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
    2
    0
    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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