【Practical Exercise】Simulink Simulation Implementation of Incremental PID

# 2.1 Introduction to the Simulink Simulation Environment

Simulink is a graphical environment for modeling, simulating, and analyzing dynamic systems within MATLAB. It offers an intuitive user interface that allows users to create system models using blocks and connecting lines. Simulink models consist of the following elements:

- **Subsystems:** Decompose complex systems into smaller, manageable modules.
- **Blocks:** Represent components in the system, such as sensors, actuators, and controllers.
- **Connecting Lines:** Indicate the flow of signals between blocks.

The Simulink simulation environment provides a wide range of block libraries covering various engineering disciplines, including control systems, electronics, and mechanical engineering. It also supports the creation of user-defined blocks to meet specific simulation requirements.

# 2. Building and Modeling the Simulink Simulation Environment

### 2.1 Introduction to the Simulink Simulation Environment

Simulink is a graphical programming environment in MATLAB for simulating dynamic systems. It offers an intuitive interface that allows users to construct and simulate complex systems using modular components. The Simulink simulation environment includes the following main features:

- **Model Libraries:** Contain various predefined modules, such as gains, integrators, differentiators, etc., that can be used to build complex systems.
- **Simulation Engine:** Executes the model and computes the system response.
- **Visualization Tools:** Used for plotting system responses and analyzing simulation results.

### 2.2 Incremental PID Controller Simulink Model Construction

The Simulink model of an incremental PID controller includes the following modules:

- **Reference Signal:** Represents the desired system output.
- **Process Model:** Represents the system dynamics.
- **Incremental PID Controller:** Calculates the control signal.
- **Actuator:** Applies the control signal to the system.
- **Feedback Signal:** Measures the actual system output.

**Code Block 1: Incremental PID Controller Simulink Model**

% Simulink Model
simulink_model = 'pid_controller_model';

% Reference Signal
reference_signal = Simulink.Signal;
reference_signal.Value = 1;

% Process Model
process_model = Simulink.TransferFcn;
process_model.Numerator = [1];
process_model.Denominator = [1, 2, 1];

% Incremental PID Controller
pid_controller = Simulink.PIDController;
pid_controller.Kp = 1;
pid_controller.Ki = 0.1;
pid_controller.Kd = 0.01;

% Actuator
actuator = Simulink.Gain;
actuator.Gain = 1;

% Feedback Signal
feedback_signal = Simulink.Feedback;

% Model Connections
add_block(reference_signal, simulink_model);
add_block(process_model, simulink_model);
add_block(pid_controller, simulink_model);
add_block(actuator, simulink_model);
add_block(feedback_signal, simulink_model);

connect_blocks(simulink_model, 'Reference Signal/Out1', 'Process Model/In1');
connect_blocks(simulink_model, 'Process Model/Out1', 'PID Controller/In1');
connect_blocks(simulink_model, 'PID Controller/Out1', 'Actuator/In1');
connect_blocks(simulink_model, 'Actuator/Out1', 'Feedback Signal/In1');
connect_blocks(simulink_model, 'Feedback Signal/Out1', 'Process Model/In2');

**Code Logic Analysis:**

- The `add_block` function adds modules to the Simulink model.
- The `connect_blocks` function connects the input and output ports of modules.
- The `reference_signal` block generates the reference signal.
- The `process_model` block represents system dynamics.
- The `pid_controller` block implements the incremental PID control algorithm.
- The `actuator` block applies the control signal to the system.
- The `feedback_signal` block measures the actual system output.

**Parameter Description:**

- `Kp`: Proportional gain.
- `Ki`: Integral gain.
- `Kd`: Derivative gain.

**Flowchart 1: Incremental PID Controller Simulink Model Flowchart**

graph LR
subgraph Simulink Model
     A[Reference Signal] --> B[Process Model]
     B --> C[PID Controller]
     C --> D[Actuator]
     D --> E[Feedback Signal]
     E --> B
end

# 3. Incremental PID Controller Parameter Tuning

### 3.1 Overview of Para