Collections of notes for the oral exam Matlab

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1 REQUEST AND NOTES FOR THE ORAL EXAM NOTES: - Report for the exam: can be done in team (3/4 people) REQUESTS: • LAB1: Consider a proportional control (P controller) with the data given during the lesson and plot the diagrams for the 3 cases: - A value of Kp which gives k* > 0 - A value of Kp which gives k* = 0 - A value of Kp which gives k* < 0 Modify the program to consider a PD and a PI controller (just for one of the 3 cases of K* at your choice) • LAB2: 2 LAB 1 % Always write initial commands to close al clear all clear all close all clc % SYSTEM DATA m = 3; L = 4; J = 1/12*m*L^2; k = 150; c = 10; g = 9.81; % EQUIVALENT PARAMETERS OF THE SYSTEM mx = J+m*L^2/4 cx = c*L^2/4 kx = k*L^2/4 - m*g*L/2 if kx>0 disp('Natural frequency of the undamped system [rad/s]:') omega_n = sqrt(kx/mx) end % STATE SPACE FORM % we compute the state space form of the system in order to study % stability through the eignevalues P = [m 0; 0 1]; Q = [cx kx; -1 0]; N = [1;0]; % we compute state matrix computed as the inverse of P times Q and % than we can compute its eigenvalues A = -inv(P)*Q B = inv(P)*N lambda = eig(A) % function eing: with one putput gives the eigenvalues and with 2 % outputs gives also the eigenvectors % for example [eigvect, eigval]=eig(A) 3 % EXAMPLE: P CONTROLLER % same procedure as before can be used to compute the eigenvalues % of the controlled system kp = 100; if kx+kp>0 disp ('Natural frequency of the controlled undamped system [rad/s]:') omega_nc = sqrt((kx+kp)/mx) end % the matrix P doesn't change but the matrix Q does Qc = [cx kx+kp; -1 0]; Ac = -inv(P)*Qc lambda_c = eig(Ac) % LAPLACE DOMAIN: SPECIFIC FUNCTIONS % TRANSFERT FUNCTIONS % there are specific funcions in matlab to work in the laplace % domain, such as tf, which take as inputs arreys which represents…