Question 11.8.15: By applying MATLAB and the Nyquist criterion, determine the ......
By applying MATLAB and the Nyquist criterion, determine the stability of the system whose open-loop transfer function is given by
G(s)H(s)=K G_{o}(s)={\frac{K}{s(s+1)(s+2)}}={\frac{K}{s^{3}+3s^{2}+2s}}
The input to and output from MATLAB are included in Program Listing 11.15 and Figure 11E15.
Script File
Program Listing 11.15
>> num = [0 0 0 1];
>> den = [1 3 2 0];
>> nyquist(num,den)
>> title(‘Nyquist Plot of K/[s(s + 1)(s+2)] ’)
With reference to Figure 11E15, one can observe that the system is stable since the contours do not enclose the (−1, 0) point and are on the left-hand side of this point. In addition, the c.e. of the system is
1+G(s)H(s)=1+{\frac{K}{s^{3}+3s^{2}+2s}}=0
Thus, s^{3}+3s^{2}+2s+K=0.
By the Routh array one can show that the system is stable within the range 0 < K < 6.
