Buscar

Pratica Matlab 10052014

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

>> clear all
>> ft
??? Undefined function or variable 'ft'.
>> help ft
ft not found.
Use the Help browser Search tab to search the documentation, or
type "help help" for help command options, such as help for methods.
>> help zpk]
zpk] not found.
Use the Help browser Search tab to search the documentation, or
type "help help" for help command options, such as help for methods.
>> help zpk
 ZPK Create zero-pole-gain models or convert to zero-pole-gain format.
 
 Creation:
 SYS = ZPK(Z,P,K) creates a continuous-time zero-pole-gain (ZPK) 
 model SYS with zeros Z, poles P, and gains K. The output SYS is 
 a ZPK object. 
 
 SYS = ZPK(Z,P,K,Ts) creates a discrete-time ZPK model with sample
 time Ts (set Ts=-1 if the sample time is undetermined).
 
 S = ZPK('s') specifies H(s) = s (Laplace variable).
 Z = ZPK('z',TS) specifies H(z) = z with sample time TS.
 You can then specify ZPK models directly as rational expressions in 
 S or Z, e.g.,
 z = zpk('z',0.1); H = (z+.1)*(z+.2)/(z^2+.6*z+.09)
 
 SYS = ZPK creates an empty zero-pole-gain model.
 SYS = ZPK(D) specifies a static gain matrix D.
 
 In all syntax above, the input list can be followed by pairs
 'PropertyName1', PropertyValue1, ...
 that set the various properties of ZPK models (type LTIPROPS for 
 details). To make SYS inherit all its LTI properties from an 
 existing LTI model REFSYS, use the syntax SYS = ZPK(Z,P,K,REFSYS).
 
 Data format:
 For SISO models, Z and P are the vectors of zeros and poles (set 
 Z=[] if no zeros) and K is the scalar gain.
 
 For MIMO systems with NY outputs and NU inputs, 
 * Z and P are NY-by-NU cell arrays where Z{i,j} and P{i,j} 
 specify the zeros and poles of the transfer function from
 input j to output i
 * K is the 2D matrix of gains for each I/O channel. 
 For example,
 H = zpk( {[];[2 3]} , {1;[0 -1]} , [-5;1] )
 specifies the two-output, one-input ZPK model
 [ -5 /(s-1) ]
 [ (s-2)(s-3)/s(s+1) ] 
 
 Arrays of zero-pole-gain models:
 You can create arrays of ZPK models by using ND cell arrays for Z,P 
 above, and an ND array for K. For example, if Z,P,K are 3D arrays 
 of size [NY NU 5], then 
 SYS = ZPK(Z,P,K) 
 creates the 5-by-1 array of ZPK models
 SYS(:,:,m) = ZPK(Z(:,:,m),P(:,:,m),K(:,:,m)), m=1:5.
 Each of these models has NY outputs and NU inputs.
 
 To pre-allocate an array of zero ZPK models with NY outputs and NU 
 inputs, use the syntax
 SYS = ZPK(ZEROS([NY NU k1 k2...])) .
 
 Conversion:
 SYS = ZPK(SYS) converts an arbitrary LTI model SYS to the ZPK 
 representation. The result is a ZPK object. 
 
 See also ltimodels, exp, set, get, lti/zpkdata, zpk, ss, frd.
 Overloaded methods:
 lti/zpk
 mfilt.zpk
 adaptfilt.zpk
 idmodel/zpk
 idfrd/zpk
 mpc/zpk
 dfilt.zpk
>> G = zpk([],[2 3],[1])
 
Zero/pole/gain:
 1
-----------
(s-2) (s-3)
 
>> G = zpk([],[0 -36 -100],[1])
 
Zero/pole/gain:
 1
----------------
s (s+36) (s+100)
 
>> G = zpk([],[0 -36 -100],[144000])
 
Zero/pole/gain:
 144000
----------------
s (s+36) (s+100)
 
>> G = zpk([],[0 -36 -100],[144000])
 
Zero/pole/gain:
 144000
----------------
s (s+36) (s+100)
 
>> H = 1
H =
 1
>> help feedback
 FEEDBACK Feedback connection of two LTI models. 
 
 SYS = FEEDBACK(SYS1,SYS2) computes an LTI model SYS for
 the closed-loop feedback system
 
 u --->O---->[ SYS1 ]----+---> y
 | | y = SYS * u
 +-----[ SYS2 ]<---+
 
 Negative feedback is assumed and the resulting system SYS 
 maps u to y. To apply positive feedback, use the syntax
 SYS = FEEDBACK(SYS1,SYS2,+1).
 
 SYS = FEEDBACK(SYS1,SYS2,FEEDIN,FEEDOUT,SIGN) builds the more
 general feedback interconnection:
 +--------+
 v --------->| |--------> z
 | SYS1 |
 u --->O---->| |----+---> y
 | +--------+ |
 | |
 +-----[ SYS2 ]<---+
 
 The vector FEEDIN contains indices into the input vector of SYS1
 and specifies which inputs u are involved in the feedback loop.
 Similarly, FEEDOUT specifies which outputs y of SYS1 are used for
 feedback. If SIGN=1 then positive feedback is used. If SIGN=-1 
 or SIGN is omitted, then negative feedback is used. In all cases,
 the resulting LTI model SYS has the same inputs and outputs as SYS1 
 (with their order preserved).
 
 SYS = FEEDBACK(SYS1,SYS2,'name') connects SYS1 and SYS2 by matching
 I/O names. The I/O names of SYS1 and SYS2 should be fully specified.
 
 If SYS1 and SYS2 are arrays of LTI models, FEEDBACK returns an LTI
 array SYS of the same dimensions where 
 SYS(:,:,k) = FEEDBACK(SYS1(:,:,k),SYS2(:,:,k)) .
 
 See also lft, parallel, series, connect, ltimodels.
 Overloaded methods:
 lti/feedback
 idmodel/feedback
 iddata/feedback
 uss/feedback
 umat/feedback
 ufrd/feedback
 atom/feedback
 Reference page in Help browser
 doc feedback
>> FTMF = feedback(G,H)
 
Zero/pole/gain:
 144000
-------------------------------
(s+115.6) (s^2 + 20.36s + 1245)
 
>> G
 
Zero/pole/gain:
 144000
----------------
s (s+36) (s+100)
 
>> step(FTMF)
>> grid on
>> step(FTMF)
>> step(FTMF)
>> grid on
>> impulse(FTMF)
>> grid on
>> ramp(FTMF)
??? Undefined function or method 'ramp' for input arguments of type 'zpk'.
>> bode (G)
>> grid on
>> sisotool(G)
>> help logspace
 LOGSPACE Logarithmically spaced vector.
 LOGSPACE(X1, X2) generates a row vector of 50 logarithmically
 equally spaced points between decades 10^X1 and 10^X2. If X2
 is pi, then the points are between 10^X1 and pi.
 
 LOGSPACE(X1, X2, N) generates N points.
 For N < 2, LOGSPACE returns 10^X2.
 
 Class support for inputs X1,X2:
 float: double, single
 
 See also linspace, :.
 Reference page in Help browser
 doc logspace
>> W = logspace(-3 4 1000)
??? W = logspace(-3 4 1000)
 |
Error: Unexpected MATLAB expression.
>> W = logspace(-3,4,1000)
W =
 1.0e+004 *
 Columns 1 through 7
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 8 through 14
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 15 through 21
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 22 through 28
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 29 through 35
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 36 through 42
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 43 through 49
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 50 through 56
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 57 through 63
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 64 through 70
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 71 through 77
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 78 through 84
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 85 through 91
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 92 through 98
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 99 through 105
 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 106 through 112
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 113 through 119
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 120 through 126
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 127 through 133
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 134 through 140
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 141 through 147
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 148 through 154
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 155 through 161
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 162 through 168
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 169 through 175
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 176 through 182
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 183 through 189
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 190 through 196
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 197 through 203
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 204 through 210
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 211 through 217
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 218 through 224
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 225 through 231
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 232 through 238
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 239 through 245
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 246 through 252
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 253 through 259
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 260 through 266
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 267 through 273
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 274 through 280
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 281 through 287
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 288 through 294
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 295 through 301
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 302 through 308
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 309 through 315
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 316 through 322
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 323 through 329
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 330 through 336
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 337 through 343
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 344 through 350
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 351 through 357
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 358 through 364
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 365 through 371
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 372 through 378
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 379 through 385
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 386 through 392
 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 393 through 399
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 400 through 406
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 407 through 413
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 414 through 420
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 421 through 427
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 428 through 434
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 435 through 441
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 442 through 448
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 449 through 455
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002
 Columns 456 through 462
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 463 through 469
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 470 through 476
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 477 through 483
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 484 through 490
 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 491 through 497
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 498 through 504
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 505 through 511
 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 512 through 518
 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 519 through 525
 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005
 Columns 526 through 532
 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
 Columns 533 through 539
 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006
 Columns 540 through 546
 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007
 Columns 547 through 553
 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
 Columns 554 through 560
 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008
 Columns 561 through 567
 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009
 Columns 568 through 574
 0.0009 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010
 Columns 575 through 581
 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012
 Columns 582 through 588
 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013
 Columns 589 through 595
 0.0013 0.0013 0.0014 0.0014 0.0014 0.0014 0.0015
 Columns 596 through 602
 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016
 Columns 603 through 609
 0.0017 0.0017 0.0017 0.0017 0.0018 0.0018 0.0018
 Columns 610 through 616
 0.0019 0.0019 0.0019 0.0019 0.0020 0.0020 0.0020
 Columns 617 through 623
 0.0021 0.0021 0.0021 0.0022 0.0022 0.0022 0.0023
 Columns 624 through 630
 0.0023 0.0024 0.0024 0.0024 0.0025 0.0025 0.0026
 Columns 631 through 637
 0.0026 0.0026 0.0027 0.0027 0.0028 0.0028 0.0029
 Columns 638 through 644
 0.0029 0.0030 0.0030 0.0031 0.0031 0.0032 0.0032
 Columns 645 through 651
 0.0033 0.0033 0.0034
0.0034 0.0035 0.0035 0.0036
 Columns 652 through 658
 0.0036 0.0037 0.0038 0.0038 0.0039 0.0039 0.0040
 Columns 659 through 665
 0.0041 0.0041 0.0042 0.0043 0.0044 0.0044 0.0045
 Columns 666 through 672
 0.0046 0.0046 0.0047 0.0048 0.0049 0.0050 0.0050
 Columns 673 through 679
 0.0051 0.0052 0.0053 0.0054 0.0055 0.0055 0.0056
 Columns 680 through 686
 0.0057 0.0058 0.0059 0.0060 0.0061 0.0062 0.0063
 Columns 687 through 693
 0.0064 0.0065 0.0066 0.0067 0.0068 0.0069 0.0071
 Columns 694 through 700
 0.0072 0.0073 0.0074 0.0075 0.0077 0.0078 0.0079
 Columns 701 through 707
 0.0080 0.0082 0.0083 0.0084 0.0086 0.0087 0.0089
 Columns 708 through 714
 0.0090 0.0091 0.0093 0.0094 0.0096 0.0097 0.0099
 Columns 715 through 721
 0.0101 0.0102 0.0104 0.0106 0.0107 0.0109 0.0111
 Columns 722 through 728
 0.0113 0.0115 0.0116 0.0118 0.0120 0.0122 0.0124
 Columns 729 through 735
 0.0126 0.0128 0.0130 0.0132 0.0135 0.0137 0.0139
 Columns 736 through 742
 0.0141 0.0144 0.0146 0.0148 0.0151 0.0153 0.0156
 Columns 743 through 749
 0.0158 0.0161 0.0163 0.0166 0.0169 0.0171 0.0174
 Columns 750 through 756
 0.0177 0.0180 0.0183 0.0186 0.0189 0.0192 0.0195
 Columns 757 through 763
 0.0198 0.0202 0.0205 0.0208 0.0212 0.0215 0.0218
 Columns 764 through 770
 0.0222 0.0226 0.0229 0.0233 0.0237 0.0241 0.0245
 Columns 771 through 777
 0.0249 0.0253 0.0257 0.0261 0.0265 0.0269 0.0274
 Columns 778 through 784
 0.0278 0.0283 0.0287 0.0292 0.0297 0.0302 0.0307
 Columns 785 through 791
 0.0312 0.0317 0.0322 0.0327 0.0332 0.0338 0.0343
 Columns 792 through 798
 0.0349 0.0354 0.0360 0.0366 0.0372 0.0378 0.0384
 Columns 799 through 805
 0.0390 0.0397 0.0403 0.0410 0.0417 0.0423 0.0430
 Columns 806 through 812
 0.0437 0.0444 0.0451 0.0459 0.0466 0.0474 0.0482
 Columns 813 through 819
 0.0489 0.0497 0.0505 0.0514 0.0522 0.0531 0.0539
 Columns 820 through 826
 0.0548 0.0557 0.0566 0.0575 0.0584 0.0594 0.0604
 Columns 827 through 833
 0.0613 0.0623 0.0634 0.0644 0.0654 0.0665 0.0676
 Columns 834 through 840
 0.0687 0.0698 0.0709 0.0721 0.0733 0.0745 0.0757
 Columns 841 through 847
 0.0769 0.0781 0.0794 0.0807 0.0820 0.0834 0.0847
 Columns 848 through 854
 0.0861 0.0875 0.0889 0.0904 0.0918 0.0933 0.0948
 Columns 855 through 861
 0.0964 0.0979 0.0995 0.1012 0.1028 0.1045 0.1062
 Columns 862 through 868
 0.1079 0.1097 0.1114 0.1133 0.1151 0.1170 0.1189
 Columns 869 through 875
 0.1208 0.1228 0.1248 0.1268 0.1289 0.1310 0.1331
 Columns 876 through 882
 0.1352 0.1374 0.1397 0.1420 0.1443 0.1466 0.1490
 Columns 883 through 889
 0.1514 0.1539 0.1564 0.1589 0.1615 0.1641 0.1668
 Columns 890 through 896
 0.1695 0.1723 0.1751 0.1779 0.1808 0.1838 0.1868
 Columns 897 through 903
 0.1898 0.1929 0.1960 0.1992 0.2024 0.2057 0.2091
 Columns 904 through 910
 0.2125 0.2159 0.2195 0.2230 0.2266 0.2303 0.2341
 Columns 911 through 917
 0.2379 0.2418 0.2457 0.2497 0.2537 0.2579 0.2621
 Columns 918 through 924
 0.2663 0.2707 0.2751 0.2795 0.2841 0.2887 0.2934
 Columns 925 through 931
 0.2982 0.3030 0.3080 0.3130 0.3181 0.3232 0.3285
 Columns 932 through 938
 0.3338 0.3393 0.3448 0.3504 0.3561 0.3619 0.3678
 Columns 939 through 945
 0.3737 0.3798 0.3860 0.3923 0.3987 0.4051 0.4117
 Columns 946 through 952
 0.4184 0.4252 0.4322 0.4392 0.4463 0.4536 0.4610
 Columns 953 through 959
 0.4685 0.4761 0.4838 0.4917 0.4997 0.5078 0.5161
 Columns 960 through 966
 0.5245 0.5330 0.5417 0.5505 0.5594 0.5685 0.5778
 Columns 967 through 973
 0.5872 0.5967 0.6064 0.6163 0.6263 0.6365 0.6469
 Columns 974 through 980
 0.6574 0.6681 0.6789 0.6900 0.7012 0.7126 0.7242
 Columns 981 through 987
 0.7360 0.7480 0.7601 0.7725 0.7850 0.7978 0.8108
 Columns 988 through 994
 0.8240 0.8374 0.8510 0.8648 0.8789 0.8932 0.9077
 Columns 995 through 1000
 0.9225 0.9375 0.9528 0.9682 0.9840 1.0000
>> bode (G)
>> bode (G),W
W =
 1.0e+004 *
 Columns 1 through 7
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 8 through 14
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 15 through 21
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 22 through 28
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 29 through 35
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 36 through 42
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 43 through 49
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 50 through 56
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 57 through 63
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 64 through 70
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 71 through 77
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 78 through 84
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 85 through 91
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 92 through 98
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 99 through 105
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 106 through 112
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 113 through 119
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 120 through 126
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 127 through 133
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 134 through 140
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 141 through 147
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 148 through 154
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 155 through 161
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 162 through 168
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 169 through 175
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 176 through 182
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 183 through 189
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 190 through 196
 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
 Columns 197 through 203
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 204 through 210
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 211 through 217
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 218 through 224
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 225 through 231
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 232 through 238
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 239 through 245
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 246 through 252
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 253 through 259
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 260 through 266
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 267 through 273
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 274 through 280
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 281 through 287
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 288 through 294
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 295 through 301
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 302 through 308
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 309 through 315
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 316 through 322
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 323 through 329
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 330 through 336
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 337 through 343
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 344 through 350
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 351 through 357
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 358 through 364
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 365 through 371
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 372 through 378
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 379 through 385
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 386 through 392
 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 393 through 399
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 400 through 406
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 407 through 413
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 414 through 420
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 421 through 427
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 428 through 434
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 435 through 441
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 442 through 448
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 449 through 455
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002
 Columns 456 through 462
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 463 through 469
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 470 through 476
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 477 through 483
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 484 through 490
 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 491 through 497
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 498 through 504
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 505 through 511
 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 512 through 518
 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 519 through 525
 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005
 Columns 526 through 532
 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
 Columns 533 through 539
 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006
 Columns 540 through 546
 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007
 Columns 547 through 553
 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
 Columns 554 through 560
 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008
 Columns 561 through 567
 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009
 Columns 568 through 574
 0.0009 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010
 Columns 575 through 581
 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012
 Columns 582 through 588
 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013
 Columns 589 through 595
 0.0013 0.0013 0.0014 0.0014 0.0014 0.0014 0.0015
 Columns 596 through 602
 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016
 Columns 603 through 609
 0.0017 0.0017 0.0017 0.0017 0.0018 0.0018 0.0018
 Columns 610 through 616
 0.0019 0.0019 0.0019 0.0019 0.0020 0.0020 0.0020
 Columns 617 through 623
 0.0021 0.0021 0.0021 0.0022 0.0022 0.0022 0.0023
 Columns 624 through 630
 0.0023 0.0024 0.0024 0.0024 0.0025 0.0025 0.0026
 Columns 631 through 637
 0.0026 0.0026 0.0027 0.0027 0.0028 0.0028 0.0029
 Columns 638 through 644
 0.0029 0.0030 0.0030 0.0031 0.0031 0.0032 0.0032
 Columns 645 through 651
 0.0033 0.0033 0.0034 0.0034 0.0035 0.0035 0.0036
 Columns 652 through 658
 0.0036 0.0037 0.0038 0.0038 0.0039 0.0039 0.0040
 Columns 659 through 665
 0.0041 0.0041 0.0042 0.0043 0.0044 0.0044 0.0045
 Columns 666 through 672
 0.0046 0.0046 0.0047 0.0048 0.0049 0.0050 0.0050
 Columns 673 through 679
 0.0051 0.0052 0.0053 0.0054 0.0055 0.0055 0.0056
 Columns 680 through 686
 0.0057 0.0058 0.0059 0.0060 0.0061 0.0062 0.0063
 Columns 687 through 693
 0.0064 0.0065 0.0066 0.0067 0.0068 0.0069 0.0071
 Columns 694 through 700
 0.0072 0.0073 0.0074 0.0075 0.0077 0.0078 0.0079
 Columns 701 through 707
 0.0080 0.0082 0.0083 0.0084 0.0086 0.0087 0.0089
 Columns 708 through 714
 0.0090 0.0091 0.0093 0.0094 0.0096 0.0097 0.0099
 Columns 715 through 721
 0.0101 0.0102 0.0104 0.0106 0.0107 0.0109 0.0111
 Columns 722 through 728
 0.0113 0.0115 0.0116 0.0118 0.0120 0.0122 0.0124
 Columns 729 through 735
 0.0126 0.0128 0.0130 0.0132 0.0135 0.0137 0.0139
 Columns 736 through 742
 0.0141 0.0144 0.0146 0.0148 0.0151 0.0153
0.0156
 Columns 743 through 749
 0.0158 0.0161 0.0163 0.0166 0.0169 0.0171 0.0174
 Columns 750 through 756
 0.0177 0.0180 0.0183 0.0186 0.0189 0.0192 0.0195
 Columns 757 through 763
 0.0198 0.0202 0.0205 0.0208 0.0212 0.0215 0.0218
 Columns 764 through 770
 0.0222 0.0226 0.0229 0.0233 0.0237 0.0241 0.0245
 Columns 771 through 777
 0.0249 0.0253 0.0257 0.0261 0.0265 0.0269 0.0274
 Columns 778 through 784
 0.0278 0.0283 0.0287 0.0292 0.0297 0.0302 0.0307
 Columns 785 through 791
 0.0312 0.0317 0.0322 0.0327 0.0332 0.0338 0.0343
 Columns 792 through 798
 0.0349 0.0354 0.0360 0.0366 0.0372 0.0378 0.0384
 Columns 799 through 805
 0.0390 0.0397 0.0403 0.0410 0.0417 0.0423 0.0430
 Columns 806 through 812
 0.0437 0.0444 0.0451 0.0459 0.0466 0.0474 0.0482
 Columns 813 through 819
 0.0489 0.0497 0.0505 0.0514 0.0522 0.0531 0.0539
 Columns 820 through 826
 0.0548 0.0557 0.0566 0.0575 0.0584 0.0594 0.0604
 Columns 827 through 833
 0.0613 0.0623 0.0634 0.0644 0.0654 0.0665 0.0676
 Columns 834 through 840
 0.0687 0.0698 0.0709 0.0721 0.0733 0.0745 0.0757
 Columns 841 through 847
 0.0769 0.0781 0.0794 0.0807 0.0820 0.0834 0.0847
 Columns 848 through 854
 0.0861 0.0875 0.0889 0.0904 0.0918 0.0933 0.0948
 Columns 855 through 861
 0.0964 0.0979 0.0995 0.1012 0.1028 0.1045 0.1062
 Columns 862 through 868
 0.1079 0.1097 0.1114 0.1133 0.1151 0.1170 0.1189
 Columns 869 through 875
 0.1208 0.1228 0.1248 0.1268 0.1289 0.1310 0.1331
 Columns 876 through 882
 0.1352 0.1374 0.1397 0.1420 0.1443 0.1466 0.1490
 Columns 883 through 889
 0.1514 0.1539 0.1564 0.1589 0.1615 0.1641 0.1668
 Columns 890 through 896
 0.1695 0.1723 0.1751 0.1779 0.1808 0.1838 0.1868
 Columns 897 through 903
 0.1898 0.1929 0.1960 0.1992 0.2024 0.2057 0.2091
 Columns 904 through 910
 0.2125 0.2159 0.2195 0.2230 0.2266 0.2303 0.2341
 Columns 911 through 917
 0.2379 0.2418 0.2457 0.2497 0.2537 0.2579 0.2621
 Columns 918 through 924
 0.2663 0.2707 0.2751 0.2795 0.2841 0.2887 0.2934
 Columns 925 through 931
 0.2982 0.3030 0.3080 0.3130 0.3181 0.3232 0.3285
 Columns 932 through 938
 0.3338 0.3393 0.3448 0.3504 0.3561 0.3619 0.3678
 Columns 939 through 945
 0.3737 0.3798 0.3860 0.3923 0.3987 0.4051 0.4117
 Columns 946 through 952
 0.4184 0.4252 0.4322 0.4392 0.4463 0.4536 0.4610
 Columns 953 through 959
 0.4685 0.4761 0.4838 0.4917 0.4997 0.5078 0.5161
 Columns 960 through 966
 0.5245 0.5330 0.5417 0.5505 0.5594 0.5685 0.5778
 Columns 967 through 973
 0.5872 0.5967 0.6064 0.6163 0.6263 0.6365 0.6469
 Columns 974 through 980
 0.6574 0.6681 0.6789 0.6900 0.7012 0.7126 0.7242
 Columns 981 through 987
 0.7360 0.7480 0.7601 0.7725 0.7850 0.7978 0.8108
 Columns 988 through 994
 0.8240 0.8374 0.8510 0.8648 0.8789 0.8932 0.9077
 Columns 995 through 1000
 0.9225 0.9375 0.9528 0.9682 0.9840 1.0000
>> bode (G),W
W =
 1.0e+004 *
 Columns 1 through 7
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 8 through 14
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 15 through 21
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 22 through 28
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 29 through 35
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 36 through 42
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 43 through 49
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 50 through 56
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 57 through 63
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 64 through 70
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 71 through 77
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 78 through 84
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 85 through 91
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 92 through 98
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 99 through 105
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 106 through 112
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 113 through 119
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 120 through 126
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 127 through 133
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 134 through 140
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 141 through 147
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 148 through 154
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 155 through 161
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 162 through 168
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 169 through 175
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 176 through 182
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 183 through 189
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 190 through 196
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 197 through 203
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 204 through 210
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 211 through 217
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 218 through 224
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 225 through 231
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 232 through 238
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 239 through 245
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 246 through 252
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 253 through 259
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 260 through 266
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 267 through 273
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 274 through 280
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 281 through 287
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns
288 through 294
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 295 through 301
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 302 through 308
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 309 through 315
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 316 through 322
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 323 through 329
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 330 through 336
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 337 through 343
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 344 through 350
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 351 through 357
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 358 through 364
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 365 through 371
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 372 through 378
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 379 through 385
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 386 through 392
 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 393 through 399
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 400 through 406
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 407 through 413
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 414 through 420
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 421 through 427
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 428 through 434
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 435 through 441
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 442 through 448
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 449 through 455
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002
 Columns 456 through 462
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 463 through 469
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 470 through 476
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 477 through 483
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 484 through 490
 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 491 through 497
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 498 through 504
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 505 through 511
 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 512 through 518
 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 519 through 525
 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005
 Columns 526 through 532
 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
 Columns 533 through 539
 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006
 Columns 540 through 546
 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007
 Columns 547 through 553
 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
 Columns 554 through 560
 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008
 Columns 561 through 567
 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009
 Columns 568 through 574
 0.0009 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010
 Columns 575 through 581
 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012
 Columns 582 through 588
 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013
 Columns 589 through 595
 0.0013 0.0013 0.0014 0.0014 0.0014 0.0014 0.0015
 Columns 596 through 602
 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016
 Columns 603 through 609
 0.0017 0.0017 0.0017 0.0017 0.0018 0.0018 0.0018
 Columns 610 through 616
 0.0019 0.0019 0.0019 0.0019 0.0020 0.0020 0.0020
 Columns 617 through 623
 0.0021 0.0021 0.0021 0.0022 0.0022 0.0022 0.0023
 Columns 624 through 630
 0.0023 0.0024 0.0024 0.0024 0.0025 0.0025 0.0026
 Columns 631 through 637
 0.0026 0.0026 0.0027 0.0027 0.0028 0.0028 0.0029
 Columns 638 through 644
 0.0029 0.0030 0.0030 0.0031 0.0031 0.0032 0.0032
 Columns 645 through 651
 0.0033 0.0033 0.0034 0.0034 0.0035 0.0035 0.0036
 Columns 652 through 658
 0.0036 0.0037 0.0038 0.0038 0.0039 0.0039 0.0040
 Columns 659 through 665
 0.0041 0.0041 0.0042 0.0043 0.0044 0.0044 0.0045
 Columns 666 through 672
 0.0046 0.0046 0.0047 0.0048 0.0049 0.0050 0.0050
 Columns 673 through 679
 0.0051 0.0052 0.0053 0.0054 0.0055 0.0055 0.0056
 Columns 680 through 686
 0.0057 0.0058 0.0059 0.0060 0.0061 0.0062 0.0063
 Columns 687 through 693
 0.0064 0.0065 0.0066 0.0067 0.0068 0.0069 0.0071
 Columns 694 through 700
 0.0072 0.0073 0.0074 0.0075 0.0077 0.0078 0.0079
 Columns 701 through 707
 0.0080 0.0082 0.0083 0.0084 0.0086 0.0087 0.0089
 Columns 708 through 714
 0.0090 0.0091 0.0093 0.0094 0.0096 0.0097 0.0099
 Columns 715 through 721
 0.0101 0.0102 0.0104 0.0106 0.0107 0.0109 0.0111
 Columns 722 through 728
 0.0113 0.0115 0.0116 0.0118 0.0120 0.0122 0.0124
 Columns 729 through 735
 0.0126 0.0128 0.0130 0.0132 0.0135 0.0137 0.0139
 Columns 736 through 742
 0.0141 0.0144 0.0146 0.0148 0.0151 0.0153 0.0156
 Columns 743 through 749
 0.0158 0.0161 0.0163 0.0166 0.0169 0.0171 0.0174
 Columns 750 through 756
 0.0177 0.0180 0.0183 0.0186 0.0189 0.0192 0.0195
 Columns 757 through 763
 0.0198 0.0202 0.0205 0.0208 0.0212 0.0215 0.0218
 Columns 764 through 770
 0.0222 0.0226 0.0229 0.0233 0.0237 0.0241 0.0245
 Columns 771 through 777
 0.0249 0.0253 0.0257 0.0261 0.0265 0.0269 0.0274
 Columns 778 through 784
 0.0278 0.0283 0.0287 0.0292 0.0297 0.0302 0.0307
 Columns 785 through 791
 0.0312 0.0317 0.0322 0.0327 0.0332 0.0338 0.0343
 Columns 792 through 798
 0.0349 0.0354 0.0360 0.0366 0.0372 0.0378 0.0384
 Columns 799 through 805
 0.0390 0.0397 0.0403 0.0410 0.0417 0.0423 0.0430
 Columns 806 through 812
 0.0437 0.0444 0.0451 0.0459 0.0466 0.0474 0.0482
 Columns 813 through 819
 0.0489 0.0497 0.0505 0.0514 0.0522 0.0531 0.0539
 Columns 820 through 826
 0.0548 0.0557 0.0566 0.0575 0.0584 0.0594 0.0604
 Columns 827 through 833
 0.0613 0.0623 0.0634 0.0644 0.0654 0.0665 0.0676
 Columns 834 through 840
0.0687 0.0698 0.0709 0.0721 0.0733 0.0745 0.0757
 Columns 841 through 847
 0.0769 0.0781 0.0794 0.0807 0.0820 0.0834 0.0847
 Columns 848 through 854
 0.0861 0.0875 0.0889 0.0904 0.0918 0.0933 0.0948
 Columns 855 through 861
 0.0964 0.0979 0.0995 0.1012 0.1028 0.1045 0.1062
 Columns 862 through 868
 0.1079 0.1097 0.1114 0.1133 0.1151 0.1170 0.1189
 Columns 869 through 875
 0.1208 0.1228 0.1248 0.1268 0.1289 0.1310 0.1331
 Columns 876 through 882
 0.1352 0.1374 0.1397 0.1420 0.1443 0.1466 0.1490
 Columns 883 through 889
 0.1514 0.1539 0.1564 0.1589 0.1615 0.1641 0.1668
 Columns 890 through 896
 0.1695 0.1723 0.1751 0.1779 0.1808 0.1838 0.1868
 Columns 897 through 903
 0.1898 0.1929 0.1960 0.1992 0.2024 0.2057 0.2091
 Columns 904 through 910
 0.2125 0.2159 0.2195 0.2230 0.2266 0.2303 0.2341
 Columns 911 through 917
 0.2379 0.2418 0.2457 0.2497 0.2537 0.2579 0.2621
 Columns 918 through 924
 0.2663 0.2707 0.2751 0.2795 0.2841 0.2887 0.2934
 Columns 925 through 931
 0.2982 0.3030 0.3080 0.3130 0.3181 0.3232 0.3285
 Columns 932 through 938
 0.3338 0.3393 0.3448 0.3504 0.3561 0.3619 0.3678
 Columns 939 through 945
 0.3737 0.3798 0.3860 0.3923 0.3987 0.4051 0.4117
 Columns 946 through 952
 0.4184 0.4252 0.4322 0.4392 0.4463 0.4536 0.4610
 Columns 953 through 959
 0.4685 0.4761 0.4838 0.4917 0.4997 0.5078 0.5161
 Columns 960 through 966
 0.5245 0.5330 0.5417 0.5505 0.5594 0.5685 0.5778
 Columns 967 through 973
 0.5872 0.5967 0.6064 0.6163 0.6263 0.6365 0.6469
 Columns 974 through 980
 0.6574 0.6681 0.6789 0.6900 0.7012 0.7126 0.7242
 Columns 981 through 987
 0.7360 0.7480 0.7601 0.7725 0.7850 0.7978 0.8108
 Columns 988 through 994
 0.8240 0.8374 0.8510 0.8648 0.8789 0.8932 0.9077
 Columns 995 through 1000
 0.9225 0.9375 0.9528 0.9682 0.9840 1.0000
>> bode (G),W
W =
 1.0e+004 *
 Columns 1 through 7
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 8 through 14
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 15 through 21
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 22 through 28
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 29 through 35
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 36 through 42
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 43 through 49
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 50 through 56
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 57 through 63
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 64 through 70
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 71 through 77
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 78 through 84
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 85 through 91
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 92 through 98
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 99 through 105
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 106 through 112
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 113 through 119
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 120 through 126
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 127 through 133
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 134 through 140
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 141 through 147
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 148 through 154
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 155 through 161
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 162 through 168
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 169 through 175
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 176 through 182
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 183 through 189
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 190 through 196
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 197 through 203
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 204 through 210
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 211 through 217
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 218 through 224
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 225 through 231
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 232 through 238
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 239 through 245
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 246 through 252
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 253 through 259
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 260 through 266
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 267 through 273
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 274 through 280
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 281 through 287
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 288 through 294
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 295 through 301
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 302 through 308
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 309 through 315
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 316 through 322
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 323 through 329
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 330 through 336
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 337 through 343
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 344 through 350
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 351 through 357
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 358 through 364
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 365 through 371
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 372 through 378
 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 379 through 385
 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
 Columns 386 through 392
 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 393 through 399
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 400 through 406
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 407 through 413
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 414 through 420
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 421 through 427
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 428 through 434
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 435 through 441
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 442 through 448
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
 Columns 449 through 455
 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002
 Columns 456 through 462
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 463 through 469
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 470 through 476
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 477 through 483
 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
 Columns 484 through 490
 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 491 through 497
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 498 through 504
 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
 Columns 505 through 511
 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 512 through 518
 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
 Columns 519 through 525
 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005
 Columns 526 through 532
 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
 Columns 533 through 539
 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006
 Columns 540 through 546
 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007
 Columns 547 through 553
 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
 Columns 554 through 560
 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008
 Columns 561 through 567
 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009
 Columns 568 through 574
 0.0009 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010
 Columns 575 through 581
 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012
 Columns 582 through 588
 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013
 Columns 589 through 595
 0.0013 0.0013 0.0014 0.0014 0.0014 0.0014 0.0015
 Columns 596 through 602
 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016
 Columns 603 through 609
 0.0017 0.0017 0.0017 0.0017 0.0018 0.0018 0.0018
 Columns 610 through 616
 0.0019 0.0019 0.0019 0.0019 0.0020 0.0020 0.0020
 Columns 617 through 623
 0.0021 0.0021 0.0021 0.0022 0.0022 0.0022 0.0023
 Columns 624 through 630
 0.0023 0.0024 0.0024 0.0024 0.0025 0.0025 0.0026
 Columns 631 through 637
 0.0026 0.0026 0.0027 0.0027 0.0028 0.0028 0.0029
 Columns 638 through 644
 0.0029 0.0030 0.0030 0.0031 0.0031 0.0032 0.0032
 Columns 645 through 651
 0.0033 0.0033 0.0034 0.0034 0.0035 0.0035 0.0036
 Columns 652 through 658
 0.0036 0.0037 0.0038 0.0038 0.0039 0.0039 0.0040
 Columns 659 through 665
 0.0041 0.0041 0.0042 0.0043 0.0044 0.0044 0.0045
 Columns 666 through 672
 0.0046 0.0046 0.0047 0.0048 0.0049 0.0050 0.0050
 Columns 673 through 679
 0.0051 0.0052 0.0053 0.0054 0.0055 0.0055 0.0056
 Columns 680 through 686
 0.0057 0.0058 0.0059 0.0060 0.0061 0.0062 0.0063
 Columns 687 through 693
 0.0064 0.0065 0.0066 0.0067 0.0068 0.0069 0.0071
 Columns 694 through 700
 0.0072 0.0073 0.0074 0.0075 0.0077 0.0078 0.0079
 Columns 701 through 707
 0.0080 0.0082 0.0083 0.0084 0.0086 0.0087 0.0089
 Columns 708 through 714
 0.0090 0.0091 0.0093 0.0094 0.0096 0.0097 0.0099
 Columns 715 through 721
 0.0101 0.0102 0.0104 0.0106 0.0107 0.0109 0.0111
 Columns 722 through 728
 0.0113 0.0115 0.0116 0.0118 0.0120 0.0122 0.0124
 Columns 729 through 735
 0.0126 0.0128 0.0130 0.0132 0.0135 0.0137 0.0139
 Columns 736 through 742
 0.0141 0.0144 0.0146 0.0148 0.0151 0.0153 0.0156
 Columns 743 through 749
 0.0158 0.0161 0.0163 0.0166 0.0169 0.0171 0.0174
 Columns 750 through 756
 0.0177 0.0180 0.0183 0.0186 0.0189 0.0192 0.0195
 Columns 757 through 763
 0.0198 0.0202 0.0205 0.0208 0.0212 0.0215 0.0218
 Columns 764 through 770
 0.0222 0.0226 0.0229 0.0233 0.0237 0.0241 0.0245
 Columns 771 through 777
 0.0249 0.0253 0.0257 0.0261 0.0265 0.0269 0.0274
 Columns 778 through 784
 0.0278 0.0283 0.0287 0.0292 0.0297 0.0302 0.0307
 Columns 785 through 791
 0.0312 0.0317 0.0322 0.0327 0.0332 0.0338 0.0343
 Columns 792 through 798
 0.0349 0.0354 0.0360 0.0366 0.0372 0.0378 0.0384
 Columns 799 through 805
 0.0390 0.0397 0.0403 0.0410 0.0417 0.0423 0.0430
 Columns 806 through 812
 0.0437 0.0444 0.0451 0.0459 0.0466 0.0474 0.0482
 Columns 813 through 819
 0.0489 0.0497 0.0505 0.0514 0.0522 0.0531 0.0539
 Columns 820 through 826
 0.0548 0.0557 0.0566 0.0575 0.0584 0.0594 0.0604
 Columns 827 through 833
 0.0613 0.0623 0.0634 0.0644 0.0654 0.0665 0.0676
 Columns 834 through 840
 0.0687 0.0698 0.0709 0.0721 0.0733 0.0745 0.0757
 Columns 841 through 847
 0.0769 0.0781 0.0794 0.0807 0.0820 0.0834 0.0847
 Columns 848 through 854
 0.0861 0.0875 0.0889 0.0904 0.0918 0.0933 0.0948
 Columns 855 through 861
 0.0964 0.0979 0.0995 0.1012 0.1028 0.1045 0.1062
 Columns 862 through 868
 0.1079 0.1097 0.1114 0.1133 0.1151 0.1170 0.1189
 Columns 869 through 875
 0.1208 0.1228 0.1248 0.1268 0.1289 0.1310 0.1331
 Columns 876 through 882
 0.1352 0.1374 0.1397 0.1420 0.1443 0.1466 0.1490
 Columns 883 through 889
 0.1514 0.1539 0.1564 0.1589 0.1615 0.1641 0.1668
 Columns 890 through 896
 0.1695 0.1723 0.1751 0.1779 0.1808 0.1838 0.1868
 Columns 897 through 903
 0.1898 0.1929 0.1960 0.1992 0.2024 0.2057 0.2091
 Columns 904 through 910
 0.2125 0.2159 0.2195 0.2230 0.2266 0.2303 0.2341
 Columns 911 through 917
 0.2379 0.2418 0.2457 0.2497 0.2537 0.2579 0.2621
 Columns 918 through 924
 0.2663 0.2707 0.2751 0.2795 0.2841 0.2887 0.2934
 Columns 925 through 931
 0.2982 0.3030 0.3080 0.3130
0.3181 0.3232 0.3285
 Columns 932 through 938
 0.3338 0.3393 0.3448 0.3504 0.3561 0.3619 0.3678
 Columns 939 through 945
 0.3737 0.3798 0.3860 0.3923 0.3987 0.4051 0.4117
 Columns 946 through 952
 0.4184 0.4252 0.4322 0.4392 0.4463 0.4536 0.4610
 Columns 953 through 959
 0.4685 0.4761 0.4838 0.4917 0.4997 0.5078 0.5161
 Columns 960 through 966
 0.5245 0.5330 0.5417 0.5505 0.5594 0.5685 0.5778
 Columns 967 through 973
 0.5872 0.5967 0.6064 0.6163 0.6263 0.6365 0.6469
 Columns 974 through 980
 0.6574 0.6681 0.6789 0.6900 0.7012 0.7126 0.7242
 Columns 981 through 987
 0.7360 0.7480 0.7601 0.7725 0.7850 0.7978 0.8108
 Columns 988 through 994
 0.8240 0.8374 0.8510 0.8648 0.8789 0.8932 0.9077
 Columns 995 through 1000
 0.9225 0.9375 0.9528 0.9682 0.9840 1.0000
>> bode (G,W)
>> margin (G)
>> OS = 20
OS =
 20
>> ZETA = -log (OS/100)/sqrt(pi^2+log(OS/100)^2)
ZETA =
 0.4559
>> MF=ZETA*100
MF =
 45.5950
>> margin
 Here is an example of how the function margin works:
 Consider a randomly generated stable Transfer Function Model:
 of the form G(s)=num(s)/den(s):
num =
 0 0 0 1.1892 -1.4162
den =
 1.0000 2.9737 2.8217 0.9142 0.0908
Call margin using the following command (see also, help margin):
margin(tf(num,den));
>> help margin
 MARGIN Gain and phase margins and crossover frequencies.
 
 [Gm,Pm,Wcg,Wcp] = MARGIN(SYS) computes the gain margin Gm, the
 phase margin Pm, and the associated frequencies Wcg and Wcp, 
 for the SISO open-loop model SYS (continuous or discrete). 
 The gain margin Gm is defined as 1/G where G is the gain at 
 the -180 phase crossing. The phase margin Pm is in degrees. 
 
 The gain margin in dB is derived by 
 Gm_dB = 20*log10(Gm)
 The loop gain at Wcg can increase or decrease by this many dBs
 before losing stability, and Gm_dB<0 (Gm<1) means that stability 
 is most sensitive to loop gain reduction. If there are several 
 crossover points, MARGIN returns the smallest margins (gain 
 margin nearest to 0 dB and phase margin nearest to 0 degrees).
 
 For a S1-by...-by-Sp array SYS of LTI models, MARGIN returns 
 arrays of size [S1 ... Sp] such that
 [Gm(j1,...,jp),Pm(j1,...,jp)] = MARGIN(SYS(:,:,j1,...,jp)) . 
 
 [Gm,Pm,Wcg,Wcp] = MARGIN(MAG,PHASE,W) derives the gain and phase
 margins from the Bode magnitude, phase, and frequency vectors 
 MAG, PHASE, and W produced by BODE. Interpolation is performed 
 between the frequency points to estimate the values. 
 
 MARGIN(SYS), by itself, plot the open-loop Bode plot with 
 the gain and phase margins marked with a vertical line. 
 
 See also allmargin, bode, ltiview, ltimodels.
 Overloaded methods:
 lti/margin
 Reference page in Help browser
 doc margin
>> [MG,MF,WMG,WMF]= margin(G)
MG =
 3.4000
MF =
 34.0572
WMG =
 60.0000
WMF =
 29.6177
>> MFcomp=ZETA*100
MFcomp =
 45.5950
>> [MG,MF,WMG,WMF]= margin(G)
MG =
 3.4000
MF =
 34.0572
WMG =
 60.0000
WMF =
 29.6177
>> MS
??? Undefined function or variable 'MS'.
>> MS = 10
MS =
 10
>> PHImax = MFcomp - MF + MS 
PHImax =
 21.5377
>> ALPHA = (1 - sin(PHImax)/(1 + sin(PHImax)
??? ALPHA = (1 - sin(PHImax)/(1 + sin(PHImax)
 |
Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.
>> sin help
??? Undefined function or method 'sin' for input arguments of type 'char'.
>> help sin
 SIN Sine of argument in radians.
 SIN(X) is the sine of the elements of X.
 
 See also asin, sind.
 Overloaded methods:
 darray/sin
 sym/sin
 Reference page in Help browser
 doc sin
>> ALPHA = (1 - sin(PHImax) / (1 + sin(PHImax)
??? ALPHA = (1 - sin(PHImax) / (1 + sin(PHImax)
 |
Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.
>> ALPHA = (1 - sin(PHImax)) / (1 + sin(PHImax))
ALPHA =
 0.3908
>> GANHOcomp = 10*log10(1 / ALPHA)
GANHOcomp =
 4.0806
>> bode (G,W)
>> TAU = sqrt(inv(ALPHA*39.6^2) 
??? TAU = sqrt(inv(ALPHA*39.6^2) 
 |
Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.
>> TAU = sqrt(inv(ALPHA*39.6^2))
TAU =
 0.0404
>> C = TF([0.0404 1])
Warning: Could not find an exact (case-sensitive) match for 'TF'.
C:\Arquivos de programas\MATLAB\R2007b\toolbox\control\control\@tf\tf.m is a
case-insensitive match and will be used instead.
You can improve the performance of your code by using exact
name matches and we therefore recommend that you update your
usage accordingly. Alternatively, you can disable this warning using
warning('off','MATLAB:dispatcher:InexactMatch').
 
Transfer function from input 1 to output:
0.0404
 
Transfer function from input 2 to output:
1
 
>> C = TF([0.0404 1],[ALPHA*TAU 1]
??? C = TF([0.0404 1],[ALPHA*TAU 1]
 |
Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.
>> C = TF([0.0404 1],[ALPHA*TAU 1])
 
Transfer function:
0.0404 s + 1
-------------
0.01579 s + 1
 
>> bode (G,C)
??? Undefined function or method 'localCreateUIContextMenu' for input
arguments of type 'graphics.datacursormanager'.
Error in ==> uitools.uimode.modeControl>localModeWindowButtonDownFcn at 127
hThis.modeWindowButtonDownFcn(hFig,evd,hThis,newValue);
??? Error while evaluating figure WindowButtonDownFcn
>> bode (G,C)
>> WHOIS
??? Undefined function or variable 'WHOIS'.
>> whois
??? Undefined function or variable 'whois'.
>> who is
>> whos
 Name Size Bytes Class Attributes
 ALPHA 1x1 8 double 
 C 1x1 1874 tf 
 FTMF 1x1 2008 zpk 
 G 1x1 2008 zpk 
 GANHOcomp 1x1 8 double 
 H 1x1 8 double 
 MF 1x1 8 double 
 MFcomp 1x1 8 double 
 MG 1x1 8 double 
 MS 1x1 8 double 
 OS 1x1 8 double 
 PHImax 1x1 8 double 
 TAU 1x1 8 double 
 W 1x1000 8000 double 
 WMF 1x1 8 double 
 WMG 1x1 8 double 
 ZETA 1x1 8 double 
>> P = SERIES (G,C)
Warning: Could not find an exact (case-sensitive) match for 'SERIES'.
C:\Arquivos de programas\MATLAB\R2007b\toolbox\control\control\@lti\series.m
is a case-insensitive match and will be used instead.
You can improve the performance of your code by using exact
name matches and we therefore recommend that you update your
usage accordingly. Alternatively, you can disable this warning using
warning('off','MATLAB:dispatcher:InexactMatch').
 
Zero/pole/gain:
 368527.9935 (s+24.75)
--------------------------
s (s+63.35) (s+100) (s+36)
 
>>

Teste o Premium para desbloquear

Aproveite todos os benefícios por 3 dias sem pagar! 😉
Já tem cadastro?

Outros materiais