Gyan: Created page with '{|border="1" width=100% ! width=20% | Visual Cue ! width=60% | Narration |- | Show first slide | Now we see how to represent a system in state space. We use the following A, B, …'

2012-12-24T10:36:26Z

Created page with '{|border="1" width=100% ! width=20% | Visual Cue ! width=60% | Narration |- | Show first slide | Now we see how to represent a system in state space. We use the following A, B, …'

New page

{|border="1" width=100%
! width=20% | Visual Cue
! width=60% | Narration

|-
|
Show first slide
|
Now we see how to represent a system in state space. We use the following A, B, C, D parameters:
|-
|

A = [0, 1; -1, -0.5]
B = [0; 1]
C = [1, 0]
D = [0]
|
We must define the initial state of the system. In order to show the true utility of this method, we choose a non-zero initial state; let it be 1:
|-
|

x0=[1; 0]
|
We formally define the system with the above parameters as follows using the same 'syslin' function we used earlier:
|-
|

SSsys = syslin('c', A, B, C, D, x0)
|
We simulate this system for 50 seconds:
|-
|

t = [0: 0.1: 50];
|
However, since the initial state of the system is at 1, we choose a step of 0.5:
|-
|

u = 0.5*ones(1, length(t));
|
We simulate the system:
|-
|

[y,x] = csim(u, t, SSsys);
|
We plot the output:
|-
|

scf(1); plot(t, y)
|
We can also plot the internal state of the system:
|-
|

scf(2); plot(t, x)
|
We can view the root locus of this sytem:
|-
|

evans(SSsys) //zoom in
|
For a more intuitive view of this system, we can convert this system from state space to its transfer function representation using the ss2tf function:
|-
|

ss2tf(SSsys)
|
To verify that this is indeed the same system, we compare the roots of this transfer function to the eigenvalues of the system matrix:
|-
|

roots(denom(ans))
spec(A)
|
END
|}

State space representation - Revision history

Gyan: Created page with '{|border="1" width=100% ! width=20% | Visual Cue ! width=60% | Narration |- | Show first slide | Now we see how to represent a system in state space. We use the following A, B, …'