## anonymous one year ago linearise: dy/dt=a[(1-b)/b]+ba^2+sin(c*a) ; where c is constant.

1. anonymous

i am unsure how to linearise this when only 1 variable is constant. could someone enlighten me how to linearise this with multiple variables?

2. anonymous

sorry that should be db/dt

3. anonymous

not dy/dt

4. freckles

hey what does linearise mean exactly?

5. freckles

does that mean to solve the differential equation or something else?

6. anonymous

clearly, this is a non-linear function, so to make it linear we try to make a general equation of all the tangents where our condition is at steady state.

7. anonymous

|dw:1438924011903:dw|

8. anonymous

so we try to fit that curve with linear tangents

9. anonymous

where the point we know as a basis is the steady state condition.

10. anonymous
11. anonymous

its along these lines..

12. anonymous

this is mearly the fundementals for laplace transforms

13. freckles

@zzr0ck3r do you know how to do this ?

14. zzr0ck3r

Nah, this is some physics/engineering b.s. :) I spent a summer doing it at Uof O but that was 4 years ago and I forgot...

15. freckles

I was trying to find something easy to follow online but I can't find anything.

16. anonymous

haha thanks for helping anyway

17. anonymous

we are doing this for process control but i think ive nutted it out

18. freckles

you think you nutted it out? lol I take that as you did it! :) I would like to see your solution if and when you get time.

19. anonymous

to linearise ba^2 we need to partial differentiate each term at steady state

20. freckles

$z=ba^2 \\ z_b=a^2 \\ z_a=2ab ?$

21. anonymous

so we get|dw:1438925115302:dw|

22. anonymous

so thats a linear approximation of ab^2

23. anonymous

so you apply that with all the other non linear terms

24. freckles

hmm...weird I see where you got the last two terms

25. freckles

so hey would sin(ca) be $\approx \sin( c a_{ss})+c \cos(ca)a'$

26. freckles

though that isn't linear :p

27. anonymous

yeah i havent figured the sin term yet haha

28. anonymous

might have to use an iterative procedure for that...hmm

29. anonymous

this is interesting. its only the sin term which is weird to linearise

30. anonymous

suggestions?