Let the desired poles be conjugate complex. By applying (17) the range for selecting a real part of the desired pole is received
6, and the results from Table V and Table VI shows that in case of the selection of the real poles a longer settling time and much worse IAE of the output is received compared with the PI-control of the same process where controller parameters are received by choosing conjugate complex poles.
Figure 10(a) indicates that [n.sub.p] mainly affects the conjugate complex roots and can be modified to fine-tune the dynamic response of the system.
When the cut-off frequency increases to a certain value, the main pole of the system turns into a pair of conjugate complex roots that move right with the increase of the cut-off frequency.
If the characteristic polynomial has a pair of conjugate complex numbers, the moduli of conjugate complex numbers are less than one.
When a1 increased from [a.sub.*] - [epsilon] to [[alpha].sub.1]* + [epsilon], the Jury stability condition was violated with [f.sub.1] > 0 and [f.sub.2] > 0, so a pair of conjugate complex eigenvalues occur with their moduli equal to one.
(ii) If the equation u(s) = 0 has two conjugate complex
roots ([p.sub.1] = [alpha] + j[omega], [p.sub.2] = [alpha] - j[omega]), we thus have
[a.sub.i] and [a.sub.i+1], [c.sub.i] and [c.sub.i+i] Are Conjugate Complex
where [A.sub.1], [A.sub.2], [B.sub.i] & [[GAMMA].sub.i] = 1, 2: constant coefficients the magnitudes of which is defined in the context of relations (A.10), (A.11), (A.5), and (15) respectively, Q = [square root of (term)] v [c.sub.1]: the absolute value of the conjugate complex characteristic roots, and [theta]: an arc the magnitude of which is given by relation (A.14).
This restriction resulted to the determination of two conjugate complex characteristic roots, ensuring the sinusoidal diachronic evolution of income.
Rovba , on the other hand, considers mixtures of real and conjugate complex
poles, all of order 2, and a value of n such that 2n - 1 - m = 1; making [R.sub.n](g) = 0 if g [element of] [Q.sub.m] [direct sum] [P.sub.1].
After incubation to allow the tacrolimus analog-coated Cr[O.sub.2] particles to scavenge the excess amount of antibody-[beta]-galactosidase conjugates that were not bound to tacrolimus, the Cr[O.sub.2] particles were magnetically separated from the reaction mixture in the vessel and an aliquot of supernatant containing tacrolimus: antibody-[beta]-galactosidase conjugate complexes
was transferred from the reaction vessel to a photometric cuvette containing chlorophenol red-[beta]-D-galactopyranoside (CPRG).