Answer Happy

Q3. (30% of Assignment 1B mark) 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) P 10 9. 10 The values of w and v 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 + 12.1285 (b) Use the root-locus angle criterion to prove that the desired dominant closed-loop values do not lic 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 ,st21 Ge(s) = K SP: