1

1. >> %EJEMPLO1
>> num=[10];
>> den=[1 4];
>> sys=tf(num,den)
sys =
10
-----
s + 4
Continuous-time transfer function.
>> %EJEMPLO2
>> num=[1 4];
>> den=[1 1 10];
>> sys=tf(num,den)
sys =
s + 4
------------
s^2 + s + 10
Continuous-time transfer function.

2. >> %EJEMPLO3
>> num=[3 2 1];
>> den1=[1 4 1];
>> den2=[1 5];
>> den3=conv(den1,den2);
>> sys=tf(num,den3)
sys =
3 s^2 + 2 s + 1
----------------------
s^3 + 9 s^2 + 21 s + 5
Continuous-time transfer function.
>> %EJEMPLO5
>> k=4;
>> z=[-1;-2];
>> p=[-3;-4;-5];
>> [NUM,DEN]=zp2tf(z,p,k)
NUM =
0 4 12 8

3. DEN =
1 12 47 60
>> home
>> %caso1
>> k=20;
>> help tf2zp
tf2zp - Convert transfer function filter parameters to zero-pole-gain form
This MATLAB function finds the matrix of zeros z, the vector of poles p, and the
associated vector of gains k from the transfer function parameters b and a:
[z,p,k] = tf2zp(b,a)
Reference page for tf2zp
See also sos2zp, ss2zp, tf2sos, tf2ss, tf2zpk, zp2tf
>> %CASO1
>> num1=[20];
>> num2=[1 10];
>> num3=[1 0 0 1];

4. >> num4=conv(num1,num2);
>> numT=conv(num4,num3);
>> den1=[1 0];
>> den2=[1 4 4];
>> den3=[1 10 100];
>> den4=[1 2 0 0 -10];
>> den5=conv(den1,den2);
>> den6=conv(den3,den4);
>> denT=conv(den5,den6);
>> sys=tf(numT,denT)
sys =
20 s^4 + 200 s^3 + 20 s + 200
------------------------------------------------------------------------------------
s^9 + 16 s^8 + 172 s^7 + 728 s^6 + 1270 s^5 + 660 s^4 - 1440 s^3 - 4400 s^2 - 4000 s
Continuous-time transfer function.
>> [z,p,k] = tf2zp(numT,denT)
z =
-10.0000 + 0.0000i
0.5000 + 0.8660i

5. 0.5000 - 0.8660i
-1.0000 + 0.0000i
p =
0.0000 + 0.0000i
-5.0000 + 8.6603i
-5.0000 - 8.6603i
1.4287 + 0.0000i
-0.4237 + 1.5912i
-0.4237 - 1.5912i
-2.5814 + 0.0000i
-2.0000 + 0.0000i
-2.0000 - 0.0000i
k =
20
>> %CASO2
>> num1=[1 1];
>> num2=[1 2 1];
>> numT=conv(num1,num2);

6. >> den1=[1 4];
>> den2=[1 3];
>> den3=[1 3];
>> den4=[1 1 1 0 2];
>> den5=conv(den1,den2);
>> den6=conv(den3,den4);
>> denT=conv(den5,den6);
>> sys=tf(numT,denT)
sys =
s^3 + 3 s^2 + 3 s + 1
------------------------------------------------------------
s^7 + 11 s^6 + 44 s^5 + 79 s^4 + 71 s^3 + 56 s^2 + 66 s + 72
Continuous-time transfer function.
>> [z,p,k] = tf2zp(numT,denT)
z =
-1.0000 + 0.0000i
-1.0000 + 0.0000i
-1.0000 - 0.0000i

7. p =
-4.0000 + 0.0000i
-3.0000 + 0.0000i
-3.0000 - 0.0000i
0.5000 + 0.8660i
0.5000 - 0.8660i
-1.0000 + 1.0000i
-1.0000 - 1.0000i
k =
1
>> %CASO3
>> %CASO3.1
>> num1=[1 2];
>> den1=[1 2 5];
>> sys1=tf(num1,den1);
>> num2=[1];
>> den2=[1];
>> sys2=tf(num2,den2);
>> sysT=feedback(sys1,sys2)

8. sysT =
s + 2
-------------
s^2 + 3 s + 7
Continuous-time transfer function.
>> [z,p,k] = tf2zp(sys)