State Space Model-Control Systems-Lab Reports, Exercises of Control Systems

This is lab report Control Systems lab. It was assigned by and submitted to Dr. Anbu Manghirmalani at Birla Institute of Technology and Science. It includes: State, Space, Model, Responce, Matlab, Frequency, System, Damping, Overshoot, Simulink

Typology: Exercises

2011/2012

Uploaded on 07/30/2012

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Lab 8: Studying State Space FA06_BET_012
Lab Task
Find state space model and plot their response:
1. T(s) = (s + 10) / (s3 + 6s2 + 9s + 10)
2. T(s) = 5(s + 20) / s(s + 4.59) (s2 + 3.41s + 16.35)
3. T(s) = (6s2 + 1) / (s3 + 3s2 + 3s + 1)
num1 = [1 10];
den1 = [1 6 9 10];
[A,B,C,D] = tf2ss(num1 , den1)
figure,pzmap(num1,den1)
figure,step(A,B,C,D)
num2 = [5 10];
den2 = conv([1 4.59 0],[1 3.41 16.35]);
[A2,B2,C2,D2] = tf2ss(num2 , den2)
figure,step(A2,B2,C2,D2)
figure,pzmap(num2,den2)
num3 = [6 0 1];
den3 = [1 3 3 1]
[A3,B3,C3,D3] = tf2ss(num3 , den3)
figure,pzmap(num3,den3)
figure,step(A3,B3,C3,D3)
Matlab Code:
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Lab 8: Studying State Space FA06_BET_

Lab Task

Find state space model and plot their response:

1. T(s) = (s + 10) / (s^3 + 6s^2 + 9s + 10)

2. T(s) = 5(s + 20) / s(s + 4.59) (s^2 + 3.41s + 16.35)

3. T(s) = (6s^2 + 1) / (s^3 + 3s^2 + 3s + 1)

num1 = [1 10]; den1 = [1 6 9 10]; [A,B,C,D] = tf2ss(num1 , den1) figure,pzmap(num1,den1) figure,step(A,B,C,D) num2 = [5 10]; den2 = conv([1 4.59 0],[1 3.41 16.35]); [A2,B2,C2,D2] = tf2ss(num2 , den2) figure,step(A2,B2,C2,D2) figure,pzmap(num2,den2) num3 = [6 0 1]; den3 = [1 3 3 1] [A3,B3,C3,D3] = tf2ss(num3 , den3) figure,pzmap(num3,den3) figure,step(A3,B3,C3,D3)

Matlab Code:

Lab 8: Studying State Space FA06_BET_

A =

B =

C =

D =

A2 =

B2 =

Results:

Lab 8: Studying State Space FA06_BET_

Figure 2. For second system Figure 3. For third system

Simulink Block Diagrams:

Figure 4. Block diagram for the three functions

Lab 8: Studying State Space FA06_BET_

Figure 7. Step response of 3rd^ system in Simulink Figure 6. Step response of 2 nd^ system in Simulink Figure 5. Step response of 1 st^ system in Simulink