Apparatus and methods for generating aircraft control commands using nonlinear feedback gain

Altitude rate commands are generated and fed to an aircraft autopilot to cause the aircraft to transition to a non-level flight path which corresponds to a portion of a calculated flight path profile stored in a flight management computer. When capture of the non-level path is initiated, altitude rate commands are generated in accordance with the equation h.sub.cmd =h.sub.path +k.sub.h .DELTA.h where h.sub.path is the altitude rate of the non-level segment, .DELTA.h is an altitude difference between current aircraft altitude and an altitude point on the non-level segment, and k.sub.h is an altitude error gain which is a nonlinear inverse function of altitude rate error, .DELTA.h, and which is calcuated in accordance with the equation k.sub.h =k.sub.1 -k.sub.2 .vertline..DELTA.h.vertline. where k.sub.1 and k.sub.2 are predetermined constants.

TECHNICAL FIELD 
The present invention relates to a control law for interfacing a 
conventional aircraft autopilot system with an aircraft flight management 
computer, and more particularly to a controller for generating altitude 
rate commands, in accordance with a flight path profile stored in the 
flight management computer, which are fed to the autopilot to capture a 
non-level path segment of the profile. 
BACKGROUND OF THE INVENTION 
The flight systems of modern commercial aircraft are operated extensively 
under the control of one or more computers. For example, the Boeing 
737-300 and 757/767 commercial aircraft utilize a flight management 
computer in which a flight path profile from takeoff to landing may be 
stored. Flight commands such as aircraft heading, altitude, and altitude 
rate are generated within the flight management computer and are fed to an 
autopilot system which manipulates the aircraft flight control surfaces to 
cause the aircraft to fly a path corresponding to the stored flight path 
profile. 
In order for the integrated system of the autopilot system and the flight 
management computer to function properly, the computer must generate 
commands to which the autopilot system is responsive. Integration of the 
autopilot system with a computer requires an interface controller which 
generates commands as a function of a stored flight profile to cause the 
autopilot to respond in the desired manner. 
SUMMARY OF THE INVENTION 
The embodiments of the present invention described more fully hereinafter 
pertain to apparatus and methods for generating control commands which are 
fed to an autopilot system to cause an aircraft to capture a predetermined 
flight path segment, and preferably to capture a non-level flight path 
segment. Altitude rate commands, to which the autopilot is responsive, are 
developed by comparing present aircraft altitude, h.sub.ac, to the 
altitude of the upcoming non-level path segment (climb or descent path, 
h.sub.path, and generating an error signal .DELTA.h. This altitude error 
(.DELTA.h) is scaled by an altitude error gain factor k.sub.h and then 
added to a calculated altitude rate h.sub.path of the upcoding non-level 
segment to generate an altitude rate command h.sub.cmd which is fed to the 
autopilot. 
When the aircraft is outside of a calculated capture range of the non-level 
segment, altitude rate commands are fed to the autopilot to cause the 
aircraft to fly toward the non-level path, and to within a calculated 
capture range. Capture begins when the sum of altitude rate error 
(h.sub.ac -h.sub.path) and the scaled altitude error (.DELTA.h*k.sub.h) 
equal zero. With the initiation of capture, altitude error gain k.sub.h is 
calculated as a function of altitude rate error, .DELTA.h, in accordance 
with the equation k.sub.h =k.sub.max -k.sub.1 
.vertline..DELTA.h.vertline.. The effect of the altitude error gain 
equation is to increase k.sub.h from a predetermined minimum to a 
predetermined maximum, k.sub.max, which is preferably equivalent to the 
altitude hold gain of the autopilot. The nonlinear increase in the gain 
factor k.sub.h due to a decrease in .DELTA.h as the aircraft approaches 
the flight path segment results in a transition to the non-level segment 
which is smooth with very little overshoot or undershoot. 
It is therefore an object of the present invention to provide a control 
system for generating steering commands to transition an aircraft from a 
first path to a second path. 
It is another object to provide a control system for generating steering 
commands to transition an aircraft to a non-level flight path.

DETAILED DESCRIPTION OF THE INVENTION 
Referring to FIG. 1, a preferred embodiment of the present invention 
pertains to a controller 20 which generates vertical steering commands 
which are fed to a conventional aircraft autopilot system 22 to cause 
movement of aircraft elevators 24. This enables the aircraft to capture 
and track a predetermined descent or climb flight path in accordance with 
a flight path profile stored in a conventional flight management computer 
26. A side profile of a portion of the projected flight path is shown in 
FIG. 2 wherein the flight path is made up of a number of non-level 
segments 28 and level segments 29 which in turn are formed by a number of 
navigational points 30. Navigational points 30, which are stored in 
computer 26, are defined in terms of an altitude above a fixed 
geographical location referenced to earth, e.g., latitude/longitude or 
bearing/distance from a known navigational aid. Utilizing navigational 
points 30, flight path segments 28, 29 are calculated in a conventional 
manner to form the flight path profile. The flight path profile provides a 
reference path to which current aircraft location is compared in order to 
generate commands to autopilot 22 to guide aircraft 32 along the projected 
flight path. In particular, controller 20 generates altitude change 
steering commands which are fed to autopilot 22 to fly the aircraft along 
a transition path 31 to intercept and track a non-level segment, e.g. 
descent segment 28 in FIG. 2. The flight path profile also provides course 
information for generating commands to steer the aircraft relative to a 
predetermined course, however this is done in a conventional manner and 
will not be discussed further herein. 
Before proceeding with a discussion of controller 20 and the unique manner 
in which these altitude change steering commands are generated, a better 
understanding of the invention will be provided by a discussion of 
autopilot 22 and flight management computer 26. In a preferred embodiment, 
autopilot 22, which is typified by the Sperry digital flight control 
system currently onboard Boeing 737-300 aircraft, includes an altitude 
hold mode, an airspeed command mode, and a vertical speed control mode. 
Referring to FIG. 3, during conventional operation, inputs to autopilot 22 
are entered by the pilot at an autopilot control panel, indicated at 36, 
located in the aircraft cockpit. In order to command the autopilot to 
cause the aircraft to descend, for example, from 35,000 feet to 30,000 
feet, the pilot selects the desired altitude by (i) rotating a selector 
knob 38 until the desired altitude appears in an altitude window 40, and 
then (ii) engaging a vertical speed button 50. The aircraft is commanded 
to descend to the desired altitude by rotation of a thumbwheel switch 46 
until a desired vertical speed, also referred to as an altitude rate h, 
appears in a vertical speed window 48. The autopilot generates the 
necessary internal commands to cause the aircraft to descend at the 
selected vertical speed. Autopilot 22 includes an autothrottle function 
which moves the engine control throttle to an appropriate location so that 
a selected airspeed is maintained along the non-level segment. On 
approaching the selected altitude displayed at window 40, the autopilot 
generates the necessary commands for transitioning the aircraft from a 
non-level condition to level flight. These commands for capturing and 
tracking the selected altitude are generated in accordance with 
conventional altitude acquire/hold control laws present in the autopilot 
system. 
Conventional operation of autopilot system 22 is further illustrated in 
reference to FIG. 4 where command signal h.sub.sel, which is 
representative of the altitude rate selected by the pilot at thumbwheel 
46, is fed to a low pass filter 50 which removes high frequency transient 
signals. From filter 50 the signal is fed to an altitude rate feedback 
summing junction 52 which subtracts the current altitude rate of the 
aircraft from the altitude rate selected at thumbwheel 46 to generate an 
altitude rate error signal. This error signal is integrated and amplified 
at an integrator and gain amplifier 54 to generate an aircraft pitch angle 
command. The pitch angle command is fed to a pitch angle summing junction 
58 where signals representing the current pitch angle of the aircraft are 
subtracted from the pitch angle signal to generate a pitch angle error 
signal. The pitch angle error signal is fed to a gain amplifier 60 where 
the signal is scaled by a selected gain in accordance with a conventional 
gain function. 
Signals output from the gain amplifier 60 are fed in the form of elevator 
commands via filters 61 to an elevator servo 62 which causes the elevator 
to deflect in accordance with the received commands thereby producing a 
change in pitch attitude of the aircraft. During this change in pitch 
attitude, (1) current aircraft pitch angle is sensed and fed back to 
summing junction 58 to generate the pitch angle error signal, and (2) 
current aircraft altitude rate h.sub.ac is sensed and fed back to summing 
junction 52 where altitude rate error signals are generated. Thus, a 
selected altitude rate h.sub.sel entered at thumbwheel 46 produces a 
corresponding change in aircraft pitch angle. 
Having described the operation of a conventional autopilot system, a 
further understanding of the present invention will be obtained by a 
discussion of conventional flight management computer 26 and its 
operation. Computer 26 is a programmable digital computer which stores 
information relating to locations of known navigational aids, selected 
geographical reference points, and waypoints. In order to establish a 
flight path profile, selected navigational aids, geographical references 
and waypoints which correspond to the desired route of flight are 
retrieved from computer 26. By assigning a discrete altitude to each of 
these selected navigational aids, geographical references and waypoints 
along the route of flight, navigational points 30 are generated. By 
connecting each of these navigational points 30, a number of level and 
non-level path segments are generated which form the flight path profile. 
Navigation of the aircraft is accomplished by comparing the current 
location of the aircraft with the computed profile and making corrections 
to the aircraft location based upon a difference between the current 
location and the computed profile. These corrections may be made by the 
aircraft pilot when the flight path profile is displayed visually, or by 
the autopilot system if the computer system and autopilot are properly 
integrated. 
Having completed a description of the conventional components of the 
autopilot 22 and flight management computer 26, a description of 
controller 20 and its operation in accordance with the present invention 
is provided. Although controller 20 is described herein as a computer 
based system separate from flight management computer 26, in the preferred 
embodiment, controller 20 is a part of flight management computer 26. In 
the preferred embodiment, controller 20 generates altitude rate commands 
for transitioning the aircraft (1) from a level flight condition to an 
non-level flight condition, or (2) from a first non-level flight condition 
to a second non-level flight condition, e.g. from a lower altitude rate to 
a higher altitude rate. Transition to a level flight condition and 
tracking a level flight path, however, is controlled by conventional 
control laws which function within the autopilot 22 as discussed 
previously. 
The altitude rate commands generated in accordance with the present 
invention correspond to a flight path profile stored in computer 26. 
Controller 20 is activated by engaging a VNAV button 68 (FIG. 3) on the 
autopilot control panel 36. Although the present invention retains the 
capability to manually select a vertical speed at thumbwheel 46 to 
transition to a non-level flight condition in a manner described 
previously, the generation of altitude rate commands to cause the aircraft 
to capture and track a non-level flight path corresponding to a stored 
flight path profile is unique to the present invention. 
To generate altitude rate commands which cause the autopilot to fly the 
aircraft in accordance with the stored profile, reference is made to FIG. 
5 where there is shown an aircraft 69, and a portion of a flight path 
profile including level segment 29 extending between navigational points 
72, 74, and descent segment 28 extending between navigational points 74, 
78. For ease of explanation, the intersection of level segment 29 and 
non-level segment 28 is shown to occur at navigational point 74, however, 
the level and non-level segments may intersect at locations other than 
navigational points. Descent segment 28 is defined by a characteristic 
altitude descent rate h.sub.path, as well as by a number of points along 
segment 28, each of which represents a separate descent path altitude, 
h.sub.path. In FIG. 5, aircraft 69 is flying a path corresponding to level 
segment 29 which is represented by an aircraft altitude, h.sub.ac, and an 
aircraft altitude rate h.sub.ac. When the aircraft is in level flight, the 
aircraft altitude rate, h.sub.ac, is equal to zero. In the present 
example, the aircraft is approaching descent segment 28. Transition to the 
descent segment 28 will be complete when (1) the difference .DELTA.h 
between current aircraft altitude, h.sub.ac, and the altitude, h.sub.path, 
of descent path 28 equals approximately zero, and (2) the difference 
.DELTA.h between current aircraft altitude rate, h.sub.ac, and the 
altitude rate h.sub.path of descent segment 28 also equals approximately 
zero. The present invention operates in a manner that values of .DELTA.h 
and .DELTA.h are constantly calculated beginning at a predetermined 
distance from navigation point 74 along path segment 29. Controller 20 
functions so that altitude rate commands are generated which cause the 
aircraft to fly a transition path which drives the values .DELTA.h and 
.DELTA.h toward zero. 
Transition from level flight path 29 to descent path 28 begins when a 
capture equation .DELTA.h+k.sub.h .DELTA.h=0 is satisfied, where 
.DELTA.h=h.sub.path -h.sub.ac and .DELTA.h=h.sub.path -h.sub.ac. In 
general, the capture equation is satisfied whenever either (1) the 
quantity .DELTA.h+k.sub.h .DELTA.h changes from a positive value to a 
negative value when the quantity (h.sub.path -h.sub.ac) is positive, i.e. 
when the non-level segment is captured from below as in FIG. 5, or (2) the 
quantity .DELTA.h+k.sub.h .DELTA.h changes from a negative value to a 
positive value when the quantity (h.sub.path -h.sub.ac) is negative, i.e. 
capture from above. The altitude rate, h.sub.path, of descent segment 29 
is computed as a function of flight path angle .gamma. in a manner to be 
discussed later. However, in order to calculate an altitude error .DELTA.h 
between aircraft altitude h.sub.ac and descent path altitude h.sub.path, 
the altitude of an extension segment 28' of descent path 28 is calculated 
as a function of the distance of the aircraft from a navigational point on 
the descent segment 28, e.g. navigational point 74. Extension segment 28' 
extends upwardly and rearwardly from descent path 28 to provide a 
reference for generating an altitude error signal in advance of aircraft 
69 reaching descent path 28. As aircraft 69 approaches navigational point 
74, continuous updates of .DELTA.h as a function of a horizontal distance 
d between aircraft 69 and navigational point 74 are available. Continuous 
updates of .DELTA.h are also available by comparing current aircraft 
altitude rate, which is a conventional measurement, to the calculated 
altitude rate h.sub.path of segment 28. 
Once capture begins, i.e. the equation .DELTA.h+k.sub.h .DELTA.h=0 is 
satisfied, altitude rate commands h.sub.cmd are generated by controller 20 
and fed to autopilot 22 in a manner to cause the aircraft to smoothly 
transition the aircraft to the descent path 28. These commands are 
generated in accordance with the equation h.sub.cmd =h.sub.path +k.sub.h 
.DELTA.h where k.sub.h is a gain factor which increases as .DELTA.h 
decreases. Gain factor k.sub.h is calculated in accordance with the 
equation k.sub.h =k.sub.max -k.sub.1 .vertline..DELTA.h.vertline., where 
k.sub.max constitutes a maximum gain which is preferably equal to a 
tracking gain of the altitude hold function of autopilot 22, 
.vertline..DELTA.h.vertline. is the absolute value of the quantity 
(h.sub.path -h.sub.ac), and k.sub.1 is a selected constant. K.sub.max and 
k.sub.1 are dependent upon the type of aircraft, however in a preferred 
embodiment of the present invention wherein the Sperry autopilot is 
utilized aboard a Boeing 737 aircraft, k.sub.max =0.14 and k.sub.1 =0.001. 
During capture, the gain equation k.sub.h =k.sub.max -k.sub.1 
.vertline..DELTA.h.vertline. operates in a manner that during the initial 
portion of capture when .DELTA.h is relatively large, feedback gain 
k.sub.h is relatively small; however, as the aircraft altitude rate 
approaches the altitude rate of the non-level path and .DELTA.h decreases, 
k.sub.h becomes progressively closer to the maximum feedback gain value of 
k.sub.max. This results in a gain factor which is calculated so that 
values of k.sub.h increase, but do not decrease, as the aircraft 
approaches the non-level segment. A closer look at the altitude rate 
command equation, h.sub.cmd =h.sub.path +k.sub.h .DELTA.h, reveals that 
since h.sub.path remains constant for each non-level segment, the change 
in h.sub.cmd as the aircraft approaches the non-level segment is a 
function of the term k.sub.h .DELTA.h. The relationships of altitude error 
.DELTA.h and altitude rate command h.sub.cmd as a function of time during 
aircraft transition from a level segment to a descent segment is shown 
graphically in FIG. 6. It can be seen in FIG. 6 that upon initiation of 
capture, altitude error .DELTA.h is quite large, while altitude rate 
command is zero because of the capture equation being satisfied. However, 
when altitude rate command values are generated, the aircraft altitude 
rate h.sub.ac gradually increases in a negative direction as h.sub.cmd 
approaches h.sub.path and altitude error .DELTA.h is driven toward zero. 
It should be appreciated that term k.sub.h .DELTA.h regulates the amount of 
elevator deflection as a function of .DELTA.h and the gain factor 
equation. The gain factor k.sub.h is relatively small when aircraft 
altitude error .DELTA.h is large so as to initiate a gradual transition to 
the non-level path segment. However, as the altitude error .DELTA.h 
decreases as the aircraft approaches the non-level path segment, the 
increasing value of altitude error gain k.sub.h approximately balances the 
decreasing altitude error thereby resulting in a smooth, approximately 
constant normal acceleration (g) transition to the non-level flight path. 
Although discussion of the present invention has been limited to capture of 
a non-level path segment from a path segment which intersects the 
non-level segment, the aircraft may operate in an airmass mode where the 
aircraft is flying a path which is not part of the flight path profile and 
does not intersect the non-level path segment. In this case, it cannot be 
assumed that the aircraft flight path will be in a direction which will 
bring the aircraft within the capture limits of the non-level segment to 
satisfy the capture equation h+k.sub.h .DELTA.h=0. Therefore, if it is 
desired to transition to the non-level segment portion of a programmed 
flight path profile while in the airmass mode, engagement of VNAV button 
68 causes predetermined altitude rate commands to be fed to autopilot 22 
to cause the aircraft to fly in a direction toward the non-level segment. 
For example, if it is determined that path 28 (FIG. 5) is below aircraft 
69, then altitude rate commands are generated which will cause the 
aircraft to descend at a faster predetermined rate than h.sub.path of 
segment 28. On the other hand, if it is determined that the path 28 is 
located above the aircraft, altitude rate commands are generated which 
cause the aircraft to descend at a predetermined rate slower than 
h.sub.path. Once the capture equation is satisfied, however, transition to 
the non-level segment is initiated in accordance with the altitude rate 
command equation h.sub.cmd =h.sub.path +k.sub.h .DELTA.h in a manner 
discussed previously. 
A further understanding of the present invention is provided by referring 
to the flow chart in FIG. 7A together with the flight path profile diagram 
in FIG. 5. In order to begin capture within a reasonable distance of the 
descent path 28, calculation of .DELTA.h, .DELTA.h is initiated when the 
horizontal distance d (FIG. 5) between the aircraft and navigational point 
74 satisfies the relationship d&lt;1.5/k.sub.min * GSP.sub.ac where 
GSP.sub.ac =the groundspeed of the aircraft in feet per second and 
k.sub.min =a selected minimum value of feedback gain, which in the 
preferred embodiment is a value of 0.06. The distance d is calculated in a 
conventional manner at block 87 (FIG. 7A). If it is determined that 
d&lt;1.5/k.sub.min * GSP at decision block 88, values of h.sub.path and 
h.sub.path are calculated for path extension 28' at block 90. Path 
altitude rate h.sub.path is computed by the equation h.sub.path =GSP * 
tangent .gamma., whereas path altitude is calculated by the equation 
h.sub.path =h.sub.nav -d * tangent .gamma., where GSP=aircraft current 
groundspeed in feed per second, d is the horizontal distance between the 
aircraft 69 and a navigational point on the non-level segment, e.g. 
navigational point 74, h.sub.nav is the altitude of navigational point 74, 
and .gamma. is the flight path angle of descent segment 28 and which is 
computed in a conventional manner. 
For example, assume that the aircraft is at point A in FIG. 5 at an 
altitude of 30,000 feet which also happens to be the altitude of 
navigational point 74, a distance of 14,000 feet from navigational point 
74, aircraft groundspeed is 600 feet per second, and the flight path 
descent angle .gamma. of segment 28 is -3.degree.. The equation 
d&lt;1.5/k.sub.min * GSP is satisfied for a value of d of less than 15,000. 
Therefore, assuming that distance d=14,000 feet at point A, 
.DELTA.h=h.sub.path -h.sub.ac =[30,000-14,000 * 
tan(-3.degree.)]-30,000=734 feet. The h.sub.path of descent path 28 equals 
600 * tan(-3.degree.)=-31.45 feet per second. This value of h.sub.path is 
a constant and only calculated once for each non-level segment. 
As the aircraft approaches the non-level segment, values of .DELTA.h and 
.DELTA.h are calculated at block 94. A value of k.sub.h is calculated at 
block 95 in accordance with the feedback gain equation k.sub.h =k.sub.1 
-k.sub.2 .vertline..DELTA.h.vertline.. Arrival at a capture point where 
the aircraft is caused to transition to the non-level path is determined 
at decision block 100 when the capture equation .DELTA.h+k.sub.h 
.DELTA.h=0 is satisfied. In the present example, capture occurs when 
.DELTA.h=288 feet. This can be shown mathematically by solving for 
.DELTA.h in the capture equation as follows: (h.sub.path 
-h.sub.ac)+K.sub.h (h.sub.path -h.sub.ac)=0, or by substitution 
(-31.45-0)+K.sub.h .DELTA.h=0. Since K.sub.h =K.sub.max -K.sub.1 
.vertline..DELTA.h.vertline. then K.sub.h =0.14-0.001 * 
.vertline.31.45-0.vertline.=0.10855. Substituting this value of K.sub.h 
into the capture equation, .DELTA.h=288 feet at capture. This occurs at a 
distance d from navigation point 74 of 
##EQU1## 
When d=5495 feet, transition to the descent segment 28 is effected by 
setting k.sub.h =k.sub.min at block 102 (FIG. 7A) and calculating 
h.sub.cmd at block 104. The value of h.sub.cmd is then fed to the 
autopilot 22 to cause a change in aircraft pitch angle which in turn 
causes a change in altitude rate error .DELTA.h which is calculated at 
block 106. In order to generate an increasing feedback gain, k.sub.h is 
updated at block 108, fed back to the h.sub.cmd equation at block 104 and 
a new h.sub.cmd is generated which is fed to the autopilot 22. As the 
aircraft transitions to the descent path 28 and .DELTA.h decreases to 
zero, k.sub.h increases to k.sub.max. 
As discussed previously, if the aircraft is flying a programmed path which 
intersects the non-level segment, calculated values of .DELTA.h and 
.DELTA.h will decrease as the aircraft approaches the non-level segments 
and the capture equation will be satisfied. On the other hand, if the 
determination is made at decision block 92 that the aircraft is flying in 
an airmass mode along a path which does not intersect with the non-level 
segment, then the appropriate commands are generated as discussed 
previously at block 93 to cause the aircraft to fly toward the non-level 
segment until the capture equation is satisfied, and capture is initiated. 
During transition to a non-level segment, the aircraft 69 may fly within 
the capture range of a succeeding non-level segment as illustrated in FIG. 
8. This typically results when the current descent segment, e.g. descent 
segment 28, is relatively short. Therefore, to fly a transition path which 
smoothly intercepts the succeeding segment, e.g. descent segment 28", 
capture of the succeeding descent segment 28" occurs when the capture 
equation for that segment is satisfied. To prepare for a transition to a 
descent segment 28" which is along a subsequent portion of the flight 
profile and which is defined by navigational points 78, 112, a 
determination is made at block 116 of the flow chart (FIG. 7B) whether the 
maximum range equation, d&lt;1.5/k.sub.min * GSP, is satisfied with respect 
to a distance d2 between the aircraft and navigational point on descent 
segment 28", e.g. navigational point 78. When the relationship is 
satisfied, values of .DELTA.h.sub.2, .DELTA.h.sub.2 are calculated at 
block 116 in a manner discussed previously and a determination is made at 
decision block 118 whether the capture equation .DELTA.h.sub.2 +k.sub.h 
.DELTA.h.sub.2 =0 has been satisfied, where k.sub.h =the current feedback 
gain calculated for the transition to descent segment 28. If the capture 
equation is satisfied, then the aircraft occupies a location within the 
capture criteria of descent segment 28". 
Upon satisfying the capture equation for descent segment 28", k.sub.h is 
reset at block 120 to a value of k.sub.h that satisfies the capture 
equation. A new value of h.sub.cmd2 is calculated at block 122 and then 
fed to autopilot 22 to initiate transition to descent segment 28". As 
aircraft altitude and altitude rate changes in response to h.sub.cmd2, 
updated values of .DELTA.h, .DELTA.h and k.sub.h2 are fed back to 
h.sub.cmd at block 122 to generate an updated altitude rate command. 
Integration of controller 20 and autopilot 22 is further described with 
reference to the simplified block diagram of FIG. 9 where incoming values 
of h.sub.ac, h.sub.path, hhd ac and h.sub.path are processed. If the 
aircraft is in a path mode, path tracking continues until the capture 
equation is satisfied. On the other hand, if the aircraft is in an airmass 
mode, predetermined altitude rate commands are generated to bring the 
aircraft within capture range. To limit acceleration normal to the 
aircraft, a generated h.sub.cmd is fed through a conventional acceleration 
limiter 130 which determines the amount of aircraft acceleration which the 
generated h.sub.cmd will produce, and reduces that h.sub.cmd if the 
resulting acceleration value will exceed 1 g.+-.0.1 g. If not limited, a 
generated altitude rate command h.sub.cmd may cause aircraft normal 
acceleration well in excess of 1 g. A situation likely to generate normal 
acceleration in excess of 1 g.+-.0.1 g is shown in FIG. 10 where the VNAV 
button 68 (FIG. 9) was not engaged until after aircraft 69 had passed 
navigation point 74. In the present example, the generated h.sub.cmd will 
be quite large due to the large gain k.sub.h which began increasing when 
the capture equation was satisfied at point B. Therefore to provide for a 
smooth transition to the descent path 28, the generated h.sub.cmd is 
limited to a command which produces an acceleration during transition of 
1.1 g. The resulting h.sub.cmd is fed via lead/lag filter 132 (FIG. 9) to 
compensate for any lag. The generated h.sub.cmd signal is then fed to the 
autopilot 22 which responds to the h.sub.cmd signal in the same manner as 
described previously with reference to an h.sub.cmd signal generated by a 
manual input at thumbwheel 46. 
In the embodiment discussed herein, the operation of controller 20 has been 
described with reference to a transition to a descent path, however it 
should be appreciated that the present invention also may be used to 
transition to a flight climb path.