University study material for Control and Actuating Devices for Mechanical Systems in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: 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 -
University study material for Control and Actuating Devices for Mechanical Systems in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: 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 -
Import quality: text was extracted directly from the original document.
Representative passages recognised in different parts of the material. The full extracted text remains available to search, while this compact preview makes the page easier to read.
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…
First page of the document.
