Path: Common/Control
% Use eigenvector assignment to design a controller.
Complex lambdas must be in pairs. Their corresponding eigenvectors
must also be complex.
The design matrix, d.
One column per state. Each row relates vD to the
plant matrix. For example, rows 7 and 8 relate column 3 in vD to
the plant. In this case vD(1,3) relates to state 2 and vD(2,4)
relates to state 3. vD need not have as many columns as states.
If the desired vD are eigenvectors then d is the identity matrix
If the desired vectors are directions in the output then D = c
If components of v are no concern the corresponding column of D
should be zero.
rD gives the rows in D per eigenvalue
Each column is for one eigenvalue
i.e. column one means that the first three rows of D relat
to eigenvalue 1
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Form:
[k, v] = EVAssgnC( g, lambda, vD, d, rD, w )
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Inputs
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g (:) State space system of type statespace
lambda (n) Desired eigenvalues
vD (:,n) Desired eigenvectors
d (:,n) Design matrix
rD (n) Rows in d per eigenvalue
w (:,n) Weighting vectors
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Outputs
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k Gain matrix
v Achieved eigenvectors
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Reference: Stevens, B.L., Lewis, F.L. Aircraft Control and Simulation
John Wiley & Sons, 1992, pp. 342-358.
Andry, A. N., Jr., Shapiro, E.Y. and J.C. Chung, "Eigenstructure
Assignment for Linear Systems," IEEE Transactions on Aerospace
and Electronic Systems, Vol. AES-19, No. 5. September 1983.
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Math: Solvers/LSSVD
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