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The block diagram attached is a PI controlled robotic joint system where:

G(s)=Kp+(Ki/s)

P(s)=48500/(s^2+2.89s)

R(s)= joint’s desired angular position

C(s)= joint’s angular position

D(s)= external disturbance

G(s)= PI controller

ess= Steady State Error

My problem:

A) Find the value Ki that will result in ess=5% for a parabolic input.

B) Using this value of Ki find the range of Kp for closed-loop stability.

My solution:

ess=1/Ka=0.05

Ka=lim(s>0) s^2G(s)P(s)=20

G(s)P(s)=((sKp+Ki)/s)(48500/(s^2+2.89s))

=(48500sKp+48500Ki)/(s^3+2.89s^2)

=(48500sKp+48500Ki)/(s^2(s+2.89))

Ka=48500Ki/2.89=20

Ki=20*2.89/48500

Ki=0.0011917

I tried using this Ki value in my Simulink model (other attachment) but the system didn’t have any steady state error, and I could only manage to get steady state error by making Ki = 0.

Also, I didn’t know how to insert a parabolic input into Simulink so I used this instead:

Ramp x Ramp x 0.5 to represent (½)t^2

My questions:

1) Is my parabolic input correct?

2) Is my PI controller set out correctly in my Simulink model? (I wasn’t sure how to model the I component)

3) For this part of the question I’ve been ignoring the disturbance (D(s)), it’s not mentioned in this part, is it ok to ignore?

4) Am I going about finding Ki the right way?

5) What path should I take to get Kp after I have Ki? I’m thinking I need to do a Routh array.

Looking for a little nudge toward the right path.

Thanks for the help,

Sam

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# Homework Help: Steady State Error of a PI Controlled System (parabolic input)

**Physics Forums | Science Articles, Homework Help, Discussion**