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CME4.1 - AOCF = 0-2.0000 1.0000-3.0000 BOCF = COCF =-0.0000...

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Sheet1 Page 1 %------------------------------------------------------ % CME 4.1 %------------------------------------------------------ A = [-1 0 B = [1 C = [1 -(sqrt(2)/2)] D = [0] JbkR = ss(A,B,C,D) Q = obsv(JbkR) Q1=[C CharPoly = poly(A) % characteristic polynomial if (rank(Q) == size(A,1)) % Logic to assess % observability disp('System is observable.') else disp('System is NOT observable.') end a1 = CharPoly(2) Pccfi = [a1 1 % matrix Pccf Qocf = inv(Pccfi) Tocf=inv(Q)*Qocf % transformation %matrix Aocf=inv(Tocf)*A*Tocf % via formula Bocf = inv(Tocf)*B Cocf = C*Tocf Docf = D [JbkROCF,TOCF] = canon(JbkR,'companion') % using canon AOCF = JbkROCF.a BOCF = JbkROCF.b COCF = JbkROCF.c DOCF = JbkROCF.d %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Answer from Matlab %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% a)System is observable.

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Sheet1 Page 2 b) Tocf = 1.0000 -1.0000 1.4142 -2.8284 Aocf = 0 -2 01/ Bocf = Cocf = 0 1 Docf = %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % the answers using canon to cmpute OCF(same as above)

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Unformatted text preview: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% AOCF = 0 -2.0000 1.0000 -3.0000 BOCF = COCF =-0.0000 1.0000 DOCF = %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % the answers from CME3.1b Sheet1 Page 3 % In this case, we can see that there is a connection % between controllability and observability known as % duality %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Tccf = 2.0000 1.0000 1.4142 1.4142 Accf = 0.0000 1.0000-2.0000 -3.0000 Bccf = Ccf = 1.0000 0.0000 Dcf = %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sheet1 Page 4 0 -2] % Define the state-space realization sqrt(2)] % Define model from state-space % Calculate observability C*A] % Check Q via the formula % Determine the system % Extract a1 1 0] % Calculate the inverse of % Calculate OCF % Transform to OCF % Compute OCF Sheet1 Page 5 Sheet1 Page 6...
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