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Decompose generalized LTI model



[H,B,S] = getLFTModel(M) decomposes the Generalized matrix or Generalized LTI model M into the components H, B, and S. The H, B, and S components relate to M as shown in this figure. For more information, see Internal Structure of Generalized Models.

Generalized LTI Model, M, comprised of components H, B, and S.

You can recombine H, B, and S into M by using the lft function.

M = lft(H,blkdiag(B{:})-S);


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Create a genss model.

G = zpk([],[-1 -1],1);
C = tunablePID("C",'PID');
a = realp("a",10);  
F = tf(a,[1 a]);
T = feedback(G*C,1)*F;

Decompose the generalized LTI model.

[H,B,S] = getLFTModel(T)
H =
  A = 
       x1  x2  x3
   x1  -1   1   0
   x2   0  -1   0
   x3   0   0   0
  B = 
       u1  u2  u3  u4
   x1   0   0   0   0
   x2   0   1   0   0
   x3   1   0  -1   0
  C = 
       x1  x2  x3
   y1   1   0   0
   y2  -1   0   0
   y3   0   0   1
   y4   0   0   1
  D = 
       u1  u2  u3  u4
   y1   0   0   0   0
   y2   0   0   0   1
   y3   0   0   0   0
   y4   0   0   0   0
Continuous-time state-space model.
B=3×1 cell array
    {1x1 tunablePID}
    {1x1 realp     }
    {1x1 realp     }

S = 3×3

     0     0     0
     0     0     0
     0     0     0

Input Arguments

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Generalized LTI model or matrix, specified as a genss object, genfrd object, or a genmat object. For more information on generalized LTI models, see Generalized and Uncertain LTI Models. For more information on generalized matrices, see Generalized Matrices.

Output Arguments

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Nonparametric component of the generalized model, returned as a matrix. The component H is a numeric matrix, ss model, or frd model that describes the fixed portion of M and the interconnections between the blocks of B.

Parametric component of the generalized model, returned as a cell array. Each cell of the cell array B contains a Control Design Block of M, such as realp or tunableSS block.

Offset values, returned as a matrix. This value is a block diagonal matrix of numeric offsets, where each row contains the offset for the block in the corresponding cell of B. The offsets ensure well-defined interconnection when the current (nominal) value of M is finite.

Version History

Introduced in R2011a