Question

Y(s) s216 s 128 R(s) k (s212 s52) (s 1) (s + 4) (s +8) We desire the dominant roots to have damping ratio equal to 0.5. For the dominant roots, Design the following parameters: Controller gain value Settling time, Percentage Overshoot and Rise time Check by MATLAB the above parameters and include the MATLAB results in your o report

Answer 1

S 6 12 8 S+1) (4) (s+8) (s^+ 125+ Sa) at There two 2e1os ond Cne polos at S2 4J -1, -4, -8 teemina at -64J poles at he at -88J eie 3- nanches e oot-loCu Thene st anch sTonth atpole at me tuminat and blanchese lo Cus eteen The Two buak ot bneak point Aryle m potā Cs) and and dl ong nno Doles Kro),2 W-u Qu N 600, 80, 300 Centwod tAtymp dota i iven The 2SReal Part e pele Poal pant 2en W-u 3

bneall (U) The pont iven whene (s4 Cs2612 8 o R6u 138725+ 3130885 35+ 45+ 20925 t 20 8645+ ds + (S 12?) gives -89 162丁, -6. S-po - S.61 2J ds 2.1 betuisen o Cus and 4 Pont 1-8 Ces C(o- dhaum loCus el ow The

ain t20 The Porst at gan Peal heoment ar Fmeginony meen Pm Tan (60) 4 n Colule red a bl qw Con tao1l aun The P 2.4 a palas 2 433 Jaut 2 2.S384 7.0228

86SS e 2- 215 4.703 46 6 g 2 L433)3. 5384y 1.0228 x 4.? 103 x 7.8816 6SS6X12 31S 21.268S on 4 SS 253 5 3010 St 44 S0 S> AUST ane The S b / and S-42 UT uhch palus Jmi nant Cme Tme ane 1nat SeConds 2.8ST

e 16-3 / p O163 o 872 Gnds 2 4

matlab:

clc;

clear all;

close all;

s=tf('s');

g=(s^2+16*s+128)/((s+1)*(s+4)*(s+8)*(s^2+12*s+52));

k=21.7685;

rlocus(g);

figure

step(feedback(k*g,1));grid

File Edit View Insert Tools Desktop Window Help Root Locus Real Axis (seconds Imaginary Axs (seconds )

Step Response Sysem: untnedt 17 Overshoot 145 At time (seconds): 1.54 System: untitied Serting tme - ands): 3.05 . . Rise time (socondsk 0.008 02 0.1 2.5 Time (seconds)