clc clear all % Initial Values P1 = [1, 7, -3, 23]; P2 = [5, 6, 10,]; % Store polynomial (s+2)(s+5)(s+6) as P3 and display the coefficients P3 = poly([-2,-5,-6]); % Begin Root Calculations P4 = [1, 7, 20]; R4 = roots(P4) P5 = [5, 7, 9, -3, 2]; R5 = roots(P5) % Begin Symbolic Math F=sym('(s^2 + 5*s + 6)*(s^2 + 7*s + 10)'); pretty(F) v = [1, -4, 0, 2, 45]; y = poly2sym(v) pretty(y) syms x; F = x^4 - 4*x^3 + 2*x + 45; sym2poly(F) P6 = [3, 15, 0, -10, -3, 15, -40]; P7 = [3, 0, -2, -6]; Psum = P6 + [0, 0, 0, P7] P8 = conv([0, 1, 7, 10, 9],[1, -3, 6, 2, 1]) num1 = [2, 9, 7, -6]; den1 = [1, 3]; [a1, b1] = deconv(num1, den1) sys1 = poly2sym(a1) rem1 = poly2sym(b1) num2 = [2, -13, 75, 2, -60]; den2 = [1, -5]; [a2, b2] = deconv(num2, den2) sys2 = poly2sym(a2) rem2 = poly2sym(b2)
clear all; clc; syms s G1 = (s+2)/((s+3)*(s+4)); pretty(G1) g1=ilaplace(G1); pretty(g1) syms s G3 = (100*(s + 2))/(s*(s + 1)*(s^2 + 13*s + 36)); pretty (G3) g3=ilaplace(G3); pretty(g3)
%% set up clear all close all clc %% Gain pos=0.3; z=((-log(pos))/(sqrt((pi^2) + (-log(pos))^2))); k1=122; k2=4.65; pdom= -2.3159 + 2.3286i; pdes=2*pdom; ades=angle((pdes+6)/((pdes+2)*(pdes+3)*(pdes+5)))*(180/pi); zc=(4.6318-4.6572)/(tan(ades*(pi/180))); k3=1/abs(((pdes + zc)*(pdes+6))/((pdes+2)*(pdes+3)*(pdes+5))); %% System G1=zpk([-0.1],[0 -1 -3 -10],1); T1=feedback(G1*k1,1); G2=zpk([-6],[-2 -3 -5],1); T2=feedback(G2*k2,1); G3=zpk([-zc -6],[-2 -3 -5],1) T3=feedback(k3*G3,1) %% Step figure step(T1) figure step(T3) figure step(T2,'r',T3,'b') legend('Original','PD Compensated')
%% Maintenance clear all close all clc syms n x z s %% Original Systems, Inputs, and Sampling Fs1=300; %Sample Frequency 1 Fs2=1000; %Sample Frequency 2 Fs3=100; %Sample Frequence 3 %Yn1=0.5*x(n) + 0.5x(n-1); %System EQ Y2(n) b1=[0.5 0.5]; %System 1 Coefficients %Yn2=0.5*n(n) - 0.5x(n-1); %System EQ Y2(n) b2=[0.5 -0.5]; %System 2 Coefficients %Yn3=(1/4)*(x(n) + x(n-1) + x(n-2) + x(n-3)) %System EQ Y3(n) b3=[1/4 1/4 1/4 1/4]; %System 3 Coefficients %% Frequency Responses figure freqz(b1,1,256,Fs1) %Frequency Response of System 1 title('Low Pass') figure freqz(b2,1,256,Fs1) %Frequency Response of System 2 title('High Pass') figure freqz(b3,1,256,Fs2) %Frequency Response of System 3 title('Band Pass') %% SP Tool sptool a=[1 0 0 0]; %% Spectrums n=0:999; x1=8*cos(2*pi*250*n*(1/Fs2) + (pi/3)); x2=8*cos(2*pi*250*n*(1/Fs3) + (pi/3)); %% FDA Tool fdatool %% Chirp f1=200; f2=2200; T=10; fs=8000; t=0:(1/fs):T; y=chirp(t,f1,T,f2); sound(y,fs)