1. Objectives Students should be able to use basic MATLAB commands for control s
ID: 2291553 • Letter: 1
Question
1. Objectives Students should be able to use basic MATLAB commands for control systems engineering. 2. System Representations Find a state space represent by typing A"[0 1 0; 001;-4-3-2); B 2: 3: 1 C-[2 3 51; sys ss (A, B, C, D) Find the A, B,C, D matrices by typing sys.a sys.b sys. ? sys.d We can use tf or ss2tf to convert a state-space representation into a transfer function Gi-tf (sys) or [num den] -ss2tf (A, B,C,D) Gl-tf (num, den) We can also convert a transfer function into a state-space representation num [18 50 58]; den[1 2 3 41; A B C D-tf2ss (num, den) or H1ss (G1) Compare the answers with the A, B, C, D matrices you created. We can plot the step response of a system using step (Note that 1 is a state-space representation not a transfer function) step (H1) stepinfo returns step response characteristics. For example stepinfo (H1) will returnExplanation / Answer
Problem 1:
The following is the MATLAB code to find state space representation:
(a)
MATLAB code:
>> num=[1 5];
>> den=[1 2 10 2];
>> [A B C D]=tf2ss(num,den)
MATLAB output:
A =
-2 -10 -2
1 0 0
0 1 0
B =
1
0
0
C =
0 1 5
D =
0
(b)
MATLAB code:
>> num=[1 3 2];
>> den=[1 4 7];
>> [A B C D]=tf2ss(num,den)
MATLAB output:
A =
-4 -7
1 0
B =
1
0
C =
-1 -5
D =
1
Problem 2:
(a)
MATLAB code:
>> A=[0 1 0;0 0 1;-3 -2 -5];
>> B=[0;0;10];
>> C=[1 0 0];
>> D=0;
>> [num den]=ss2tf(A,B,C,D);
>> G=tf(num, den)
MATLAB output:
G =
10
---------------------
s^3 + 5 s^2 + 2 s + 3
Continuous-time transfer function.
(b)
MATLAB code:
>> A=[2 -3 -8;0 5 3;-3 -5 -4];
>> B=[0;1;2];
>> C=[1 3 0];
>> D=0;
>> [num den]=ss2tf(A,B,C,D);
>> G=tf(num, den)
MATLAB output:
G =
3 s^2 + 5 s - 42
------------------------
s^3 - 3 s^2 - 27 s + 103
Continuous-time transfer function.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.