(Solved): 19:28 Files chrome://external-file important steps are skipped by the student. All late submi ...
19:28 Files ? © chrome://external-file important steps are skipped by the student. All late submissions will attract a penalty of 1 point per day from the assessment submission cut-off date, which is always a day after the due date. ACT3701 ASSESSMENT 3 Assessment 3 Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system that has the following characteristic equations. Determine the number of roots of each equation that are in the right-half-plane and on the j
\omega -axis. (a)
s^(3) 25s^(2) 10s 450=0(5) (b)
2s^(4) 10s^(3) 5.5s^(2) 10=0(6) [11 marks] Consider a unity feedback system with the closed-loop transfer function
(Y(s))/(x(s))=(\omega _(n)^(2))/(s^(2) 2\omega _(n)s \omega _(n)^(2))For a unit step input, calculate the following performance indices a)
IAE=\int_0^(\infty ) |e(t)|dt. (4) b)
ITAE=\int_0^(\infty ) |e(t)|dt. (5) c) Calculate the values of
\omega _(n)which minimize IAE and ITAE respectively. Are these values of
\omega _(n)practical? If not, then choose suitable values of
\omega _(n)and determine the corresponding performance indices. (10) Hint: (i) Since damping factor
\zeta =1, the system does not overshoot. Therefore
|e(t)|=e(t)(ii)
\int_0^(\infty ) |e(t)|dt=\lim_(s->0)E(s),and
\int_0^(\infty ) |e(t)|dt=\lim_(s->0)[-(d)/(ds)E(s)][19 marks] [30] --- End of Questions--- 2 19
