% Practice Problems 6.2, 6.3, 6.12

% Practice problems 6.2, 6.3, 6.12 % Jeff Pieper % March 2004 clear % Problem 6.2 w = [ 1 2 5 10 20 50 100 ] ; G = tf(1,[1 10]) ; [m,p]=bode(G,w) ; for k=1:length(w), mdb(k) = 20*log10(m(:,:,k)) ; ph(k) = p(:,:,k) ; end mlow = 20*log10(1/10) ; figure(1) clf subplot(2,1,1) semilogx(w,mdb,'x',[1 10],[mlow mlow],'-b',[10 100],[mlow mlow-20],'-b') xlabel('Frequency (r/s)') ylabel('magnitude (dB)') title('Exact versus asymptote frequency response of 1/s+10') axis([1 100 -50 -10]) subplot(2,1,2) semilogx(w,ph,'x',[1 10],[0 0],'-b',[10 10],[0 -90],'-b',[10 100],[-90 -90],'-b') xlabel('Frequency (r/s)') ylabel('phase (deg)') axis([1 100 -100 10])

% problem 6.3 clear Ga = tf(4000,[1 400 0]) ; Gb = tf(100,conv([0.1 1 0],[0.5 1])) ; Gc = tf(1,conv([1 1 0],[0.02 1])) ; Gd = tf(1,conv([1 2 1],[1 2 4])) ; Ge = tf([10 40],conv([1 1 0],[1 2 5])) ; Gf = tf([1000 100],conv([1 1 0],[1 8 64])) ; Gg = tf(conv([1 5],[1 3]),conv([1 1 0],[1 1 4])) ; Gh = tf([4 40 0],conv([1 100],[4 5 4])) ; Gi = tf([1 0],conv([1 1],conv([1 10],[1 2 2500]))) ; w= logspace(-2,4,200) ; for j=1:9, switch j case 1 G=Ga ; msg = 'part a' ; case 2 G=Gb ; msg = 'part b' ; case 3 G=Gc ; msg = 'part c' ; case 4 G=Gd ; msg = 'part d' ; case 5 G=Ge ; msg = 'part e' ; case 6 G=Gf ; msg = 'part f' ; case 7 G=Gg ; msg = 'part g' ; case 8 G=Gh ; msg = 'part h' ; case 9 G=Gi ; msg = 'part i' ; end [m,p]=bode(G,w) ; for k=1:length(w), mdb(k) = 20*log10(m(:,:,k)) ; ph(k) = p(:,:,k) ; end figure(1+j) clf subplot(2,1,1) semilogx(w,mdb) xlabel('Freq (r/s)') ylabel('mag (dB)') title(msg) subplot(2,1,2) semilogx(w,ph) xlabel('Freq (r/s)') ylabel('Phase (deg)') end % problem 6.12 clear pole=[0.01 0.1 1 10 100] ; w = logspace(-2,2,100) ; figure(11) clf hold on for j=1:5, G = tf(1,conv([1/pole(j) 1],[1 1 1])) ; [m,p] = bode(G,w) ; for k=1:length(w), mdb(k) = 20*log10(m(:,:,k)) ; ph(k) = p(:,:,k) ; end msg = ['pole = ',num2str(pole(j))] ; subplot(2,1,1) semilogx(w,mdb) hold on xlabel('Freq (r/s)') ylabel('mag (dB)') text(1,mdb(50),msg) subplot(2,1,2) semilogx(w,ph) hold on xlabel('Freq (r/s)') ylabel('Phase (deg)') text(1,ph(50),msg) end

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