Question 11.8.16: 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^{2}(s+1)(s+2)}}
Step-by-Step
The open-loop transfer function is
G(s)H(s)={\frac{K}{s^{2}(s+1)(s+2)}}={\frac{K}{s^{4}+3s^{3}+2s^{2}}}.
The input to and output from MATLAB are included in Program Listing 11.16 and Figure 11E16, respectively.
With reference to the Nyquist criterion, one can observe that the system is unstable since the contours do enclose the (−1, 0) point.
Script File
Program Listing 11.16
>> num = [0 0 0 0 1];
>> den = [1 3 2 0 0];
>> nyquist(num,den)
>> title(‘Nyquist Plot of K /[s²(s+1)(s+2)]’)
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