Question

Consider the following ODE where m= 10 kg, b = 2 N-s/m and u(t) = 0. Assume initial conditions of z(0) = 15 and ż(0) = 25. Use MATLAB control system toolbox commands to simulate the dynamic response of the system for 0 st 35. m2 + bż = u(t) PLOT 2(t) and ż(t) on two sets of axes using the subplot command. REPORT: max 2 = max ż

Answer 1

Given system, m 2 + b Ź s ult) where ms 10 kg. b 2 N-5/m И. 0 => 1 10 2 + 2 2 = 0 Writing in state-space form, x = 2 states B, 22 M Z 2 No 2 X2 こ Z ar 10 24. = 22 Z, -0.2 2₂ t u X output, ya Z [10] 24 74 d [] Lo [1]-[:] 0.2 It 4. y = [! 전

MATLAB CODE

A=[0 1;0 -0.2];

B=[0;1];

C=[1 0];

D=[0];

sys=ss(A,B,C,D);

x0=[15 25];

t=linspace(0,35,360);

[y,t,x]=initial(sys,x0,t);

figure()

subplot(2,1,1)

plot(t,x(:,1))

grid on

xlabel('time in seconds')

ylabel('amplitude of z')

title('z Vs time')

subplot(2,1,2)

plot(t,x(:,2))

grid on

xlabel('time in seconds')

ylabel('amplitude of z_dot')

title('z dot Vs time')

display(max(x(:,1)),'max z')

display(max(x(:,2)),'max z_dot')

MATLAB OUTPUT

max z =

  139.8860

max z_dot =

    25

z Vs time 150 100 amplitude of z 50 0 0 5 10 25 30 35 15 20 time in seconds z dot Vs time 30 20 amplitude of zot 10 0 0 5 10 25 30 35 15 20 time in seconds