Recent content by Mugged

its something like what you wrote: C(s) = (s + a)/(s + b), where conditions on a,b determine if its lead or lag. Your lead network form is more useful because there exists equations for T and beta. Have you tried to solve for T,beta? Then its likely the 1/sqrt(2) falls out of the stability...

Ah..ok, my bad. This problem is harder than I thought...KKT coming in a statistics problem. Thanks.

Ray, log((b^a)^N) = a^N*log(b) ≠ aNlog(b)?

Whats the representation for lead compensator? Closed loop stability implies you're using feedback, and the stability condition is: 1 + G(s)*C(s) = 0, where C(s) is your compensator. Edit: You'll also want to add a gain K in front of the compensator...so K doesn't just appear out of nowhere...

Are you sure? What if b = 1 + i and c = 2 + 2i ?

Rework the integral, i don't understand where you get that x in the denominator. An answer of y2 = 1 seems trivial..y2 could be any constant and it would satisfy the differential equation.

Hang on, if P(x) = 1/x, why did you plug in ln(x) in the exponential integral term? Edit: Also you can't multiply ln(x) into the integral.

So there might be some mistakes in the way you computed the log (LL) function. The term premultiplying log(β) should probably be reworked. Hint: log(β^y) = ylog(β). But what is y? It is not αn.

Ok you probably should try the find root function. FindRoot[x == 2Cos[x], {x,0}] the 0 is an initial starting point in the numerical solver. I haven't used mathematica in a while but the problem might be that the solve function looks for an exact solution while your equation is...

Have you tried it without the curly braces on the x at the end?

Well, suppose you wanted to know the arc length of a portion of a circle; the typical formula is arc length = radius*angle. So the units would be meters*radians in standard SI. Although radians is a dimensionless unit, so you could also say units are just meters.

1. Are you sure you didn't mistype that determinant formula? 2. anti-symmetry implies M^T = -M

Can you define the notation a bit? Are you solving for Θ? Is Θ a function of ε -> Θ(ε)? Is β just a constant? are there any initial conditions or you just need a general solution?

To be perfectly honest, a math masters is do-able for you if you only do courses. A thesis masters or PhD requires talent...people that do those usually start in multivariable calculus or higher as freshmen. But here's the thing, there's nothing stopping you from taking interesting math...

Yes, keep the 1 inside. I understand your idea for breaking up the sum, but you forgot about the other term. Your split idea is good: (1+2^n)/(3^n) = 1/3^n + 2^n/3^n. Use your formula for both these terms. Hint: 1 = 1^n.