Answer Happy

p=8
q=2
w=10.8
The response C(s) of the unity-feedback system shown below to a unit-step input does not meet desired transient specifications and requires a controller. The desired transient specifications for the system are overshoot percentage of approximately 7.5% and settling time of 0.4 seconds (using 2% criterion). plant R(S)+ 1 C(s) s(s+w) (s + v) 10 The values of w and u are given by w = 10 + and v= 50+ where the values of p and q are the two last digits of your student number. For example, if your student number is 12345678, p = 7 and q = 8, therefore w = 10.7 and v= 50.8. (a) Show that the desired dominant closed-loop pole locations should be around s= -10 ±j12.1285 (b) Use the root-locus angle criterion to prove that the desired dominant closed-loop values do not lie on the root-locus of the uncompensated system (c) Using root-locus methods, design a lead-compensator in the form shown below to achieve the desired transient specifications Ge(s) = K S+Z₁ S + Pi