9 - 5 Instructions: Show procedure (if applicable). An electro-mechanical vibrat

Question

9 - 5 Instructions: Show procedure (if applicable).

An electro-mechanical vibrator is schematically shown below. The electro magnetic force induced in the mass m is F ai and the induced voltage is e 3ar 34 2- 2 Write your own matlab program to generate the Bode plots (ie A on log log scale, p c) on semi-log scale). From the plots, determine the frequency of the voltage source beyond which the amplitude of the vibrator displacement is less than 10% of that when is near zero. Also, determine the phase angle between the input and output at this driving frequency. Make sure you use ATAN2 function to calculate 00a) and the plot should be a smooth curve. If you see a jump in 21t in your plot, program in a correction to bring it to a smooth curve. Turn in your plots and the matlab program.

Explanation / Answer

To code this problem in matlab we need modle this entire system in s-domain

modeling of given system

Applying KVL to elctrical loo

e=i*R+Ld(i)/dt+e34

taking laplace of above system

e(s)=i(s)*R+L*s*i(s)+v(s) .......eq 1 ( as e34=v)

now we need v(s) and replace in terms of x(s) and i(s)

for that we can use mechanical diffrential equation

F=m*d(v)/dt+b*v+k*x

taking laplace of above equation

*i(s)=m*s*v(s)+b*v(s)+k*x(s).........eq2 ( because F=i)

now v=d(x)/dt so v(s)=sx(s)

i(s)=ms2x(s)+bsx(s)+kx(s).......eq3

final using eq1,eq2,eq3 we get expression of this form

x(s)/e(s)=1/(Lms3+(Rm+bL)s2+(Rb+2+k)s+kR)

for appropriate constant values of L,m,R,,b,k u can plot this equation in matlab

syntax to matlab equation is as below

take num=[all numerator coefficients of above equation] ie., for above example num=[1] because no s terms

den=[ all denominator coeffients of above equation]

bode plot commond in matlab is

transfrefunction=tf(num,den)

bode(transfrefunction)

by using gain adustment curcser check the gain value which is 10% less the 0 frequency value and check the phase angle for that value you will get the phase value

Related Questions

Navigate

• Browse (All)
• Browse 9
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.