# Control system with equation C = A*x + B*dx/dt

1. May 13, 2012

### zsero

1. The problem statement, all variables and given/known data
This question came up in a computer science / robotics exam and I still don't know the solution for it. I figured out that it's classical mechanics related, so I thought this might be the best place to ask it.

2. Relevant equations
C = A*x + B*dx/dt

3. The attempt at a solution
I've figured out that the steady state doesn't change, as it happens when dx/dt is 0, thus B is not affecting the solution.

And this is how far I understand it. Can you explain to me, what kind of movement is this, what is the real-life meaning of the steady state and half-life for this movement and that how to calculate the change in the half-life?

2. May 13, 2012

### tiny-tim

hi zsero!

write it Bdx/dt = C - Ax, then solve it by "separating the variables"

3. May 13, 2012

### zsero

OK, I arrive at the following equation:

-B/A*ln(x) = c*t + k1

My problem here is that I don't understand the meaning of the equations and that what is asked by half-life and steady state.

How can I get the half-time from this equation?

4. May 13, 2012

### tiny-tim

ok, now multiply by -1/B and then e-to-the on both sides …

x = xoe-ACt/B (where xo = e-kA/B)

does that look familiar?

5. May 13, 2012

### zsero

Thanks for the help! Actually, I'm not a Physics student, so I don't really know, but I'd guess it's the exponential delay. So if B doubles then the constant becomes half, thus the half-life becomes double. Is this correct?

6. May 13, 2012

### tiny-tim

good guess!

but you really should make yourself familiar with half-life (and exponential decay generally) …

look it up in wikipedia or the pf library

7. May 13, 2012

### zsero

Thanks for the help!