fprintf('The date and time: %s \n \n', datestr(now)) disp('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%') disp('% %') disp('% Test 3. %') disp('% Programer: Aaron Klapheck %') disp('% %') disp('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%') fprintf('\n') % Solve: y'' + y = F/m*sin(t); y(0) = 0, y'(0) = 0, F = m = 1 % Solution: y(t) = 1/2*sin(t) - 1/2*t*cos(t) % % Analytic solution: % t = [0:.1:30]; % y = 1/2.*sin(t) - 1/2.*t.*cos(t); % % % % % got solution from: http://www.ibiblio.org/links/devmodules/forcedsm/ % % Their problem: y'' + w^2*y = F/m*sin(wt), y(0) = x_0, y'(0) = v_0. % where w, F, and m are constants. % % Their solution: y(t) = A*cos(wt) + B*sin(wt) - (F/m)/(2w)*t*cos(wt). % where A = x_0, and B = v_0/w + (F/m)/(2w^2). %
The date and time: 16-Apr-2008 10:43:52 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Test 3. % % Programer: Aaron Klapheck % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('%%%% Number 1. %%%%%') % Solve Using MATLAB's ODE45 solver. Tspan = [0 30]; initc = [0, 0]; p = [1, 1]; [T, Y] = ode45(@SolveODE2nd, Tspan, initc, [], p); % Anilytical function. t = [0:.1:30]; y = 1/2.*sin(t) - 1/2.*t.*cos(t); % Plot both figure(1) plot(T, Y(:,1),t, y), ... legend('Numerical MATLAB', 'Exact')
%%%% Number 1. %%%%%
disp('%%%% Number 2. %%%%%') % Solve Using Simulink's Embedded function block. fprintf('\nDirrectory is: \n') dir load SecondOrderEmbed.mat fprintf('\nDisplay all variables: \n') whos % Anilytical function. t = [0:.1:30]; y = 1/2.*sin(t) - 1/2.*t.*cos(t); % Plot both figure(2) plot(SecondTransferEmbed(1,:), SecondTransferEmbed(2,:),t, y), ... legend('Numerical Simulink Embedded Function', 'Exact')
%%%% Number 2. %%%%% Dirrectory is: . SimSolveDE2ndEmbed_sfun.dll .. SimSolveDE2ndTransfer.mdl PracticeTest3_Driver.asv SimSolveDE2ndTransferScopeOut.mdl PracticeTest3_Driver.m SolveODE1st.m SecondOrder.mat SolveODE2nd.m SecondOrderEmbed.mat Transfer_Functions.asv SecondOrderTransfer.mat Transfer_Functions.m SimSolveDE1st.mdl firstOrder.mat SimSolveDE2nd.mdl html SimSolveDE2ndEmbed.mdl Display all variables: Name Size Bytes Class ScopeData 52x2 832 double array SecondTransferEmbed 2x53 848 double array SecondTransfered 2x52 832 double array T 157x1 1256 double array Tspan 1x2 16 double array Y 157x2 2512 double array initc 1x2 16 double array p 1x2 16 double array t 1x301 2408 double array tout 52x1 416 double array y 1x301 2408 double array Grand total is 1445 elements using 11560 bytes
Simulink Model:
disp('%%%% Number 3. %%%%%') % Solve Using Simulink's Transfer function block. fprintf('\nDirrectory is: \n') dir load SecondOrderTransfer.mat fprintf('\nDisplay all variables: \n') whos % Anilytical function. t = [0:.1:30]; y = 1/2.*sin(t) - 1/2.*t.*cos(t); % Plot both figure(3) plot(SecondTransfered(1,:), SecondTransfered(2,:),t, y), ... legend('Numerical Simulink Transfer Function', 'Exact')
%%%% Number 3. %%%%% Dirrectory is: . SimSolveDE2ndEmbed_sfun.dll .. SimSolveDE2ndTransfer.mdl PracticeTest3_Driver.asv SimSolveDE2ndTransferScopeOut.mdl PracticeTest3_Driver.m SolveODE1st.m SecondOrder.mat SolveODE2nd.m SecondOrderEmbed.mat Transfer_Functions.asv SecondOrderTransfer.mat Transfer_Functions.m SimSolveDE1st.mdl firstOrder.mat SimSolveDE2nd.mdl html SimSolveDE2ndEmbed.mdl Display all variables: Name Size Bytes Class ScopeData 52x2 832 double array SecondTransferEmbed 2x53 848 double array SecondTransfered 2x52 832 double array T 157x1 1256 double array Tspan 1x2 16 double array Y 157x2 2512 double array initc 1x2 16 double array p 1x2 16 double array t 1x301 2408 double array tout 52x1 416 double array y 1x301 2408 double array Grand total is 1445 elements using 11560 bytes
Simulink Model:
disp('%%%% Number 4. %%%%%') % Solve Using Simulink's Transfer function block. Alter the scope so that % it will output the variables. Remember to run the Simulink model first! fprintf('\nDisplay all variables: \n') whos % Anilytical function. t = [0:.1:30]; y = 1/2.*sin(t) - 1/2.*t.*cos(t); % Plot both figure(4) plot(ScopeData(:, 1), ScopeData(:, 2),t, y), ... legend('Numerical Simulink Transfer Function', 'Exact')
%%%% Number 4. %%%%% Display all variables: Name Size Bytes Class ScopeData 52x2 832 double array SecondTransferEmbed 2x53 848 double array SecondTransfered 2x52 832 double array T 157x1 1256 double array Tspan 1x2 16 double array Y 157x2 2512 double array initc 1x2 16 double array p 1x2 16 double array t 1x301 2408 double array tout 52x1 416 double array y 1x301 2408 double array Grand total is 1445 elements using 11560 bytes
Simulink Model:
