【Advanced】Simulating and Modeling with MATLAB: Building Models and Running Simulations

# 1. Fundamental Theories of MATLAB Simulation and Emulation

MATLAB is an advanced programming language designed for technical computing, and it is extensively used in the domains of simulation and emulation. This chapter will introduce the fundamental theories of MATLAB simulation and emulation, encompassing the concepts of simulation and emulation, the advantages of MATLAB in simulation-emulation field, and the MATLAB emulation environment.

# 2. MATLAB Model Building and Simulation Principles

### 2.1 Model Building and Simulation Process

The process of MATLAB model building and simulation follows these steps:

1. **Problem Definition:** Clearly define the goals and scope of the simulation.
2. **Model Selection:** Choose the appropriate model type based on the simulation goals, such as physical, mathematical, or data models.
3. **Model Construction:** Create the model using MATLAB functions and toolboxes, including defining the model structure, parameters, and variables.
4. **Simulation Setup:** Configure simulation parameters, such as simulation time, step size, and termination conditions.
5. **Simulation Execution:** Run the simulation to generate data.
6. **Result Analysis:** Analyze the simulation results to extract valuable information and insights.

### 2.2 Model Structure and Parameter Settings

The structure of a MATLAB model typically consists of the following elements:

- **State Variables:** Variables that describe the system’s state.
- **Input Variables:** External inputs that affect the system’s behavior.
- **Output Variables:** Measurements of the system’s response.
- **Equations:** Mathematical equations that describe the system’s behavior.

Model parameters are constants within these equations and are used to adjust the model’s behavior. Parameter settings are crucial, as they affect the accuracy of simulation outcomes.

### 2.3 Simulation Algorithms and Error Analysis

MATLAB offers various simulation algorithms, including:

- **Euler’s Method:** An explicit integration method for solving differential equations.
- **Runge-Kutta Method:** An implicit integration method that is more accurate than Euler’s method.
- **Adams-Bashforth Method:** A predictor-corrector method for solving differential-algebraic equations.

Simulation error is the difference between the simulation results and the actual system behavior. Error analysis involves evaluating the sources and magnitude of simulation errors and taking measures to minimize them.

**Code Block:**

% Define state variables
x = [1; 2];

% Define input variables
u = 3;

% Define equations
f = @(x, u) [x(2); -x(1) + u];

% Set simulation parameters
t_span = [0, 10];
dt = 0.1;

% Run simulation
[t, x] = ode45(f, t_span, x, [], u);

% Plot simulation results
plot(t, x);
xlabel('Time');
ylabel('State Variables');
title('Simulation Results');

**Logical Analysis:**

This code block uses MATLAB’s ode45 function to solve a nonlinear system of differential equations. The ode45 function utilizes the Runge-Kutta method to solve the equations and returns simulation time and state variables.

**Parameter Description:**

- `f`: Handle to the differential equation system function.
- `t_span`: Range of simulation time.
- `x`: Initial state variables.
- `[]`: Additional parameters, which are empty in this case.
- `u`: Input variable.

# 3. MATLAB Emulation Techniques in Practice

### 3.1 Time Domain and Frequency Domain Emulation

#### 3.1.1 Time Domain Emulation Methods

Time domain emulation involves simulating the behavior of a system within the time domain, which means directly solving for the system’***monly used time domain emulation methods in MATLAB are:

- **ode45() function:** Uses the Runge-Kutta 4th order method to solve ordinary differential equation systems, suitable for most nonlinear systems.

% Define a system of differential equations
dydt = @(t, y) [y(2); -y(1) - y(2)];

% Initial conditions
y0 = [1; 0];

% Time range
t_span = [0, 10];

% Solve the differential equation system
[t, y] = ode45(dydt, t_span, y0);

% Plot time domain response
plot(t, y);

- **sim() function:** Used to emulate Simulink models, capable of simulating complex dynamic systems.

% Create Simulink model
model = 'my_model.slx';

% Set simulation parameters
sim_params = simset('SrcWorkspace', 'current');

% Simulate the model
sim(model, sim_params);

% Retrieve simulation results
t = simout.time;
y = simout.signals.values;

% Plot time domain response
plot(t, y);

#### 3.1.2 Frequency Domain Emulation Methods

Frequency domain emulation involves sim