CLOSED-LOOP ROLL CONTROL

The pilot model of Sec. 12.2 has been used by Ashkenas (ref. 12.21) to study the handling qualities associated with the closed-loop control of bank angle. This application demonstrates the use of pilot models in analyzing the pilot/aircraft system. Figure 12.16 presents the closed-loop situation. It is assumed that the pilot is functioning in a compensatory fashion to

control external disturbances [represented by %($)] to the vehicle’s bank angle. [Note that this control situation is similar to that of Fig. 12.3b with »i(<) = —*(*)•] In an attempt to achieve the equalization outlined in Sec. 12.2 the pilot adopts a form of describing function that reduces the combined transfer function of the pilot and aircraft as nearly as possible to Kjs. This results in an attempt by the pilot to generate a lead equalization term to cancel the 1 j(TBs + 1) lag present in the aircraft. In addition, if the analysis is restricted to frequencies near the system crossover frequency, it is found that to a reasonable approximation all the dynamics associated with the pilot’s neuromuscular system can be lumped in with the effective time delay as te. This is found to be sufficient for the present application. The forward-loop transfer function is thus of the form

Г(-~) j K»e~T£S(Tvs + }) • A*T*

Ada S(^7KS + 1)

which reduces to

Kve• АфТп
s

if the pilot can generate TL = TR. It is found that human pilots are generally limited to TL < 5 sec because of physiological factors. In addition, as TR is reduced to zero it is found that pilots do not attempt to keep TL equal to TR – It appears that as soon as the phase lag contributed by TR becomes acceptably small the pilot no longer feels the need to compensate for it. Figure 12.17 shows the TL adopted by pilots for a range of TR’s.

In this isolated control situation, it would appear that the pilot rating could depend upon closed-loop system performance, the gain generated by the pilot, Kp, and TL. Since the forward-loop transfer function always appears

to be approximately Kjs, all systems studied will tend to have similar response characteristics. If an experiment is performed wherein TR is varied and the pilot is allowed to select the system gain Аф at each step so as to be optimum in his opinion, then the rating assigned to each configuration should be mainly influenced by the TL required of the pilot. The results of such an experiment (ref. 12.21) are given in Fig. 12.18. Here ДR is the increase in pilot rating associated with TL above the basic rating for the complete vehicle. The rating becomes less favorable as the pilot is required to generate

Fig. 12.18 Effect of TR on pilot rating (from ref. 12.21).

lead (the generation of lead can be thought of as an attempt to anticipate the future input signal).

The optimum gain Аф selected by the pilot for a particular value of TR is assumed to be uniquely related to the pilot gain generated at the crossover frequency, coc. At crossover Y(icoc) • fjA5a(icoc) = 1, and for a particular value of TR, the optimum value of pilot gain, | F(«oc)|opt, is assumed to be unique. Based on these assumptions the gain Аф selected by the pilot can be found from (12.9,4) to be

A =