<p>% 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])</p><p>% 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</p><p>E x a c t v e r s u s a s y m p t o t e f r e q u e n c y r e s p o n s e o f 1 / s + 1 0 - 1 0</p><p>- 2 0 ) B d (</p><p> e d</p><p> u - 3 0 t i n g a</p><p> m - 4 0</p><p>- 5 0 0 1 2 1 0 1 0 1 0 F r e q u e n c y ( r / s )</p><p>0</p><p>- 2 0 ) g e d</p><p>( - 4 0</p><p> e s a</p><p> h - 6 0 p</p><p>- 8 0</p><p>- 1 0 0 0 1 2 1 0 1 0 1 0 F r e q u e n c y ( r / s ) p a r t a 1 0 0</p><p>5 0 ) B d (</p><p>0 g a m</p><p>- 5 0</p><p>- 1 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>- 8 0</p><p>- 1 0 0 ) g</p><p> e - 1 2 0 d ( e s a - 1 4 0 h P</p><p>- 1 6 0</p><p>- 1 8 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p> p a r t b 1 0 0</p><p>5 0</p><p>0 ) B d (</p><p>- 5 0 g a m - 1 0 0</p><p>- 1 5 0</p><p>- 2 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>- 5 0</p><p>- 1 0 0 ) g</p><p> e - 1 5 0 d ( e s a - 2 0 0 h P</p><p>- 2 5 0</p><p>- 3 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p> p a r t c 5 0</p><p>0</p><p>- 5 0 ) B d (</p><p>- 1 0 0 g a m - 1 5 0</p><p>- 2 0 0</p><p>- 2 5 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>- 5 0</p><p>- 1 0 0 ) g</p><p> e - 1 5 0 d ( e s a - 2 0 0 h P</p><p>- 2 5 0</p><p>- 3 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s ) p a r t d 0</p><p>- 1 0 0 ) B d (</p><p>- 2 0 0 g a m</p><p>- 3 0 0</p><p>- 4 0 0 -2 -1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>0</p><p>- 1 0 0 ) g e d (</p><p> e - 2 0 0 s a h P - 3 0 0</p><p>- 4 0 0 -2 -1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p> p a r t e 1 0 0</p><p>0 ) B d (</p><p>- 1 0 0 g a m</p><p>- 2 0 0</p><p>- 3 0 0 -2 -1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>- 5 0</p><p>- 1 0 0 ) g e - 1 5 0 d ( e s a - 2 0 0 h P</p><p>- 2 5 0</p><p>- 3 0 0 -2 -1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p> p a r t f 5 0</p><p>0</p><p>) - 5 0 B d ( g a - 1 0 0 m</p><p>- 1 5 0</p><p>- 2 0 0 -2 -1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>0</p><p>- 5 0</p><p>) - 1 0 0 g e d (</p><p> e - 1 5 0 s a h</p><p>P - 2 0 0</p><p>- 2 5 0</p><p>- 3 0 0 -2 -1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s ) p a r t g 1 0 0</p><p>5 0</p><p>0 ) B d (</p><p>- 5 0 g a m - 1 0 0</p><p>- 1 5 0</p><p>- 2 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>- 5 0</p><p>- 1 0 0 ) g e d (</p><p> e - 1 5 0 s a h P - 2 0 0</p><p>- 2 5 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p> p a r t h - 2 0</p><p>- 4 0 ) B d (</p><p>- 6 0 g a m</p><p>- 8 0</p><p>- 1 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>1 0 0</p><p>5 0 ) g e d (</p><p> e 0 s a h P - 5 0</p><p>- 1 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p> p a r t i - 5 0</p><p>- 1 0 0 ) B d (</p><p>- 1 5 0 g a m</p><p>- 2 0 0</p><p>- 2 5 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>1 0 0</p><p>0 ) g e d (</p><p> e - 1 0 0 s a h P - 2 0 0</p><p>- 3 0 0 - 2 - 1 0 1 2 3 4 1 0 1 0 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s ) 5 0</p><p>0 p o l e = 1 0 0 p o l e = 0 . 1 p o l e = 0 . 0 1 ) - 5 0 B d ( g a - 1 0 0 m</p><p>- 1 5 0</p><p>- 2 0 0 - 2 - 1 0 1 2 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p><p>0</p><p>- 5 0 p o l e = 1 0 0 ) - 1 0 0 g e</p><p> d p o l e = 1 (</p><p> e - 1 5 0 s p o l e = 0 . 1 a p o l e = 0 . 0 1 h</p><p>P - 2 0 0</p><p>- 2 5 0</p><p>- 3 0 0 - 2 - 1 0 1 2 1 0 1 0 1 0 1 0 1 0 F r e q ( r / s )</p>