# I need guidance -Critically damped servo

Discussion in 'Homework Help' started by D.Vesa, May 21, 2015.

1. ### D.Vesa Thread Starter New Member

May 3, 2015
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Mcc with Pn=3.5kW, Vn=220V, nn=3000rpm, Ra= 1.2Ohm, La=15mH, Jr=0.025kgm2, 2ΔVp=1V, Pmec+Pfe=0.0045Ω2 (Pmec=mecanic losses , Pfe=Iron losses ) , is powered through four-quadrant static convertor with Vdon=0.85V si VIGBon=2.25V from a 230V source , acts a 2000kg trolley through a mecanism with transmission factor 1m/50rpm. The dry friction coefficient between troley and the plan is 0.01.

The requirement is :
Using differential equation I must design a feedback control strategy for a trolley position control system in which there is no output response overshoot and with minimum possible settling time - for a step change in output position demand. I need to analyze the case of a step prescriptions position x = 2m. Analize the dinamic performance of the sistem x=x0sin(ωt). If x0=2m, untill what frequency the dinamic error will be less than 1mm. Analize the sistem if on the trolley acts a disruptive force with step variation of 2000N. What happens if the force varies sinusoidal in time ?

What I have done untill now :

1. I designed the convertor using the equations in simulink . I attached a picture for you to see it. (output voltage is around 220 with small fluctuation )
2. For the Mcc I have a little problem

here are the equations

Va=(Rs+Ra)*Ia+La*(dIa/dt)+e ; e- is electromotor voltage and it's equal to
e=k*phi*omega
Ve=Re*ie+Le*(dIe/dt)
Te=electromagnetic couple
My solving attempt so far:
Pin=I*V => I=3500/220=15,9A
Ve=V-Ra*I-deltaVp=220-(1,2*15,9)-0,5=200,42V
Te=(Ve*I)/(2*pi*n)=(200,42*15,9)/(2*pi*50)=10,14N*m
n=3000/60=50rps

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