State space representation

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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:


To verify that this is indeed the same system, we compare the roots of this transfer function to the eigenvalues of the system matrix:



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