-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 0.5 1 1.5 2 2.5 3 3.5 Figure 1: Rawstep response data Solution 8.8.13 The rst step is to get the data into MATLAB. The MATLAB statements load mtr6stepc t=mtr6stepc(1:500,1);; y=mtr6stepc(1:500,2);; y=y-y(99);; t=t-t(99);; y=y(99:500);; t=t(99:500);; y(1) = 0;; t(1) = 0;; load the data and makesome adjustments so that the response is zero when t =0.Theunadjusted and adjusted time responses are shown in Figures 1 and 2, respectively. The MATLAB statements y(150:402) = mean(y(150:402));; 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 Figure 2: Adjsuted step response data y(145:149) = mean(y(145:149));; y(140:144) = mean(y(140:144));; y(135:139) = mean(y(135:139));; y(130:134) = mean(y(130:134));; y(125:129) = mean(y(125:129));; y(120:124) = mean(y(120:124));; y(115:119) = mean(y(115:119));; y(110:114) = mean(y(110:114));; y(105:109) = mean(y(105:109));; y(100:104) = mean(y(100:104));; y(95:99) = mean(y(95:99));; y(90:94) = mean(y(90:94));; y(85:89) = mean(y(85:89));; y(80:84) = mean(y(80:84));; y(75:79) = mean(y(75:79));; y(70:74) = mean(y(70:74));; y(65:69) = mean(y(65:69));; y(60:64) = mean(y(60:64));; 2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 Figure 3: Smoothed step response y(55:59) = mean(y(55:59));; y(50:54) = mean(y(50:54));; plot(t,y) print -deps sr8813a.eps representacrude smoothing that results in the step response shown in Fig- ure 3. The MATLAB statements A=mean(y(150:402)) s=-3.2 s1 = -12 Kplant = A*s*s1 T=linspace(0,4,402);; g=zpk([],[s s1],Kplant) [yhat T] = step(g,T);; plot(t,y,'k-',T,yhat,'k--') print -deps sr8813d.eps lead to the comparison of step responses shown in Figure 4. The match 3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 Figure 4: Comparison of measured and simulated step response is excellentandthesecond pole appears to be closer to s = ;12 than to s = ;15. The response of the armature voltage is shown in Figure 5. Thus weneed to reduce the gain of K =3:1263:312 = 120:03 byafactor of 27. Thus our model G(s)= 4:46 (s +3:2)(s+12) : appears to be a very good one. 4 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 5 10 15 20 25 30 Figure 5: Armature voltage 5