Question

2. (10 points each) a. Give the system type, then calculate, by hand, the error constants (Kp, K, Ka and steady state error amounts for the following transfer functions b. Use MATLAB to give the step response of each transfer function and verify the estep(0) value you calculated in part a. 12 s+15s G(s) 15 (s2 +20s +10)s3

Answer 1

G(s) = 12/s(s^2 + 5s + 8) type = 1 system kp = lt s rightarrow 0 G(s) = lt s rightarrow 0 12/s(s^2 + 5s + 8) = infinity rightleftarrow C_ss = 1/1 + kp = 0 kv = lt s rightarrow 0 SG(S) = lt s rightarrow 0 12/s(S^2 + 5s + 8) = 12/85 = 1.5 rightleftarrow c_ss = 1/k_8 = 10/15 = 2/3 ka = lt s rightarrow 0 s^2 G(S) = lt s rightarrow 0 s^2 12/s(s^2 + 5s + 8) = 0 rightleftarrow css = 1/ka = infinity type - 1 kp = rightleftarrow ess = 0 kv = 1.5 rightleftarrow ess = 2/3 = 0.667 ka = 0 rightleftarrow ess = infinity G(S) = 15/s^3(s^2 + 20s + 10) type 3 system kp = li s rightarrow 0 G(s) = lt s rightarrow 0 15/s^3(s^2 + 20 s + 10) = infinity rightleftarrow ess = 1/1 + kp = 0