HW2_2 - 0 -w2/g w2/g 0]; D = [ 0 0; 0 -fu]; eig(A) e syms t...

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% Linear Systems, Homework 2 % Date: 11/13/06 % File: HW2_2.m % Note: bicycle-rider system % Name: Feng-Li Lian, [email protected] % close all; clear all; c % specifications % g = 9.8; h = 0.08; V = 10; V mvg = 136.0; mv = 136.0/g; mhg = 9.11; mh = 9.11/g; hv = 0.334; hh = 0.465; Iv = 2.25; Ih = 0.201; L = 0.665; Lr = 0.313; L h = 0.08; V = 1; B1 = 1/L; B2 = Lr/L; l = 0.7; l w2 = ( mvg * hv + mhg * hh ) / ( Iv + Ih + mv*hv^2 + mh*hh^2 ); fu = ( mh*hh^2 + Ih )*h / ( hh*( Iv + Ih + mv*hv^2 + mh*hh^2 )); f0 = mh*h / ( mv*hv + mh*hh ); F = (f0 - fu)*g; F % state-space model % A = [ 0 0 0 0; -V 0 0 0; 0 0 0 1; 0 -w2 w2 0]; B = [ B1*V 0; -B2*V 0; 0 0; 0 F]; C = [ -l 1 0 0;
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Unformatted text preview: 0 -w2/g w2/g 0]; D = [ 0 0; 0 -fu]; eig(A) e syms t tau s s %xp0 = zeros(2,1); x0 = [ 0 0 0 0 ]'; x %u = [1 1]'; u = [ 0 0.1*sin(5*pi*tau) ]'; u expA = expm( A * t ); e zi = expA * x0; z zs = int( expm( A*(t-tau) ) * B * u, tau, 0, t ); z xt = zi + zs; x subs( xt, t, 1 ) s for i=1:21 time1(i) = (i-1)*0.1; state1(:,i) = subs( xt, t, time1(i) ); %u1 = u; u1 = subs( u, tau, time1(i) ); output1(:,i) = C*state1(:,i) + D*u1; end e figure(11) subplot(211) plot(time1,state1) xlabel('time'); ylabel('state'); subplot(212) plot(time1,output1,'g') xlabel('time'); ylabel('output'); x...
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This note was uploaded on 07/21/2009 for the course EE 901-43400 taught by Professor Feng-lilian during the Fall '08 term at National Taiwan University.

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HW2_2 - 0 -w2/g w2/g 0]; D = [ 0 0; 0 -fu]; eig(A) e syms t...

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