the `connect` method to connect modules, the `sim` method to run the simulation, the `get` method to retrieve simulation results, and the `plot` method to plot the simulation results.

# 3. ADRC Simulation Model Design

### 3.1 ADRC Algorithm Principles

Active Disturbance Rejection Control (ADRC) is a robust and adaptive control algorithm aimed at addressing uncertainties