1. CONTROL SYSTEM DESIGN by using MATLAB
Creation of Transfer Functions
sys = tf(num,den) creates a continuous-time transfer function with numerator(s) and denominator(s) specified by num and den. 
OPEN LOOP T.F 
G(s) in
OUT
tf = 𝑜𝑢𝑡 𝑖𝑛

2. CONTROL SYSTEM DESIGN by using
Creation of Transfer Functions
sys = tf(num,den) creates a continuous-time transfer function with numerator(s) and denominator(s) specified by num and den. 
CLOSED LOOP T.F  in
out
G(s)
H(s)
tf = 𝑮(𝒔) 𝟏+𝑮 𝒔 𝑯(𝒔)

3. CONTROL SYSTEM DESIGN by using MATLAB
Creation of Transfer Functions
sys = tf(num,den) creates a continuous-time transfer function with numerator(s) and denominator(s) specified by num and den. 
tf= 𝒔 𝒔 𝟐 +𝟒𝒔+𝟓

4. CONTROL SYSTEM DESIGN by using MATLAB
Creation of Transfer Functions num=[1 0]; den=[1 4 5]; h=tf(num,den) stepplot(h)
tf= 𝒔 𝒔 𝟐 +𝟒𝒔+𝟓

6. CONTROL SYSTEM DESIGN by using MATLAB
Example 2
Transfer Function Model with One-Input Two-Outputs
Create the one-input, two-output transfer function
H(s)= 𝒔+𝟏 𝒔 𝟐 +𝟐𝒔+𝟐 𝑠
with input current and outputs torque and angle velocity.
To do this, enter
num = {[1 1] ; 1};
den = {[1 2 2] ; [1 0]};
h = tf(num,den)
stepplot(h)

7. 1: 𝒔+𝟏 𝒔 𝟐 +𝟐𝒔+𝟐 2: 𝟏 𝑺

8. Second-Order Transfer Function from Damping and Natural Frequency

9. CONTROL SYSTEM DESIGN H(s)= 𝛚𝐨^𝟐 𝐬 𝟐 +𝟐𝛇𝛚𝟎𝐬+𝛚𝐨^𝟐 Example 3
Second-Order Transfer Function from Damping and Natural Frequency
Create a tf model that represents a second-order system with known natural frequency and damping ratio.
Solve the followıng second order TF. eq. Wher: wo=3 and zeta is considered underdamped ?
zeta = 0.25;
w0 = 3;
h = tf(w0^2,[1,2*zeta*w0,w0^2])
stepplot(h)
H(s)= 𝛚𝐨^𝟐 𝐬 𝟐 +𝟐𝛇𝛚𝟎𝐬+𝛚𝐨^𝟐

10. zeta = 0;
w0 = 3;
h = tf(w0^2,[1,2*zeta*w0,w0^2])
stepplot(h,'r')
hold on
zeta = 1;
i = tf(w0^2,[1,2*zeta*w0,w0^2])
stepplot(i)

11. zeta = 0.25;
w0 = 3;
h = tf(w0^2,[1,2*zeta*w0,w0^2])
stepplot(h,'r')
hold on
zeta = 2;
i = tf(w0^2,[1,2*zeta*w0,w0^2])
stepplot(i)

13. CONTROL SYSTEM DESIGN
Multiple-Input Multiple-Output Transfer Function Model
Specify the discrete MIMO transfer function
Use MATLAB to explain the following 4 MIMO systems as a Multiple input Multiple output transfer function?
with common denominator d (z) = z + 0.3 and sample time of 0.2 seconds.
num = {1 [1 0];[-1 2] 3};
ts = 0.2;
den=[1 0.3];
h=tf(num,den,ts)
stepplot(h)

15. CONTROL SYSTEM DESIGN
State-space models are models that use state variables to describe a system.
Example 5
Convert State-Space Model to Transfer Function
-Compute the transfer function of the state-space model with the following data.
sys = ss([-2 -1;1 -2],[1 1;2 -1],[1 0],[0 1]);
a=tf(sys)
stepplot(a)

17. CONTROL SYSTEM DESIGN Example 1 Pole-Zero Plot of Dynamic System
Plot the poles and zeros of the continuous-time system
num=[2 5 1];
den=[1 2 3];
h=tf(num,den)
sgrid
pzmap(h)
pole(h)
zero(h)
grid on