I want to find the range of kc that makes s is less than zero
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I want to find the range of kc that makes s is less than zero
This is the equation that I have:
16*s^3 + 280*s^2 + 1400*s + 200*Kc + 2000
Thanks...
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Voss
2021-12-4
That expression is not an equation (or an inequality), so any relationship between s and Kc is possible.
回答(1 个)
Walter Roberson
2021-12-4
syms s Kc delta real
assume(delta >= 0)
eqn = 16*s^3 + 280*s^2 + 1400*s + 200*Kc + 2000 == delta
sol = solve(eqn, s, 'MaxDegree', 3)
sol
delta_bounds = solve((25*Kc/4 - delta/32 + 625/108)^2 - 5359375/46656 == 0, delta, 'returnconditions', true)
delta_bounds.delta
delta_bounds.conditions
You asked that the value of the expression be less than or equal to 0. In the above code, delta represents the amount by which the expression is less than zero. I am going to assume that the quantities involved are not complex-valued.
if delta is positive and too large then (25*Kc/4 - delta/32 + 625/108)^2 will not be large enough to subtract 5359375/46656 from and still get a real-valued quantity out of the sqrt() for solving s. So delta is bounded by that at most, and lower bound zero.
The equation doesn't work out at all if Kc is too small; you would go imaginary.
I don't know, there just might be a configuration of small Kc that lead to the complex conjugate pairs that are the second and third solutions to be real-valued.
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