Experiment 2.1: Ques (1) Given that :
P1=s6+7s5+2s4+9s3+10s2+12s+15;P2=s6+9s5+8s4+9s3+12s2+15s+20Use
Matlab to find: P3=P1+P2, P4=P1- P2 P5=P1* P2 Solution:MATLAB
Scripts:
>> P1=[1 7 2 9 10 12 15]; % vector with coefficients of
polynomial P1>> P2=[1 9 8 9 12 15 20]; % vector with
coefficients of polynomial P2>> P3=P1+P2 % find P3 ( the sum
of P1 and P2)P3 = 2 16 10 18 22 27 35
>> P4=P1-P2 % calculate the value of P4P4 = 0 -2 -6 0 -2
-3 -5
>> P5=conv(P1,P2) % P5 is the product of the polynomials
P1 and P2P5 = 1 16 73 92 182 291 433 599 523 609 560 465 300
Results:Therefore, P3=2s6+16s5+10s4+18s3+22s2+27s+35
P4=-2s5-6s4-2s2-3s-5P5=s12+16s11+73s10+92s9+182s8+291s7+433s6+599s5+523s4+609s3+560s2+465s+300
Ques (2) P6=(s+7)(s+8)(s+3)(s+5)(s+9)(s+10)Roots of P6 are:
s=-7,-8,-3,-5,-9 & -10Matlab script>>
r=[-7,-8,-3,-5,-9,-10] ; % root vector of P6>> P6=poly(r) %
computes the coefficient of the polynomial from the rootsP6 =
Columns 1 through 6 1 42 718 6372 30817 76530 Column 7 75600Result:
P6=s6+42s5+718s4+6372s3+30817s2+ 76530s+75600
Ques (3): Use two Matlab commands to find the transfer function
G1(s) given below as a polynomial divide by a polynomial:
Solution:Matlab Script>> s=tf('s'); % Define s as a Linear
Time Invariant (LTI) object in polynomial form>>
G=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15)); % Form
G(s) as a LTI transfer function in polynomial form>> G
Transfer function:20 s^4 + 380 s^3 + 2480 s^2 + 6480 s +
5760-------------------------------------------s^5 + 41 s^4 + 613
s^3 + 3975 s^2 + 9450 s
Ques (4)Use two Matlab commands to find the transfer function
G2(s) expressed as factor in numerator divide by factor in the
denominator:
Solution:Matlab script>> s=zpk('s'); % Define s as LTI
object in factored form>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320)
Warning: Accuracy may be poor in parts of the frequency range.Use
the "prescale" command to maximize accuracy in the range of
interest. > In warning at 26 In xscale at 135 In
@zpkdata\private\utSS2ZPK at 12 In zpkdata.plus>LocalAddSISO at
41 In zpkdata.plus at 17 In lti.plus at 55 Zero/pole/gain: (s+1)
(s+4) (s+5)
(s+7)------------------------------------------------------(s+16.79)
(s^2 + 4.097s + 4.468) (s^2 + 11.12s + 57.6)
Ques (5) Using various combinations of G1(s) and G2(s), find:i)
G3(s)ii) G4(s)iii) G5(s).Solution:i) G3(s) = G1(s) + G2(s)Matlab
script:a) Various combinations for calculation of G3(s):>> %
Calculation of G3 with G1 expressed in factor form and G2 expressed
in factor form.>> s=zpk('s');>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);Warning:
Accuracy may be poor in parts of the frequency range.Use the
"prescale" command to maximize accuracy in the range of interest.
> In warning at 26 In xscale at 135 In @zpkdata\private\utSS2ZPK
at 12 In zpkdata.plus>LocalAddSISO at 41 In zpkdata.plus at 17
In lti.plus at 55>> G3=G1+G2 Zero/pole/gain: 21 (s+16.76)
(s+7.999) (s+6.003) (s^2 + 6.079s + 9.499) (s^2 + 3.033s + 2.607)
(s^2 + 11.46s + 59.47)
-----------------------------------------------------------------------------------------------------
s (s+7) (s+9) (s+10) (s+15) (s+16.79) (s^2 + 4.097s + 4.468) (s^2 +
11.12s + 57.6)
>> % Calculation of G3 with G1 expressed in polynomial
form and G2 expressed in factor form>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15)); %
Inputs G1>> G1zpk=G1; % stores G1 in G1zpk>>
G1tf=tf(G1zpk); %converts G1 to polynomial form>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);
%input G2>> G2tf=G2; % G2 stored in polynomial form>>
G2zpk=zpk(G2tf); %converts G2 to factor form>> G3=G1+G2
Transfer function: 21 s^9 + 1078 s^8 + 23309 s^7 + 284298 s^6 +
2.156e006 s^5 + 1.043e007 s^4 + 3.173e007 s^3 + 5.816e007 s^2 +
5.842e007 s + 2.488e007
---------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s>>
% Calculation of G3 with both G1 and G2 expressed in polynomial
form>> s=tf('s');>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);>>
G3=G1+G2 Transfer function: 21 s^9 + 1078 s^8 + 23309 s^7 + 284298
s^6 + 2.156e006 s^5 + 1.043e007 s^4 + 3.173e007 s^3 + 5.816e007 s^2
+ 5.842e007 s + 2.488e007
---------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s >>
% Calculation of G3 with G1 expressed in factor form and G2
expressed in polynomial form.>> s=zpk('s');>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
s=tf('s');>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);>>
G3=G1+G2 Zero/pole/gain: 21 (s+16.76) (s+7.999) (s+6.003) (s^2 +
6.079s + 9.499) (s^2 + 3.033s + 2.607) (s^2 + 11.46s + 59.47)
-----------------------------------------------------------------------------------------------------
s (s+7) (s+9) (s+10) (s+15) (s+16.79) (s^2 + 4.097s + 4.468) (s^2 +
11.12s + 57.6)
b) Various combinations for calculation of G4(s):Matlab
Script:>> % Calculation of G4 with both G1 and G2 expressed
in factor form>> s=zpk('s');>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);Warning:
Accuracy may be poor in parts of the frequency range.Use the
"prescale" command to maximize accuracy in the range of interest.
> In warning at 26 In xscale at 135 In @zpkdata\private\utSS2ZPK
at 12 In zpkdata.plus>LocalAddSISO at 41 In zpkdata.plus at 17
In lti.plus at 55>> G4=G1-G2 Zero/pole/gain:19 (s+16.81)
(s+8.001) (s+5.997) (s+3.252) (s+1.496) (s^2 + 4.335s + 6.018) (s^2
+ 10.74s +
55.47)--------------------------------------------------------------------------------------------------
s (s+7) (s+9) (s+10) (s+15) (s+16.79) (s^2 + 4.097s + 4.468) (s^2 +
11.12s + 57.6)>> % Calculation of G4 with both G1 and G2
expressed in polynomial form>> s=tf('s');>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);>>
G4=G1-G2 Transfer function:19 s^9 + 962 s^8 + 20491 s^7 + 246942
s^6 + 1.862e006 s^5 + 9.034e006 s^4 + 2.791e007 s^3 + 5.284e007 s^2
+ 5.577e007 s + 2.488e007
----------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s >>
% Calculation of G3 with G1 expressed in factor form and G2
expressed in polynomial form.>> s=zpk('s');>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
s=tf('s');>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);>>
G4=G1-G2Zero/pole/gain:19 (s+16.81) (s+8.001) (s+5.997) (s+3.252)
(s+1.496) (s^2 + 4.335s + 6.018) (s^2 + 10.74s +
55.47)--------------------------------------------------------------------------------------------------
s (s+7) (s+9) (s+10) (s+15) (s+16.79) (s^2 + 4.097s + 4.468) (s^2 +
11.12s + 57.6) >> % Calculation of G4 with G1 expressed in
polynomial form and G2 expressed in factor form>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15)); %
Inputs G1>> G1zpk=G1; % stores G1 in G1zpk>>
G1tf=tf(G1zpk); %converts G1 to polynomial form>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);
%input G2>> G2tf=G2; % G2 stored in polynomial form>>
G2zpk=zpk(G2tf); %converts G2 to factor form>> G4=G1-G2
Transfer function: 19 s^9 + 962 s^8 + 20491 s^7 + 246942 s^6 +
1.862e006 s^5 + 9.034e006 s^4 + 2.791e007 s^3 + 5.284e007 s^2 +
5.577e007 s + 2.488e007
---------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s c)
Various combinations for calculation of G5(s):Matlab
script:>> % Calculation of G5 with both G1 and G2 expressed
in factor form>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15));>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);
%input G2>> G2tf=G2; % G2 stored in polynomial form>>
G2zpk=zpk(G2tf); %converts G2 to factor form>> G5=G1*G2zpk %
calculates G5 with G1 and G2 expressed in factor form
Zero/pole/gain: 20 (s+8) (s+7) (s+6) (s+5) (s+4) (s+3) (s+2)
(s+1)----------------------------------------------------------------------------------s
(s+15) (s+16.79) (s+10) (s+9) (s+7) (s^2 + 4.097s + 4.468) (s^2 +
11.12s + 57.6)
>> % Calculation of G5 with both G1 and G2 expressed in
polynomial form>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15)); %
Inputs G1>> G1zpk=G1; % stores G1 in G1zpk>>
G1tf=tf(G1zpk); %converts G1 to polynomial form >>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);
%input G2>> G5=G1tf*G2 % calculates G5 with G1 and G2
expressed in polynomial form Transfer function: 20 s^8 + 720 s^7 +
10920 s^6 + 90720 s^5 + 448980 s^4 + 1.346e006 s^3 + 2.362e006 s^2
+ 2.192e006 s + 806400
----------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s
>> % Calculation of G5 with G1 expressed in factor form
and G2 expressed in polynomial form>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15)); %
Inputs G1>>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);
%input G2>> G5=G1*G2 % calculates G5 with G1 expressed in
factor form and G2 expressed in polynomial form Transfer function:
20 s^8 + 720 s^7 + 10920 s^6 + 90720 s^5 + 448980 s^4 + 1.346e006
s^3 + 2.362e006 s^2 + 2.192e006 s + 806400
----------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s
>> % Calculation of G5 with G1 expressed in polynomial
form and G2 expressed in factor form>>
G1=20*(s+2)*(s+3)*(s+6)*(s+8)/(s*(s+7)*(s+9)*(s+10)*(s+15)); %
Inputs G1>> G1zpk=G1; % stores G1 in G1zpk>>
G1tf=tf(G1zpk); %converts G1 to polynomial form >>
G2=(s^4+17*s^3+99*s^2+223*s+140)/(s^5+32*s^4+363*s^3+2092*s^2+5052*s+4320);
%input G2>> G2tf=G2; % G2 stored in polynomial form>>
G2zpk=zpk(G2tf); %converts G2 to factor form>> G5=G1tf*G2zpk
% calculates G5 with G1 expressed in polynomial form and G2
expressed in factor form Transfer function: 20 s^8 + 720 s^7 +
10920 s^6 + 90720 s^5 + 448980 s^4 + 1.346e006 s^3 + 2.362e006 s^2
+ 2.192e006 s + 806400
----------------------------------------------------------------------------------------------------s^10
+ 73 s^9 + 2288 s^8 + 40566 s^7 + 449993 s^6 + 3.239e006 s^5 +
1.502e007 s^4 + 4.25e007 s^3 + 6.491e007 s^2 + 4.082e007 s
Ques (4)Use Matlab to evaluate the partial fraction expansions
below:
Matlab Script(a)>> % Evaluate the partial fraction
expansion of G6>> b=[5,10]; % b is the coefficient of the
polynomial in the numerator>> a=[1,8,15,0]; %a is the
coefficient of the polynomial in the denominator>>
[r,p,k]=residue(b,a)
r =
-1.5000 0.8333 0.6667
p =
-5 -3 0
k =
[]
Result: G6= -1.5/(s+5) + 0.833/(s+3) + 0.6667/s
(b)
>> % Evaluate the partial fraction expansion of G7>>
b=[5,10]; % b is the coefficient of the polynomial in the
numerator>> a=[1,6,9,0]; %a is the coefficient of the
polynomial in the denominator>> [r,p,k]=residue(b,a)r =
-1.1111 1.6667 1.1111
p =
-3 -3 0
k =
[]
Result: G7= -1.1/(s+3) + 1.7/(s+3)2 + 1.1/s
c)>> % Evaluate the partial fraction expansion of
G8>> b=[5,10]; % b is the coefficient of the polynomial in
the numerator>> a=[1,6,34,0]; %a is the coefficient of the
polynomial in the denominator>> [r,p,k]=residue(b,a)
r =
-0.1471 - 0.4118i -0.1471 + 0.4118i 0.2941
p =
-3.0000 + 5.0000i -3.0000 - 5.0000i 0
k =
[]
Result: G8= ( -0.1471-j0.4118)/(s+3-j5) +
(-0.1471+j0.4118)/(s+3+j5) + 0.2941/s
Experiment 2.2 (LAB): Ques (1a) Use MATLAB and the Symbolic Math
Toolbox to generate symbolically the time function f(t) given
as:
Matlab script:>> %Generate a symbolically the time
function f(t)>>
f=0.0075-0.00034*exp(-2.5*t)*cos(22*t)+0.087*exp(-2.5*t)*sin(22*t)-0.0072*exp(-8*t);>>
%Generate a symbolically the time function f(t)>> syms t; %
define symbolic variable>>
ft=0.0075-0.00034*exp(-2.5*t)*cos(22*t)+0.087*exp(-2.5*t)*sin(22*t)-0.0072*exp(-8*t);>>
ft f t= (87*sin(22*t))/(1000*exp((5*t)/2)) -
(17*cos(22*t))/(50000*exp((5*t)/2)) - 9/(1250*exp(8*t)) + 3/400
1b) Generate symbolically F(s) below and obtain result
symbolically in both factored and polynomial forms.
MATLAB Script>> %Generate symbolically the function
F(s)>> syms s % Define symbolic variable>>
F=2*(s+3)*(s+5)*(s+7)/(s*(s+8)*(s^2+10*s+100));>> F F =
((2*s + 6)*(s + 5)*(s + 7))/(s*(s + 8)*(s^2 + 10*s + 100))
>> % Obtain F in factored form>> s=zpk('s');>>
Fzpk=2*(s+3)*(s+5)*(s+7)/(s*(s+8)*(s^2+10*s+100)); % Fzpk is the
factored form of F>> Fzpk Zero/pole/gain: 2 (s+3) (s+5)
(s+7)-------------------------s (s+8) (s^2 + 10s + 100) >> %
Obtain F in polynomial form>> s=tf('s');>>
Ftf=2*(s+3)*(s+5)*(s+7)/(s*(s+8)*(s^2+10*s+100)); % Ftf is the
polynomial form of F>> Ftf Transfer function: 2 s^3 + 30 s^2
+ 142 s + 210------------------------------s^4 + 18 s^3 + 180 s^2 +
800 s
1c) Find the Laplace transform of f(t) in (1a)MATLAB
script>> % Calculate the Laplace transform of ft>> syms
t s>>
ft=0.0075-0.00034*exp(-2.5*t)*cos(22*t)+0.087*exp(-2.5*t)*sin(22*t)-0.0072*exp(-8*t);>>
laplace(ft,t,s) %computes the laplace transmform of ft ans =
3/(400*s) - 9/(1250*(s + 8)) - (17*(s + 5/2))/(50000*((s + 5/2)^2 +
484)) + 957/(500*((s + 5/2)^2 + 484))
1d) Find the inverse Laplace transform of F(s) in (1b)MATLAB
Script>> % Calculate the inverse Laplace transform of
F(s)>> syms t s % Define symbolic variable>>
FS=2*(s+3)*(s+5)*(s+7)/(s*(s+8)*(s^2+10*s+100));>>
IFS=ilaplace(FS,s,t) %Computes the inverse laplace transform of FS
Result:IFS = 5/(112*exp(8*t)) + (237*(cos(5*3^(1/2)*t) +
(3^(1/2)*sin(5*3^(1/2)*t))/9))/(140*exp(5*t)) + 21/80
1f) Solve for loop currents in diagram below:
MATLAB Script>> syms s I1 I2 I3 V>> z=[7+s+(5/s)
-(2+s) -5; -(2+s) (4+2*s+3/s) -(2+s); -5 -(2+s) 8+s+4/s];>>
I=[I1; I2; I3];>> VS=[V; 0; 0];>> I=inv(z)*VS;>>
pretty(I)+- -+ | 4 3 2 | | V s (s + 16 s + 39 s + 40 s + 12) | |
----------------------------------------- | | 5 4 3 2 | | s + 26 s
+ 205 s + 396 s + 284 s + 60 | | | | 2 3 2 | | V s (s + 15 s + 30 s
+ 8) | | ----------------------------------------- | | 5 4 3 2 | |
s + 26 s + 205 s + 396 s + 284 s + 60 | | | | 2 3 2 | | V s (s + 14
s + 24 s + 15) | | ----------------------------------------- | | 5
4 3 2 | | s + 26 s + 205 s + 396 s + 284 s + 60 | Interpretation of
Result
Experiment 2.3LAB USING MATLAB2) Generate the polynomial
operations stated in P1 and P2 given
below:P1=s6+7s5+2s4+9s3+10s2+12s+15;P2=s6+9s5+8s4+9s3+12s2+15s+20MATLAB
Script:>> % Generate the polynomial P1 and P2>>
P1=s^6+7*s^5+2*s^4+9*s^3+10*s^2+12*s+15; >>
s=tf('s');>> P1=s^6+7*s^5+2*s^4+9*s^3+10*s^2+12*s+15 %P1 in
polynomial form Transfer function:s^6 + 7 s^5 + 2 s^4 + 9 s^3 + 10
s^2 + 12 s + 15 >> s=tf('s'); %define 's'as an LTI object in
polynomial form>> P2=s^6+9*s^5+8*s^4+9*s^3+12*s^2+15*s+20 %P2
defined in polynomial form Transfer function:s^6 + 9 s^5 + 8 s^4 +
9 s^3 + 12 s^2 + 15 s + 20
3) Generate the polynomial operations P3=P1+P2, P4=P1-P2,
P5=P1*P2MATLAB ScriptTransfer function:>> % Generate the
polynomial P3=P1+P2>>
P1=s^6+7*s^5+2*s^4+9*s^3+10*s^2+12*s+15;>>
P2=s^6+9*s^5+8*s^4+9*s^3+12*s^2+15*s+20;>> P3=P1+P2 Transfer
function:2 s^6 + 16 s^5 + 10 s^4 + 18 s^3 + 22 s^2 + 27 s + 35
>> % Generate the polynomial P4=P1-P2>>
P1=s^6+7*s^5+2*s^4+9*s^3+10*s^2+12*s+15;>>
P2=s^6+9*s^5+8*s^4+9*s^3+12*s^2+15*s+20;>> P4=P1-P2 Transfer
function:-2 s^5 - 6 s^4 - 2 s^2 - 3 s - 5 >> % Generate the
polynomial P5=P1*P2>>
P1=s^6+7*s^5+2*s^4+9*s^3+10*s^2+12*s+15;>>
P2=s^6+9*s^5+8*s^4+9*s^3+12*s^2+15*s+20;>> P5=P1*P2 Transfer
function:s^12 + 16 s^11 + 73 s^10 + 92 s^9 + 182 s^8 + 291 s^7 +
433 s^6 + 599 s^5 + 523 s^4 + 609 s^3 + 560 s^2 + 465 s + 300 4)
Generate the polynomial whose roots are: -7, -8, -3, -5, -9,
10MATLAB Script>> %Generate a polynomial from given
roots>> r=[-7 -8 -3 -5 -9 -10]; %roots of a
polynomial>> p=poly(r) % Find the coefficient of the
polynomial whose roots are given
p =
1 42 718 6372 30817 76530 75600
Result:
5) Generate the partial fraction expansion of the transfer
function G(s)MATLAB Script>> %Perform the partial fraction
expansion of G(s)>> num=[5,10]; % Coefficient of numerator's
polynomial>> den=[1,8,15,0]; %Coefficient of denomerator's
polynomial>> [r,p,k]=residue(num,den)
r =
-1.5000 0.8333 0.6667p =
-5 -3 0
k =
[]
Result:
6. Construct the two transfer functions enumerated in question
(5)MATLAB Script>> G1=tf([1],[1 1 2])G1 = 1 ----------- s^2 +
s + 2Continuous-time transfer function.>> G2=tf([1 1],[1 4
3])G2 = s + 1 ------------- s^2 + 4 s + 3Continuous-time transfer
function. >> F=G1+G2F = s^3 + 3 s^2 + 7 s + 5
------------------------------ s^4 + 5 s^3 + 9 s^2 + 11 s +
6Continuous-time transfer function.>> P=G1-G2P = -s^3 - s^2 +
s + 1 ------------------------------ s^4 + 5 s^3 + 9 s^2 + 11 s + 6
Continuous-time transfer function. >> T=G1*G2T = s + 1
------------------------------ s^4 + 5 s^3 + 9 s^2 + 11 s + 6
Continuous-time transfer function.
7.For G1(s) + G2(s)MATLAB Script>>num=[1 3 7 5];>>
den=[1 5 9 11 6];>> [r,p,k]=residue(num,den)
r = 1.0000 0.0000 - 0.3780i 0.0000 + 0.3780i -0.0000 p = -3.0000
-0.5000 + 1.3229i -0.5000 - 1.3229i -1.0000 k = []Result
G1(s) G2(s)MATLAB Script>>num=[-1 -1 1 1];>> den=[1
5 9 11 6];>> [r,p,k]=residue(num,den)r = -1.0000 -0.0000 -
0.3780i -0.0000 + 0.3780i 0 p = -3.0000 -0.5000 + 1.3229i -0.5000 -
1.3229i -1.0000 k = []INTERPRETATION
G1(s)G2(s)MATLAB Scriptnum=[1 1];>> den=[1 5 9 11
6];>> [r,p,k]=residue(num,den)r = 0.1250 -0.0625 - 0.1181i
-0.0625 + 0.1181i -0.0000 p =
-3.0000 -0.5000 + 1.3229i -0.5000 - 1.3229i -1.0000
k =
[]INTERPRETATION
