Routh’s array

Routh s array can be written in the form shown in Figure 5.3. In Routh s array Figure 5.3... 

Te.st 1 All eoeffieients are present and have the same sign. Proeeed to Test 2, i.e. Routh s array... 

From Routh s array, marginal stability oeeurs at A" = 70. 

Routh s method is easy to apply and is usually used in preference to the Hurwitz technique. Note that the array can also be expressed in the reverse order, commencing with row. v". 

The results are exact—we do not need to make approximations as we had to with root locus or the Routh array. The magnitude plot is the same as the first order function, but the phase lag increases without bound due to the dead time contribution in the second term. We will see that this is a major contribution to instability. On the Nyquist plot, the G(jco) locus starts at Kp on the real axis and then "spirals" into the origin of the s-plane. 

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