【Advanced】Simulink Simulation Based on MPC Model Predictive Controller

# 1. Basic Principles of the MPC Model Predictive Controller

## 2.1 Principles of Model Predictive Control

The principles of Model Predictive Control (MPC) involve controlling a system by predicting its future behavior and optimizing control actions. The steps involved are as follows:

1. **Establishing a System Model:** Initially, a mathematical model is required to accurately describe the dynamic behavior of the system.
2. **Predicting Future States:** Using the system model, the evolution of the system's state is predicted over a period of time.
3. **Optimizing Control Actions:** Based on the predicted future states, the current control action is optimized to minimize an objective function (e.g., tracking error or control effort).
4. **Implementing Control Actions:** Apply the optimized control action to the system.
5. **Repeating:** Steps 1-4 are repeated to continuously control the system.

## 2.2 Structure and Characteristics of the MPC Controller

An MPC controller typically consists of the following components:

- **Prediction Model:** A mathematical model used to predict future system states.
- **Optimizer:** An algorithm used to optimize control actions.
- **Feedback Controller:** Connects the prediction model and optimizer to the actual system.

The characteristics of an MPC controller include:

- **Predictive:** MPC optimizes control actions by predicting future states.
- **Optimizing:** MPC minimizes the objective function by optimizing control actions.
- **Robustness:** MPC is robust to system disturbances and modeling uncertainties.

# 2. Implementation of MPC Model Predictive Controller in Simulink

## 2.1 Basic Principles of the MPC Model Predictive Controller

### 2.1.1 Principles of Model Predictive Control

Model Predictive Control (MPC) is an advanced control technique that calculates control actions based on a predictive model. An MPC controller uses a system model to predict the system behavior over a period of time and optimizes control actions based on these predictions to achieve desired control objectives.

### 2.1.2 Structure and Characteristics of the MPC Controller

An MPC controller generally consists of several parts:

- **Prediction Model:** A mathematical model used to predict future behavior of the system.
- **Optimizer:** Computes optimal control actions based on the prediction model and control objectives.
- **Feedback Loop:** Compares actual system output with prediction model output and uses error signals to update the prediction model.

The main features of an MPC controller include:

- **Rolling Optimization:** At each control cycle, the MPC controller recalculates the optimal control action, rather than using a fixed control law.
- **Predictive:** The MPC controller calculates control actions based on predictions of future system behavior.
- **Robustness:** The MPC controller has strong robustness to model uncertainties and disturbances.

## 2.2 Modeling of the MPC Model Predictive Controller in Simulink

### 2.2.1 MPC Controller Module in Simulink

Simulink provides an MPC controller module, which can be conveniently used to model and simulate MPC controllers. The MPC controller module is located in the Simulink library under "Control Systems" -> "Model Predictive Control."

### 2.2.2 Setting Up MPC Controller Parameters

The parameter settings for the MPC controller module include:

- **Model:** The prediction model, which can be a state-space model, transfer function model, or nonlinear model.
- **Prediction Horizon:** The prediction range of the model, i.e., how many sampling periods into the future to predict.
- **Control Horizon:** The range of control actions, i.e., the maximum and minimum values of the control actions.
- **Weight Matrix:** A matrix used to weigh control objectives and control actions.

## 2.3 Simulation of the MPC Model Predictive Controller in Simulink

### 2.3.1 Setting Up the Simulation Environment

The simulation of an MPC controller in Simulink involves the following steps:

1. Create a system model.
2. Add the MPC controller module.
3. Set the MPC controller parameters.
4. Connect the system model and MPC controller module.
5. Set simulation parameters.

### 2.3.2 Analysis and Evaluation of Simulation Results

The simulation results of an MPC controller typically include:

- **System Output:** Output of the system under the control of the MPC controller.
- **Control Action:** Control actions calculated by the MPC