Multivariable Nyquist Plot

This plotting format contains the same information as the Bode plot. The polar plot is more compact, but the information on the frequency is not shown explicitly. If we do not have a computer, we theoretically could read numbers off a Bode plot to construct the Nyquist plot. The use of Nyquist plots is more common in multiloop or multivariable analyses. A Bode plot, on the... 

Table 16.1 gives a FORTRAN program which generates the multivariable Nyquist plot for the Wood and Berry column. The subroutines given in Chap. 15 are used for manipulating the matrices with complex elements. The subroutines PROCTF and FEEDBC calculate the and complex numbers at each value of frequency. A general process transfer function is used for each of the elements in the matrix that has the form... 

The multivariable Nyquist plots discussed above give one curve. These curves can be quite complex, particularly with high-order systems and with multiple deadtlmes. Loops can appear in the curves, making it difficult sometimes to see if the (— 1,0) point is being encircled. 

Using the guessed value of F and the resulting controller settings, a multivariable Nyquist plot of the scalar function = 1 -i- Det [/ +... 

Check the closedloop stability of the system when these ZN settings are used by making a multivariable Nyquist plot. 

Use a multivariable Nyquist plot to see if the system is closedloop stable. 

The Nyquist stability criterion that we developed in Chap. 13 can be directly applied to multivariable processes. As you should recall, the procedure is based on a complex variable theorem which says that the dilTerence between the number of zeros and poles that a function has inside a dosed contour can be found by plotting the function and looking at the number of times it endrdes the origin. 

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