Question 11.8.3: By employing MATLAB, perform the root locus plot of the foll......
By employing MATLAB, perform the root locus plot of the following control system whose open-loop transfer function
G(s)H(s)=K G_{o}(s)=\frac{K(s+1)}{s(s-1)(s^{2}+4s+16)}.
A simple expansion and simplification gives
G_{o}(s)=\frac{s+1}{s^{4}+3s^{2}+12s^{2}-16s}.
Therefore, the input to and output from MATLAB are included in Program Listing 11.3a and Figure 11E3a.
Note that in Figure 11E3a the loci on the right-hand side of the figure have two small parts on the left-hand half of the complex plane, meaning the system with the gains of these small parts are stable. In order to provide a better view of these two small parts, a statement is added to Program Listing 11.3a. The new program is presented as Program Listing 11.3b and the output is included in Figure 11E3b
Script File
Program Listing 11.3a
>> num = [0 0 0 1 1];
>> den = [1 3 12 −16 0];
>> rlocus(num,den,‘k’)
>> title(‘Root Locus Plot of Example 3 Section 11.8’)
Program Listing 11.3b
>> num = [0 0 0 1 1];
>> den = [1 3 12 -16 0];
>> rlocus(num,den,‘k’)
>> axis([−5 5 −10 10]);
>> title(‘Root Locus Plot of Example 3 Section 11.8’)
