# Closed loop Servomechanism problem

1. Jan 11, 2014

### ATRIX

1. The problem statement, all variables and given/known data[/b]

Hey Guys

Firstly thanks for looking, I really appreciate any help or interest with my problem.

The problem is a closed loop feedback system it's unlike any I have come across before.

I have been given the definition which is as follows:-

G(t)^-1 = 2.5 x 10 ^-3 {(1-400k)}D^2+10D+400

i have to prove it with the following information.

I = Inertia of the turbine blade is = 1kg/m
c.ω= viscous Damped rotation (hysteresis) = 10 rad/s Nm
T = Torque motor= 400[e + k d^2θ/dt^2] Nm
e=(θin-θout) = angular position error in rads between the input and output shaft
k.d^2θout/dt^2= defines the additional feedback signal, accelerometer i am guessing

The definition or the answer that we are trying to work it into is in D notation, or operator D. this is where we can replace the derivatives of angular acceleration or position with D
there fore
D = dθ/dt
D^2 = d^2θ/dt^2

2. Relevant equations

general format of second order system

θout/θin = k/(1/ωn^2)D^2+(2ζ/ωn)D+1

this is a general solution

Zeta is a damping coeff of the system

Newton's 2nd law

∑T=∑I.α
3. The attempt at a solution

As for the work i have carried out, is that i am trying to reverse engineer the definition of the system to get the numbers, i can see that the answer is quadratic, D^2 and D and 400. but can not seem to get from the original boundary conditions to there. i have also tried to split the loops up in to two. this did not work for me.

using basic control algebra i have deduced that the accelerometor should e k. d^2θ/dt^2 not
k.d^2θout/dt^2 this i believe is a mistake on my question paper.

thanks for looking. any advice would be welcomed.

Atrix

#### Attached Files:

• ###### servofeedback.docx
File size:
48 KB
Views:
89
2. Jan 11, 2014

### ATRIX

sorry I did not mention that there is as uploaded visual representation to help understanding, many thanks
Alex