I have an equation
q(s) = s^5 + s^4 + 4s^3 + 4Ks^2 + 2Ks + K
The answer I have indicated is 0.5361 < K < 0.9326.
Can this be done in Matlab, and if so how?
My apologies I am still feeling my way through Matlab.
Regards.
I have an equation
q(s) = s^5 + s^4 + 4s^3 + 4Ks^2 + 2Ks + K
The answer I have indicated is 0.5361 < K < 0.9326.
Can this be done in Matlab, and if so how?
My apologies I am still feeling my way through Matlab.
Regards.
Using your code pickslides I get
ans =
-(s^5 + s^4 + 4*s^3)/(4*s^2 + 2*s + 1)
To me that has not solved for K. The other way to my thinking is to go through the Routh array but for such a complex function this seems daunting and time consuming...and that's assuming it is even possible that way.
Regards.
Solve what, this is not an equation for solving? State clearly exactly what you want to find and what you have to start with. In other words tell us what the real question is.
For example do you mean find $\displaystyle $$K$ such that:
$\displaystyle s^5 + s^4 + 4s^3 + 4Ks^2 + 2Ks + K=0$ ?
(which is verging on the trivial, so not likely to be what you mean)
CB
s^5 + s^4 + 4s^3 + 2Ks + K = 0 is the denominator of a given transfer function.
The question asks to find out whether the system is stable using the Routh Hurwitz criterion, then determine its range of stability for K > 0. I thought it may be possible to be done on Matlab...
People without Mathlab may try to solve the problem searching the value of k for which the roots of...
$\displaystyle \displaystyle q(s)=s^{5} + s^{4} + 4\ s^{3} + 4\ k\ s^{2} + 2\ k\ s + k$ (1)
... have all negative real part use the following approach. Let's suppose to search the values of k for which $\displaystyle q(s)$ has a factor $\displaystyle s^{2}+ \alpha$ with $\displaystyle \alpha>0$, such that is...
$\displaystyle q(s)= (s^{2}+ \alpha)\ (s^{3} + \beta_{2} s^{2} + \beta_{1}\ s + \beta_{0})$ (2)
Comparing (1) and (2) we arrive to the following system of equation...
$\displaystyle \beta_{2}=1$
$\displaystyle \alpha + \beta_{1}=4$
$\displaystyle \beta_{0} + \alpha\ \beta_{2}=4\ k$
$\displaystyle \alpha\ \beta_{1}= 2\ k$
$\displaystyle \alpha\ \beta_{0}=k$
... which leads to the pair of equations...
$\displaystyle \alpha^{2} - 4\ \alpha + 2\ k=0$
$\displaystyle \alpha^{2} - 4\ k\ \alpha + k=0$ (3)
... the solutions of which are...
$\displaystyle \alpha=0\ ,\ k=0$
$\displaystyle \alpha=3.461072192556...\ ,\ k=.932634024069...$
$\displaystyle \alpha=.2889278074438...\ ,\ k=.53611597593...$
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$