EGLM03 Exam 2009-10: Correction to Q4(c) calculation of observer gains using Ackermann's formula

q4c_correction_2010.m

%% EGLM03 Exam 2009-10: Q4(c) Correction.
% Define system to be observed (controller canonical form)
A = [-13, -39, -27; 1, 0, 0; 0, 1, 0];
B = [1; 0; 0];
C = [0,5,2];
% Design of an observer using Ackermann's formula
At = A';
Ct = C';
Obs = [Ct, At * Ct, (At)^2 * Ct];
ObsI = inv(Obs)
% Note
% the desired observer poles alpha_e(s) = (s+3)(s + 9)(s+27) = s^3 + 39s^2 + 351s+729
alpha_e = At^3 + 29*At^2 + 351*At + 729
& Calculate observer gains (this Ackermann's formula)
Lt = [0, 0, 1] * ObsI * alpha_e
L = Lt'