How to use solve with a equation with limit

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Emanuel Thiago
Emanuel Thiago 2021-4-15
评论： Walter Roberson 2021-4-16
syms b1 c1 s
a = 1;
b = 7.598;
c = 6.784;
kp = limit(20.185/(a*s^2+b*b1*s+c),s,0)
solve(kp,b1)
answear to the code :
v = Empty sym: 0-by-1
I want to solve the equation in terms of b1, i know it is 0 but i need to be generic, i want something like b1 = kp*something, so i tried the function solve but it does not seem to work, maybe it is related to the limit, i would be gratefull if someone help me, thanks in advance.

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Walter Roberson
Walter Roberson 2021-4-15
Ran in:
syms b1 c1 s
a = 1;
b = 7.598;
c = 6.784;
kp = limit(20.185/(a*s^2+b*b1*s+c),s,0)
kp = 
Notice this is constant, not dependent on b1.
[kp, b1]
ans = 
solve(ans)
ans = Empty sym: 0-by-1
You are trying to find the value of b1 such that b1 and 20185/6784 both become 0. There is no possible value of b1 for which that happens.
We can ask the question differently: out of all the values of b1 that make the equation 0, what is the limit as s approaches 0?
eqn2 = 20.185/(a*s^2+b*b1*s+c)
eqn2 = 
b1sol = solve(eqn2, b1)
b1sol = Empty sym: 0-by-1
limit(b1sol, s, 0)
ans = Empty sym: 0-by-1
It turns out there is no finite value of b1 that makes the equation 0.
I say finite because:
limit(eqn2, b1, inf)
ans = 
but as s approaches 0, that goes to non-zero, and only goes to 0 if s is non-zero. So you have a contradiction, and there is no solution at all.
  2 个评论
Emanuel Thiago
Emanuel Thiago 2021-4-16
then is there a way to ask if a number is real ? i need to make a generic code, even if it always it is gonna be the case
Walter Roberson
Walter Roberson 2021-4-16
https://www.mathworks.com/help/matlab/ref/isreal.html
but that is for numeric values only.
For symbolic values you should test
isAlways(imag(X)==0)
where X is the thing to be tested. Be sure to add the option that deals with the result you want if matlab is not able to prove real or not.

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