Question

please can anyone help me with those 

1. For the following car-suspension dynamics below do the following: C = [0 1 0 Wheel m 2 a. Simulate using MATLAB for the following cases: Road surface For m1= 50, m2 =500, ks=20, kw=50, and b=100. Find the state-space module using MATLAB. Then find the transfer Inertial reterence function ot the module. Ans: Code Result on the MATLAB b. Use MATLAB find the Impulse response of the system for the following cases as below: Case 1: Set m2= 100, ks=5, kw =10, and b = 50. Then Plot the impulse response when m1 takes the tollowing values from 10 to 100, with five elements equally spaced in the same figure with index number Ans: Table 1: Case 1: Chonging mi Hgure 1 Code Q1. Compare the behavior ot the system tor the five cases of m1 and which one has the highest amplitude? Also, which one reaches its stable final value taster? (indicate the time using the plot)? |

Case 2: Set mi=10, ks=5, kw= 10, and b =50. Plot the impulse response when mz takes the following values from 100 to 1O00, with five elements equally spaced in the same figure with index number 2. Ans: Table 2: Case 2: Changing m2 Figure 2: Code 02. Compare the behavior of the system for the five cases of m2 and which one has the highest amplitude? Also, which one reach its stable tinal value taster (indicate the time using the plot)? -------------- ------------ - ------- - ------==---- --- -------------- -------------- Case 3: Set mi-10.m2-100, ks=5, and kw = 10. Plot the impulse response when b takes the following values from 50 to 200, with five elements equally spaced in the same figure with index number 3. Ans: able s: Case s: hanging b_ Figure3 Code Q3. Compare the behavior of the system tor the tive cases of b and which one has the highest amplitude? Also, which one reach its stable final value faster (indicate the time using the plot)?

Case 4: Set m1-10, m2=100, kw = 10, b=50. Plot the impulse response when ks takes the following values from 5 to 40, with five elements equally spaced in the same figure number 4. Ans: Table 4: Changing k Figure 4: Code 04. Compare the behavior of the system for the five cases of ks and which one has the highest amplitude? Also, which one reach its stable final value faster (indicate the time using the plot)? ---- Case 5: Set m1=10, m2=100, ks=5, and b=50. Plot the impulse response when kw takes the following values from 10 to 100, with five elements equally spaced in the same figure number 5. Ans: Table 5: Case 5: Changing KW Figure 5: Code Q5. Compare the behavior of the system for the five cases of kw and which one has the highest amplitude? Also, which one reach its stable final value faster (indicate the time using the plot the plot)?

Answer 1

CODE:

clc
close all
m1 =50;m2=500;ks=20;kw=50;b=100;
A= [0 1 0 0
-(ks+kw)/m1 -b/m1 ks/m1 b/m1
0 0 0 1
ks/m2 b/m2 -ks/m2 -b/m2]
B = [0 kw/m1 0 0]'
C = [0 0 1 0]
D = 0;
[num,den] = ss2tf(A,B,C,D)
% a)
G = tf(num,den)

% b)
m1 =50;m2=100;ks=5;kw=10;b=50;
A1= [0 1 0 0
-(ks+kw)/m1 -b/m1 ks/m1 b/m1
0 0 0 1
ks/m2 b/m2 -ks/m2 -b/m2];
B1 = [0 kw/m1 0 0]';
C1 = [0 0 1 0];
D1= 0;
[num1,den1] = ss2tf(A1,B1,C1,D1)
G = tf(num1,den1);
impulse(G)

- 0 x Figure 1 File Edit View aduĄ Insert Tools Desktop Window Help a my A. O IE O Impulse Response 0.25 0.15 Amplitude 0.05 -0.05 -0.1 F -0.15 0 20 40 60 80 Time (seconds) 100 120 140

RESULT:

Command Window New to MATLAB? See resources for Getting Started. A = 0 -1.4000 0 0.0400 1.0000 -2.0000 0 0.2000 0 0.4000 0 -0.0400 0 2.0000 1.0000 -0.2000 B = C = 0 0 1 0 num = 0 0.2000 0.0400 den = 1.0000 2.2000 1.4400 0.2000 0.0400 G = 0.2 s + 0.04 - - - - - - - - - - - - - - - - -- S^4 + 2.2 s^3 + 1.44 s^2 + 0.2 s + 0.04 fx Continuous-time transfer function.

2)

CODE:

clc
close all
m2=100;ks=5;kw=10;b=50;
for m1 =10:22.5:100
% b)
A1= [0 1 0 0
-(ks+kw)/m1 -b/m1 ks/m1 b/m1
0 0 0 1
ks/m2 b/m2 -ks/m2 -b/m2];
B1 = [0 kw/m1 0 0]';
C1 = [0 0 1 0];
D1= 0;
[num1,den1] = ss2tf(A1,B1,C1,D1);
G = tf(num1,den1);
impulse(G)
hold on
end
legend('m1 = 10','m1 = 32.5','m1 = 55','m1 = 77.5','m1 = 100');

RESULT:

Impulse Response m1 = 10 m1= 32.5 m1=55 m1= 77.5 m1 = 100 Amplitude System: m1 = 32.5 Settling time (seconds): 71.8 System: m1 = 77.5 Settling time (seconds): 133 System: m1 = 10 Settling time (seconds): 55.9 System: m1 = 55 Settling time (seconds): 101 System: m1 = 100 Settling time (seconds): 169 50 50 100 200 100 250 Time (seconds 200 150 250 Time (seconds)

Impulse Response m1 = 10 m1= 32.5 m1=55 -m1 = 77,5 m1 = 100 Amplitude 50 100 150 200 250 Time (seconds)


Impulse Response 0.23 m1 = 10 m1= 32.5 m1=55 m1 = 77.5 m1 = 100 System: m1 = 10 Peak amplitude: 0.224 At time (seconds): 4.89 E:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=:=: 0.225 System: m1 = 32.5 Peak amplitude: 0.225 At time (seconds): 5.68 System: m1 = 55 Peak amplitude: 0.22 At time (seconds): 6.38 0.22 System: m1 = 77.5 Peak amplitude: 0.214 At time (seconds): 7.05 Amplitude 0.21 System: m1 = 100 Peak amplitude: 0.208 At time (seconds): 7.62 0.205 0.2 0.195 12 10 Time (seconds) 14 16 18

m1 = 10 will give less settling time

m1 = 32.5 will give more overshoot (comparatively)