Question

The system has a steady-state gain of K = 23.8 rad/s/ and a time constant of t = 0.1 seconds. Let us further assume that you are required to design a PD position controller that has an overshoot of less than 5% and a peak time of no more than 0.2 seconds. 1. Using Equations 4 and 5 determine the required natural frequency (wn) and damping ratio (7) that will satisfy the overshoot and rise time requirements of the controller. a. What does the natural frequency of the system quantify? i. It is the frequency at which the system tends of oscillate when continuously subjected to an external harmonic force ii. It quantifies the frequency at which the system tends to oscillate in the absence of any driving force ii. None of the above b. Based on the damping ratio that you have calculated, what category best describes the system? i. Underdamped system ii. Critically damped system iii. Overdamped system

Answer 1

(a) parcend overshoof P.O. lose mp -pal Vi_s2 =lte & T / VT-22 5. fe en (05 - zetu 2 11-22 -ZT 3 :VI-3p² 0.955, tz Vi-3p2 (1-22) 0.9 ; = Ep 2 Damping Zip - 0,687. TE Peake time, to condi- 212 0.25 TE Crui-06872 Natural con frequency = 21.6 Hz frequent wn is the undamped natural It is the frequency at which eystem tends to oscillation in the absence of exodermal force. The in definiteles when there is and amplitucle remains constant with dime. eystem oscillate disturbanu. no

by Settling time e con 2 3 con 1-2 Ze 2 1-246.68733 Charau hnis fic equation of est order ts: 4. ts 4 =0.aas 0.689x216 Resonant frequency on va Q1:6 5.262 Noi of oscilla tons occaning seft & ing time The system wlith in -1.0.67 2 0.6821 튼 TV 2 o.1sf G (s) = k estl Coodh P-control the closed loop asansfer funchia of system is Go): 23.80p oris elekp+238 koa loro oportional gain of controller since the damping nactio <1. the system is uncler damped, so. the decillations is decaying exponentially Exponentiale decay sack 2 {ona