Experiment 2.3 objective To learn to use LabVIEW to generate and manipulate poly

Question

Experiment 2.3 objective To learn to use LabVIEW to generate and manipulate polynomials and transfer functions. Minimum Required Software Packages LabVIEW and the LabVIEw Control Design and Simulation Module. Prelab 1. Study Appendix D, Sections D.1 through Section D4, Example D.1. 2. Perform by hand the calculations stated in Prelab 1 of Experiment 2.1. 3. Find by a hand calculation the polynomial whose roots are -7,-8, -3, -5, 9, and -10. 5s 10 4. Perform by hand a partial-fraction expansion of G(s) 8s2 15s 5. Find by a hand calculation G (s) G2(s), G1 (s)-G2(s), and G (s)Gh(s), where s 1 and G2(s) s2 4s 3 s+ 2 Lab 1. Open the LabVIEW functionspakette and select the MathematicsPolynomialpalette. 2. Generate the polynomials enumerated in Prelab la and lb of Experiment 2.1. 3. Generate the polynomial operations stated in Prelab 1c of Experiment 2.1. 4. Generate a polynomial whose roots are those stated in Prelab3 of this experiment.

Explanation / Answer

% lab 4
r=[-7 -8 -3 -5 -9 -10]; % roots of the polynomial
C=poly(r); % returns the co-efficients of polynomial;
P=poly2sym(C); % gives the polinomial equation;

% Ans: P = x^6 + 42*x^5 + 718*x^4 + 6372*x^3 + 30817*x^2 + 76530*x + 75600

%% lab 5
T=tf([5 10],[1 8 15 0]);
b=[5 10]; % Numerator of transfer function
a=[1 8 15 0]; % Denominator of transfer function
[r,p,k]=residue(b,a); % Partial fraction of TF

% Ans: T= r(1)/(s-p(1))+r(2)/(s-p(2))+.......+k

%% Lab 5
num1=[1]; % co-effs of numerator for G1(s)
Denom1=[1 1 2]; % co-effs of denominator for G1(s)
G1=tf(num1,Denom1) % Transfer function of G1(s)

num2=[1 1]; % co-effs of numerator for G2(s)
Denom2=[1 4 3]; % co-effs of denominator for G2(s)
G2=tf(num2,Denom2) % Transfer function of G2(s)

% Ans:
% G1 = 1
% -----------
% s^2 + s + 2

% G2 = s + 1
% -------------
% s^2 + 4 s + 3
%
%% Lab 6
Gsum=G1+G2
Gsub=G1-G2
Gmul=G1*G2
% Ans

% Gsum = s^3 + 3 s^2 + 7 s + 5
% ------------------------------
% s^4 + 5 s^3 + 9 s^2 + 11 s + 6

%
% Gsub = -s^3 - s^2 + s + 1
% ------------------------------
% s^4 + 5 s^3 + 9 s^2 + 11 s + 6
%
% Gmul = s + 1
% ------------------------------
% s^4 + 5 s^3 + 9 s^2 + 11 s + 6

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