ex3_10 - pause Rerun with T = 1 sec convolution n=0:40 kf =...

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% Example 3.10 % % % numerical convolution of a continuous time system % % The example is run with 3 different values of T. % For each value of T, the numerical convolution is % compared to the exact answer. The response is calculated % for 40 sec % % T = 2 sec % numerical convolution % to determine n, note that y(40) = y(20*2) n=0:20; kf = 0.1; m = 1; T = 2; h = (1-exp(-kf*n*T/m))/kf; x = [ones(1,5) -ones(1,5) zeros(1,10)]; y = conv(T*h,x); % % exact solution t1 = 0:.1:9.9; % defines the segments of t t2 = 10:.1:19.9; t3 = 20:.1:40; ya = [100*(0.1*t1-1+exp(-0.1*t1)),-100*(0.1*t2-3+(2*exp(1)-1). .. *exp(-0.1*t2)),100*(1-2*exp(1)+exp(1)^2)*exp(-0.1*t3)]; t = [t1,t2,t3]; plot(n*T,y(1:length(n)),'o',t,ya,'-') title('Example 3.10, T = 2 sec') xlabel('Time (sec)') ylabel('y(t)') % insert legend hold on plot([23 24 25],[50 50 50],'o',[23 24 25],[45 45 45]); text(26,50,'Approximate solution') text(26,45,'Exact solution') hold off
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Unformatted text preview: pause % % Rerun with T = 1 sec % convolution n=0:40; kf = 0.1; m = 1; T = 1; h = (1-exp(-kf*n*T/m))/kf; x = [ones(1,10) -ones(1,10) zeros(1,20)]; y = conv(T*h,x); plot(n*T,y(1:length(n)),'o',t,ya,'-') title('Example 3.10, T = 1 sec') xlabel('Time (sec)') ylabel('y(t)') % insert legend hold on plot([23 24 25],[50 50 50],'o',[23 24 25],[45 45 45]); text(26,50,'Approximate solution') text(26,45,'Exact solution') hold off pause % % Rerun with T = 0.5 % convolution n=0:80; kf = 0.1; m = 1; T = .5; h = (1-exp(-kf*n*T/m))/kf; x = [ones(1,20) -ones(1,20) zeros(1,40)]; y = conv(T*h,x); % % exact solution plot(n*T,y(1:length(n)),'o',t,ya,'-') title('Example 3.10, T = 0.5 sec') xlabel('Time (sec)') ylabel('y(t)') % insert legend hold on plot([23 24 25],[50 50 50],'o',[23 24 25],[45 45 45]); text(26,50,'Approximate solution') text(26,45,'Exact solution') hold off...
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ex3_10 - pause Rerun with T = 1 sec convolution n=0:40 kf =...

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