Objectives, using Matlab to generate partial fractions expansion, put ratio of p

Question

Objectives, using Matlab to generate partial fractions expansion, put ratio of polynomials in form suitable for partial fraction expansion, and use Matlab to generate pole zero diagrams. 45 Case 1 simple roots (real) Y(s) use residue operation in matlab s +3s+2 Case 2 repeated roots (real) Y(s)- use poly and then residue matlab operations 19+2 +4s +3 Case 3 degree of numerator not less than degree of denominator (real roots) Y(s) use residue operation Case 4 roots are complex r(s)= use residue operation s +-8s +20 Directions for presentation of information from Matlab All four cases will require use of "residue" matlab operation. Information directly provided from Matlab on command line will need to be reported. For each case use following format paying attention to specific notation indicated here. [R1, P1, K1]- residue (B,A) to be applied to each case. Note any variable defined in a matlab program can be echoed to command window when desired. All four cases will require a quantitative partial fractions interpretation in standard analytic form, (definitely not Matlab format consistent with that used to cases of either simple or repeated roots( latter appropriate for case 2). I.e. residue in nume rator etc. in column or row format on screen (command window) can be reported in row format. This is only to save space in this report. Case 2 will require use of poly command from matlab you can use format Apoly (C) which will turn out to be consistent with subsequent use of residue command notation. Final explicit instructions allow for generation of Pole zero plots with matlab. All arrays regardless of it appearing FYI computer generated output used in lieu of fill in by hand is not going to be acceptable for When compute outputs simply ,use dash to fill in inputs required in this report When computer outputs long string of zeros after decimal you can and shoulddrop the zeros to save space e.g. computer outputs 2.0000 replace with 2

Explanation / Answer

b1=[1 3];
a1=[1 3 2];
[r1,p1,k1] = residue(b1,a1)
b2=[1 -2];
a2=[1 3 3 1 0];
[r2,p2,k2] = residue(b2,a2)
b3=[2 9 11 2];
a3=[1 4 3];
[r3,p3,k3] = residue(b3,a3)
b4=[1 0];
a4=[1 -8 20];
[r4,p4,k4] = residue(b4,a4)

r1 =

   2
-1

p1 =

-1
-2

k1 = [](0x0)
r2 =

   2.0000
   2.0000
   3.0000
-2.0000

p2 =

-1.00000
-1.00000
-1.00000
   0.00000

k2 = [](0x0)
r3 =

-1.0000
   2.0000

p3 =

-1
-3

k3 =

   2   1

r4 =

   0.50000 - 1.00000i
   0.50000 + 1.00000i

p4 =

   4.0000 + 2.0000i
   4.0000 - 2.0000i

k4 = [](0x0)

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