Question

6. For the following mechanical system: a) Find a mathematical model b) Find the transfer function, G(s) = c Find impulse, step and ramp response by using MATLAB functions d) Find harmonic response by using MATLAB SIMULINK T(s) 2 N-m-s/rad 2 N-m/rad N2-20 T0) l kg-m2 N3-40 010 N1-5 N4-10 0.02 N-m-s/radl

Answer 1

Anbwe for Question 6 米 As per the , Given fiqure information we have to the too geat systems N, and N2 Na and Ny The values ore Ni ,ngard N3 , N4 * Theration N2|N1 and N3/ N 4-4 the Same value . then, the orque wi be the Some * The Bett) , effected by the b th Torgue Tit) and also the toryue due to the pistona N ms rad e Toraue balaace cquation d t dt dt

Part C&D:

Applying laplace Transform TLS) function áls)-Cz(S) T5) Tranfer s+1.785+2

Programming code Using MATLAB:

clc;

clear all;

close all;
sys=tf([1],[1,1.98,2]); ############## Defining G(s)
figure(1) ######## Plot for  impulse response
impulse(sys)
figure(2)#####Plot for step response
step(sys)
########## Plotting ramp response using 'lsim' command
t=0:0.1:10;
ramp=t;
######## obtaining the response 'r' of the model for input 'ramp'
[r,t]=lsim(sys,ramp,t);
%plotting 'r' vs. time
figure(3)
plot(t,r)
title('Ramp Response')
xlabel('Time (seconds)')
ylabel('Amplitude')
######### harmonic response using 'bode' command
figure(4)
bode(sys)

MATLAB O/P:

Impulse Response::Step response:

Impulse Response 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.05 2 3 6 Time (seconds)

Step Response 0.6 0.5 0.4 0.3 0.2 0.1 2 4 5 6 Time (seconds)

Ramp Response:

Bode Diagram:

Ramp Response 5 4.5 3.5 3 2.5 2 1.5 0.5 0 123 45 678 9 10 Time (seconds)

Bode Diagram -60 -80 -45 dD 90 0 -135 -180 10-1 102 2 10 10 Frequency (rad/s) 10

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