G
grownupsara
The question shows a feedback loop, input is R(s), output is Y(s), and there is a "black box" containing K/((s+1)(s+2)). It asks you to pick a range of values for K that make the system stable.
I'm really confused about what NCEES lists in its solution: C/R=G/(1+G)=N(s)/D(s), with D(s)=(s+1)(s+2)+K, so K>-2. What are C and R? Do N and D stand for numerator and denominator?
The best I can come up with is that if G=(black box eqn), then for a closed loop (per EERM p.63-11), the denominator is G+1=1+K/((s+1)(s+2))= K/(s^2+3s+2+K). How do they get from here to D(s)=s^2+3s+2+K?
I understand that once you get to that point, K has to be >-2 to prevent the denomintor from decreasing in size and approaching zero.
Thanks in advance for any guidance. This problem is worded so generically that I can't find any specific info to help me online.
I'm really confused about what NCEES lists in its solution: C/R=G/(1+G)=N(s)/D(s), with D(s)=(s+1)(s+2)+K, so K>-2. What are C and R? Do N and D stand for numerator and denominator?
The best I can come up with is that if G=(black box eqn), then for a closed loop (per EERM p.63-11), the denominator is G+1=1+K/((s+1)(s+2))= K/(s^2+3s+2+K). How do they get from here to D(s)=s^2+3s+2+K?
I understand that once you get to that point, K has to be >-2 to prevent the denomintor from decreasing in size and approaching zero.
Thanks in advance for any guidance. This problem is worded so generically that I can't find any specific info to help me online.