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Problem 6.55PP
In one mode of operation, the autopilot of a Jet transport is used to control altitude. For the 
purpose of designing the altitude portion of the autopilot loop, only the long-period airplane 
dynamics are important. The linearized relationship between altitude and elevator angle for the 
long-period dynamics is
ft /s e ck(s) 20(1 -1- 0.01)
= 77:7 = -S{s) f ( i2 + 0 .0 1 i-l '0 .0 0 2 S ) deg
The autopilot receives from the altimeter an electrical signal proportional to altitude. This signal Is 
compared with a command signal (proportional to the altitude selected by the pilot), and the 
difference provides an error signal. The error signal is processed through compensation, and the 
result is used to command the elevator actuators. A block diagram of this system Is shown in Fig. 
You have been given the task of designing the compensation. Begin by considering a 
proportional control law Dc (s) =K.
F in u r e C o n tro l s v s to m fo r P ro b le m fi FtFt
You have been given the task of designing the compensation. Begin by considering e
proportional control law Dc (s) =K. 
Figure Control system for Problem 6.55
Hm
(a) Use Matlab to draw a Bode plot of the open-loop system for Dc (s) =K =
(b) What value of K would provide a crossover frequency (i.e., where |G | = 1) of 0.16 rad/sec?
(c) For this value of K, would the system be stable If the loop were closed?
(d) What is the PM for this value of K7
(e) Sketch the Nyquist plot of the system, and locate carefully any points where the phase angle 
is 180° or the magnitude is unity.
(f) Use Matlab to plot the root locus with respect to K, and locate the roots for your value of K 
from part (b).
(g) What steady-state error would result if the command was a step change In altitude of 1000 ft? 
For parts (h) and (i), assume a compensator of the fonn
Deis)-
T ps+ l
aroS -h l
(h) Choose the parameters K, TD, and a so that the crossover frequency is 0.16 rad/sec and the 
PM is greater than 50°. Verify your design by superimposing a Bode plot of Dc(s)G(s)/K on top of 
the Bode plot you obtained for part (a), and measure the PM directly.
(i) Use Matlab to plot the root locus with respect to K for the system, including the compensator 
you designed in part (h). Locate the roots for your value of K from part (h).
(j) Altitude autopilots also have a mode in which the rate of climb is sensed directly and 
commanded by the pilot.
(i) Sketch the block diagram for this mode;
(ii) Modiiy the G(s) stated above for the case where the variable to be controlled is the rate of 
altitude change;
(iii) Design Dc (s) so that the system has the same crossover frequency as the altitude hold 
mode and the PM is greater than 50°.
S tep -by-s tep s o lu tio n
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