Write a Matlab code which runs a Simulink model that simulates the state feedback  controller performance for a unit step input.

To create a MATLAB code that runs a Simulink model simulating a state-feedback controller with a unit step input, you’ll need to perform the following steps. I’ll provide a guide to create both the MATLAB script and an overview of what the Simulink model should contain.

The controller will assume you have a state-space system in the form:
\[
\dot{x} = Ax + Bu
\]
\[
y = Cx + Du
\]
where you want to control the system using a state-feedback gain \( K \) such that:
\[
u = -Kx
\]

### Step 1: Define the MATLAB Code

Here is a MATLAB script that sets up the system and calls the Simulink model to simulate it:

```matlab
% Define system matrices
A = [0 1; -2 -3]; % Example system matrix
B = [0; 1];       % Input matrix
C = [1 0];        % Output matrix
D = 0;            % Direct feedthrough (assume zero here for simplicity)

% Define state-feedback gain (assume designed via pole placement or LQR)
K = [5 6];        % Example feedback gain

% Create state-space model
sys = ss(A - B*K, B, C, D);

% Open the Simulink model
model_name = 'StateFeedbackControlModel'; % Ensure the model has this name in Simulink
open_system(model_name);

% Configure simulation parameters
set_param(model_name, 'StopTime', '10'); % Run for 10 seconds

% Run simulation
simOut = sim(model_name);

% Extract and plot results
t = simOut.tout;
y = simOut.yout.getElement(1).Values.Data;

% Plot results
figure;
plot(t, y);
title('Step Response of State Feedback Controlled System');
xlabel('Time (s)');
ylabel('Output');
grid on;
```

### Step 2: Configure the Simulink Model (`StateFeedbackControlModel.slx`)

1. **Create the Model in Simulink:**
   - Open Simulink and create a new model called `StateFeedbackControlModel`.
   - Save the model with the name `StateFeedbackControlModel.slx`.

2. **System Configuration:**
   - Add a **State-Space** block to define the controlled system, with the matrices `(A-B*K)`, `B`, `C`, and `D` (defined in the MATLAB workspace).
   - Use a **Step** block as the input signal, which provides a unit step input.

3. **State Feedback Controller Setup:**
   - Define `A`, `B`, `C`, `D`, and `K` in the MATLAB workspace as per the script.
   - The **State-Space** block will access these workspace variables directly.

4. **Output Scope:**
   - Add a **Scope** block to visualize the output.

### Step 3: Run the MATLAB Code

1. Ensure the MATLAB code and the Simulink model are saved in the same directory or that the path is set.
2. Run the MATLAB code.
3. MATLAB will call the Simulink model, simulate it, and plot the results.

This setup will provide a response of the closed-loop system to a unit step input. You can change `A`, `B`, `C`, `D`, and `K` to match your specific system dynamics and controller design.

Would you like more details on configuring the Simulink model or further explanation of the MATLAB code?

---

#### Relative Questions:
1. How can you design the state-feedback gain \( K \) using MATLAB’s `place` function?
2. What if you need to add an integrator to eliminate steady-state error?
3. How does the state feedback control differ from other control strategies like PID?
4. How can you use an observer with this state-feedback setup?
5. What modifications are needed if the system has multiple inputs and outputs?

#### Tip:
In MATLAB, use the `ss` function to create a state-space model easily and perform analyses, such as step responses, without requiring a Simulink model.

Write a Matlab code which runs a Simulink model that simulates the state feedback controller performance for a unit step input.

Discover how to write MATLAB code that runs a Simulink model to simulate a state feedback controller's performance for a unit step input. This guide includes key concepts in control systems, such as state feedback and linear systems modeling, with practical steps to set up and visualize the system response.

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