Report of the Second Piloted Aircraft Flight Control System - Acgsc.org

her@ is to lnake the push-rod as stiff as possible, and increase the
damping fp as much as pemissible and then live with these components.
It appears then that in the absence of the abillty to effect arg
'remarkable isprovaments in system components, the stabilloation of our
system with the simultaneous realization of high performance characteristics 4
demands the introduction of additjanal components. We ask ourselves what
distortion of the pole confiwation we mw have for the opm-loop system
would result in desirable characteristics. One particuhrly si@e
configuration is shown in Fig. 13. We leave the two poles due to the
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stick dynamics at the origin ard -8.2, but move the conjugate compleeg
poles due to the aerodynamics either onto the negative-real axis or at
least well out into the left-half plane. Now what happens as we close the
loop and increase the gain? The poles way out to the left are of little
interest to us. The imporLant loci are those stemming from the two poles
on the negative-real axis and close to the origin. At low frequencies,
these poles move as a function of gain in the manner shown in Fig. U.
the addition of a zero at -10 and the moving of all other poles way out
into the left-half plane we have kidded these two poles into thinking we
have a configuration of the farm shown in Fig. 15. It is not until we
reach reasonably large values of loop gain and fairly high frequencies,
that these two poles realize the deception and bend over toward the righthalf
plane. Then if we keep the gain at a value corresponding to these
poles located at the points A and 81, we have a closed-loop system, an
overall aerodynamical system, uhich behaves eesentially as though it had
this pole-zero configuration. The response is characteristized by one
pair of conjugate complex poles at a reasonable damping ratio and a dipole
on the negative real axis. The transient response will be roughly of the
shorn in Fig. 16.
dseenthlly the earns results can be achieved by a slightly different,
and basically more logical approach. Suppose we simply start off by saying
that we want a transient response of the form shown in Fig. 16. Int us
write the overall syatm function, the Saplace transform of this transient
response. We denote this desired closed-loop transfer fundion as ~(8).
horn this ~ (a) we determine the required open-loop transfer function, which
we migbt call p/q, the ratio of two polynomials in s. This opan-loop
tranafer function, ~/q, is related to ~(8) a8 s hom at the bottom of PZig. 17. .
p and q, the ~xumrator and denominator polynomials of the open-loop tranafer
function are readily determined from this relationship. p is simply the
numerator of ~(8). q is simply the denominator of ~(8) minus the numarator,
and can be determined in factored form by a simple graphical subtractian,
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plotting the polpomials for negative-real values of the variable s. A plot
of this form is &awn above the equations in Fig. 17.
Let us review for a moment., We have said that our fundamental
philosophy in the design of the power boost system' should be something
like the following: We first decide on suitable specifications for our