nt425416

# nt425416 - >> Bkh=Bh*K Bkh = 0 0 0 0 0 0 0 0 0 3...

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Example Consider the system A = 0 1 0 0 -2 -1 0 1 0 0 0 1 0 1 -2 -1 B = 0 1 0 0 We form the controllability matrix [A^3*B A^2*B A*B B]: C = 0 -1 1 0 0 0 -1 1 -2 1 0 0 0 -2 1 0 >> d=det(C) = 2 First transformation: >> At = inv(C)*A*C At = -2 1 0 0 -4 0 1 0 -4 0 0 1 -4 0 0 0 >> Bt=inv(C)*B Bt = 0 0 0 1
Second transformation D = 1 0 0 0 2 1 0 0 4 2 1 0 4 4 2 1 >> Ah=inv(D)*At*D Ah = 0 1 0 0 0 0 1 0 0 0 0 1 -4 -4 -4 -2 >> Bh=inv(D)*Bt Bh = 0 0 0 1 To get eigenvalues of closed loop system all equal to -1 we need the last row to be [-1 -4 -4 -4], corresponding to >> K=[3 0 -2 -2]

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Unformatted text preview: >> Bkh=Bh*K Bkh = 0 0 0 0 0 0 0 0 0 3 0 -2 -2 >> Aclh=Ah+Bkh gives the closed loop matrix, with all eigenvalues equal to -1: Aclh = 0 1 0 0 0 1 0 0 0 1-1 -4 -6 -4 To go back to the closed loop system in the original coordinates: >> Acl=C*D*Aclh*inv(D)*inv(C) Acl = 0 1.0000 0 -0.5000 -3.0000 2.5000 -0.5000 0 0 0 1.0000 0 1.0000 -2.0000 -1.0000 The feedback matrix in the original coordinates is then >> Ko = K*inv(D)*inv(C) = 1.5000 -2.0000 2.5000 -1.5000...
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nt425416 - >> Bkh=Bh*K Bkh = 0 0 0 0 0 0 0 0 0 3...

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