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Hey guys/gals,
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 closedloop 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
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 closedloop 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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