Recent content by Number2Pencil

Thanks Ray! Just so I'm clear, was the substitution of x+1=z because of that +4 offset that was impeding you from directly obtaining a characteristic polynomial equation? After finding a solution for z(t), I can just convert back to x knowing that x = z-1

Thanks Ray, I did get an satisfactory answer using the symbolic variable for x'(0), and then solving at the end for x(1) = 4. You mentioned another way to just ignore initial conditions and I will end up with 2 constants that I need to solve for. This is what I originally tried, using the...

Homework Statement Find the optimal trajectory x*(t) that minimizes: J = \int_{0}^{1} \left( \frac{\dot{x}(t)^2}{2} + 3x(t) \dot{x}(t) + 2x^2(t) + 4x(t) \right) dt with x(0) = 1 and x(1) = 4 Homework Equations Euler's equation: \frac{\partial g}{\partial x} -...

The prof didn't bother defining singular point, and yes I did pay attention in class! hah Thanks for the tip all, I had no idea singular point COULD be different than singularity. Sure enough I found something that seems helpful on Wikipedia...

Well my professor must have been confused in his response as well, because he definitely wrote the word "singularity" Could you provide any tips on how to solve this problem? From your link, it looks like the singular point is where the function intersects with another point of the function...

I talked to my professor, and he said "the singularity will hold irrespective of the value p." So it looks like I was correct about p not really making a difference. But I would still like to know WHY the point (0,0) is a singular point. Any thoughts?

Homework Statement Given the function f(x_1,x_2) = (x_1 - x_2^2)(x_1 - px_2^2) where p is a constant parameter, for what value of p will the origin (0,0) be a singular point of this function? Homework Equations The Attempt at a Solution I thought that singular meant...

Hello, I am trying to develop a software control algorithm to compensate for oscillator imperfections/frequency drift. I have a NTP server which I can get a pretty good estimation (@1Hz) of the "true" time and compare it to my system's time. I can differentiate the offset-error to calculate...

Greetings. I am not sure how to approximate a MOSFET's switching energy from datasheet parameters. I have stumbled upon a few ways, but in all cases I've found it is pretty rare to find a datasheet with all the correct parameters. Here are some ways I've found: 1) Eon and Eoff are listed...

Thanks for the patience. I do understand what you were saying about state-space and that I need to simplify my system into its equivalent state-space form. I'm not sure where to begin on actually doing this. For starters, I tried to redraw the diagram to make it more accurate. Even doing that...

A is a 2x2, and B and L are 2x1 matrices, Ro is just a constant. The OCV/VRC block is somewhat misleading as drawn, as it actually extracts the elements out of its input (let's call it x1 and x2), and performs the following math function: output = m*x1 + b - x2. So the input of this block is a...

The inputs of the system are i_t and v_t, and the output is the output of the integrator.

Homework Statement I'm having to figure out if a system is asymptotically stable, stable, or unstable. I am given the system block diagram. However, each constant block is actually a matrix. Also, there is an integral block thrown in there... Homework Equations The Attempt at a Solution In a...

I think I see my mistake now. In my subcircuit equations, I simply put things in terms of inductor currents: IL1 & IL2. Each of these actually need to be broken up in an AC and a DC component. I can calculate the AC component by integrating the voltage waveforms of the inductors, but the DC...

Homework Statement Assuming that a CUK converter is operating in DCM mode (see attached image), find the solution for M(D,k). D is the duty ratio of the switch, and k... Homework Equations \frac{V}{V_g} = M(D,k) k = \frac{4L_1L_2}{(L_1+L_2)(2RT_s)} The Attempt at a Solution...