How to Model State Space System in Simulink: Step-by-Step Guide

To model a state space system in Simulink, use the State-Space block found in the Simulink library under Continuous systems. Enter the system matrices A, B, C, and D in the block parameters to define the system dynamics and outputs.

Syntax

The State-Space block requires four matrices to define the system:

• A: State matrix defining system dynamics.
• B: Input matrix defining how inputs affect states.
• C: Output matrix defining how states affect outputs.
• D: Feedthrough matrix defining direct input to output effect.

These matrices are entered as MATLAB arrays in the block's parameters.

matlab

A = [0 1; -2 -3];
B = [0; 1];
C = [1 0];
D = [0];

Example

This example shows how to model a simple second-order system using the State-Space block in Simulink. The system matrices represent a system with two states, one input, and one output.

matlab

% Define system matrices
A = [0 1; -2 -3];
B = [0; 1];
C = [1 0];
D = [0];

% Open Simulink model
open_system(new_system('StateSpaceExample'));

% Add State-Space block
add_block('simulink/Continuous/State-Space','StateSpaceExample/State-Space');

% Set block parameters
set_param('StateSpaceExample/State-Space','A',mat2str(A),'B',mat2str(B),'C',mat2str(C),'D',mat2str(D));

% Add Step input
add_block('simulink/Sources/Step','StateSpaceExample/Step');

% Add Scope
add_block('simulink/Sinks/Scope','StateSpaceExample/Scope');

% Connect blocks
add_line('StateSpaceExample','Step/1','State-Space/1');
add_line('StateSpaceExample','State-Space/1','Scope/1');

% Run simulation
sim('StateSpaceExample');

Output

A Simulink model named 'StateSpaceExample' opens with a State-Space block connected to a Step input and a Scope showing the system output response.

Common Pitfalls

• Entering matrices with incorrect dimensions causes errors; ensure A is square and B, C, D have compatible sizes.
• For discrete systems, set the sample time parameter; otherwise, the system defaults to continuous time.
• Not connecting inputs or outputs properly in the Simulink model leads to simulation errors or no output.

matlab

% Wrong: A is not square
A_wrong = [0 1 2; -2 -3 4];
B_wrong = [0; 1];

% Correct: A is square
A_correct = [0 1; -2 -3];
B_correct = [0; 1];

Quick Reference

Parameter	Description	Notes
A	State matrix	Must be square (n x n)
B	Input matrix	Size (n x m), where m = number of inputs
C	Output matrix	Size (p x n), where p = number of outputs
D	Feedthrough matrix	Size (p x m), often zero matrix
Sample time	System sample time	0 for continuous, >0 for discrete

Key Takeaways

Use the State-Space block in Simulink to model systems by entering matrices A, B, C, and D.

Ensure matrix dimensions are correct to avoid simulation errors.

Set sample time properly for continuous or discrete systems.

Connect inputs and outputs correctly in your Simulink model.

Use Step and Scope blocks to test and visualize system response.