[MATLAB_Simulink and Control System Simulation Basics]

# 2.1 Basic Knowledge of Control Systems

A control system is a type of system that can control output signals through input signals. Control systems are widely used in industries such as industrial, transportation, communication, and national defense, making them indispensable infrastructures of modern society.

Control systems consist of three parts: sensors, controllers, and actuators. Sensors are responsible for collecting the output signals of the controlled object. Controllers calculate control signals based on the signals collected by the sensors and the given reference signals. Actuators control the controlled object based on the control signals.

The mathematical models of control systems can be divided into time-domain models and frequency-domain models. Time-domain models describe the dynamic characteristics of the system within the time domain, while frequency-domain models describe the dynamic characteristics of the system within the frequency domain. The design and analysis of control systems are usually based on their mathematical models.

# 2. Basics of Control System Modeling and Simulation

### 2.1 Basic Knowledge of Control Systems

**Definition:**
A control system is a system that controls output to achieve desired goals through measurement, comparison, calculation, and execution.

**Components:**
* Sensor: Measures the state of the controlled object
* Controller: Calculates control signals based on measured values
* Actuator: Applies control signals to the controlled object

**Classification:**
* Linear/Nonlinear
* Time-invariant/Time-varying
* Single-input single-output (SISO)/Multiple-input multiple-output (MIMO)

### 2.2 Control System Modeling in MATLAB

**Transfer Function:**

num = [1 2];
den = [1 3 2];
sys = tf(num, den);

**State-Space:**

A = [1 2; -3 -4];
B = [0; 1];
C = [1 0];
D = 0;
sys = ss(A, B, C, D);

**Simulink Block Diagram:**
* Use Transfer Function or State-Space blocks
* Connect blocks to represent signal flow
* Set parameters and initial conditions

### 2.3 Control System Simulation in Simulink

**Simulink Environment:**
* A graphical modeling and simulation platform
* Provides a rich library of control system blocks

**Simulation Process:**
* Create a model
* Set simulation parameters
* Run the simulation
* View simulation results (waveforms, data)

**Simulation Analysis:**
* Time-domain response: Analyzes how the output signal changes over time
* Frequency-domain response: Analyzes how the system responds to different frequency inputs
* Stability analysis: Determines whether the system is stable

# 3.1 Control System Design Methods

### 3.1.1 Basic Steps in Control System Design

Control system design is a complex process that usually involves the following basic steps:

1. **System Modeling:** Establish the mathematical model of the system, describing the relationship between its inputs, outputs, and internal states.
2. **Performance Criteria Definition:** Determine the performance criteria that the system must meet, such as stability, response time, and accuracy.
3. **Controller Design:** Design a controller to operate the system to achieve the desired performance criteria.
4. **Verification and Simulation:** Use simulation tools to verify the design of the controller and evaluate its performance under different operating conditions.
5. **Implementation:** Deploy the controller i