Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 603
As noted above, 23 sets of variables a, b,andcsatisfy the requirement. Unit-step response
curves of the system with any of the 23 sets are about the same. The unit-step response curve with
a=4.2, b=2, c=12
is shown in Figure 8–35(a). The maximum overshoot is 18.96%and the settling time is 0.85 sec.
Using these values of a, b,andc,the desired closed-loop poles are located at
s=–4.2_j2, s=–12
Using these closed-loop poles, the denominator of Y(s)/D(s)becomes
or
s^3 +(1+10K)s^2 +10K(a+b)s+10Kab=s^3 +20.4s^2 +122.44s+259.68
s^2 (s+1)+10K(s+a)(s+b)=(s+4.2+j2)(s+4.2-j2)(s+12)
table(k,:) = [a(i) b(j) c(h) m ts]
table =
4.2000 2.0000 12.0000 1.1896 0.8500
4.0000 2.0000 12.0000 1.1881 0.8700
4.0000 2.0000 11.8000 1.1890 0.8900
4.0000 2.0000 11.6000 1.1899 0.9000
3.8000 2.2000 12.0000 1.1883 0.9300
3.8000 2.2000 11.8000 1.1894 0.9400
3.8000 2.0000 12.0000 1.1861 0.8900
3.8000 2.0000 11.8000 1.1872 0.9100
3.8000 2.0000 11.6000 1.1882 0.9300
3.8000 2.0000 11.4000 1.1892 0.9400
3.6000 2.4000 12.0000 1.1893 0.9900
3.6000 2.2000 12.0000 1.1867 0.9600
3.6000 2.2000 11.8000 1.1876 0.9800
3.6000 2.2000 11.6000 1.1886 0.9900
3.6000 2.0000 12.0000 1.1842 0.9200
3.6000 2.0000 11.8000 1.1852 0.9400
3.6000 2.0000 11.6000 1.1861 0.9500
3.6000 2.0000 11.4000 1.1872 0.9700
3.6000 2.0000 11.2000 1.1883 0.9800
3.4000 2.0000 12.0000 1.1820 0.9400
3.4000 2.0000 11.8000 1.1831 0.9600
3.4000 2.0000 11.6000 1.1842 0.9800
3.2000 2.0000 12.0000 1.1797 0.9600
2.0000 2.0000 6.0000 1.2163 1.8900
