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Figure 9


Fig. 9. Three Nyquist plots of the system in Eqn 20 are shown for three characteristic values of the dimensionless neural delay, T, assuming that {tau}=0. Delay cannot be handled using the root locus method; thus, we resort to Nyquist's stability criterion (see Franklin et al., 1994). (A) T<1. (B) T=1. (C) T>1. Each plot is constructed by evaluating the transfer function in Eqn 20 along the imaginary axis. Because the open-loop system has no open right-half-plane poles, the closed-loop system is stable if the Nyquist plot does not encircle –1 on the complex plane. As can be seen, this is only possible for the case that (A) T<1, whereas for (B,C) T≥1, there will always be at least two encirclements of –1, and thus at least two right-half-plane poles. Stability can be greatly improved by adding a derivative feedback term, as in Eqn 11, enabling larger values of T. Imag., imaginary.





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