- #1

curiousPep

- 17

- 1

- Homework Statement:
- I have the ODE $$m*y''+c_v*y'+c_p*u = c_p*u$$, where u = -k*y. I need to identify the range of static feedback gains u = −ky that guarantee stability of the closed loop system.

- Relevant Equations:
- $$T_{u \to y}(s) = \frac{1}{s^{2}m+c_{v}s+c_{p}}$$

I have used root locus before but my confusion now is that the input is the negative feedback. Usually when I have negative feedback I consider the the error between the input (ideal) signal and the observed signal.

Also, in this case what is the tranfer function since u = -k*y, and what does the transfer function represent since the only variable is the equation is y?

For the case where we use the equation m*y''+c_v*y'+c_p*u = c_p*u, the transfer fucntion is $$T_{u \to y}(s) = \frac{1}{s^{2}m+c_{v}s+c_{p}}$$. I am no sure what to do when I consider u = -k*y.

Can someone provide me some hints please?

Also, in this case what is the tranfer function since u = -k*y, and what does the transfer function represent since the only variable is the equation is y?

For the case where we use the equation m*y''+c_v*y'+c_p*u = c_p*u, the transfer fucntion is $$T_{u \to y}(s) = \frac{1}{s^{2}m+c_{v}s+c_{p}}$$. I am no sure what to do when I consider u = -k*y.

Can someone provide me some hints please?