This document outlines an experiment in the Department of Avionics Engineering focused on transforming between state-space and classical control system representations using MATLAB. It includes objectives, theoretical background, and example MATLAB commands for obtaining state-space representations from transfer functions and vice versa. The document also details specific lab tasks for students to implement these conversions using provided block diagrams.

1. Department of Avionics Engineering
AE-3452
Modern Control Systems
Experiment No.2
Provided MATLAB functions, convert the State Space Model into a
classical control system and vice versa
Prepared for
By:
Name:
ID:
Section:
Semester:
Total Marks: ________________
Obtained Marks: _____________
Signature: __________________
Date: _____________________

2. Provided MATLAB functions, convert the State Space Model into a
classical control system and vice versa
Objective:
To transform the system model from transfer function to state space, and vice versa on MATLAB
Theory:
Given a transfer function of the form:
MATALB can be used to obtain a state-space representation of the transfer function with the following
command
It is important to note that the state space representation is not unique, i.e. there are many state-space
representations for the same system. The MATLAB command gives just one possible state-space
equation.
Example: Consider the transfer function
A possible state-space representation for this system is:
For the example transfer function, MATLAB produces the following state-space representation:
With the following program to get the matrices:

3. >> num = [0 0 1 0];
>> den = [1 14 56 160];
>> [A, B, C, D] = tf2ss(num, den)
State Space to Transfer Function
To obtain the transfer function from state-space equations, use the following MATLAB code
where num_in must be specified for systems with more than one input. For example, if there is only one
input, then num_in = 1, if there are two inputs then num_in = 2, etc. For systems with only one input,
then the following code is allowed
Example. Given the state-space equations:
MATLAB produces the following system transfer function:
The MATLAB implementation of this is given by the following code:
>> A = [0 1 0; 0 0 1; -5 -25 -5];
>> B = [0; 25; -120];
>> C = [1 0 0];
>> D = [0];
Lab Task 01: Using MATLAB, obtain the transfer function for the control system in the figure below:

4. Where:
Note: Use the series command to combine the states pace of two systems.
Lab Task 02:
By using the state-space matrices in Lab task 01, perform according to the given block diagram using
parallel command.