《Integrated Lateral Controls – An Overview》
○Automated lateral operations of an A/C:
(A) Automatic turn -- To automatically turn the A/C and perform compensation for the turn.
 Two separate tasks are involved: (a) To automatically turn the A/C and
(b) To perform necessary compensation for the turn.
 The first task may be achieved through one of the three intermediate lateral autopilots. The
second task will involve the application of a longitudinal autopilot.
(B) Automatic lateral beam guidance – To guide the A/C heading along some reference beam.
 Require an automatic control system which would guide the aircraft through a given
reference heading provided by local navigational facilities.
 Often, the operation takes place while there is a persisting crosswind. The controller so
designed, must be able to neutralize the effect of the crosswind on the A/C heading.
 This goal may be achieved with the design of a lateral beam follower.
○Common feature of the integrated longitudinal autopilot (ILA) designs:
 Need control of the aircraft heading  and bank angle  .
 A capability provided by one of the three intermediate lateral autopilots designed so far.
==> The automatic lateral control designs will constitute feedback loops that are outside
one of the intermediate lateral autopilots.
 In other word, these systems are to be engaged under the presence of one or several of the
intermediate lateral autopilots discussed thus far.
 Also because that any one of the three intermediate lateral autopilots can be used as the basic
tool for achieving the automatic lateral operations, different designs for a particular automatic
lateral operation may exist.
101
《Integrated Lateral Controller for A Steady Turn》
◎First task: To automatically turn the A/C◎
○Feasible approaches for an A/C to achieve a coordinated turn:
 A turn maneuver may be performed manually by commanding, through the control stick,
(a) a step rcom to a yaw orientation autopilot, or
(b) a pulse com to a roll orientation autopilot
 A turn maneuver may also be performed automatically by providing
(a) a step heading command com directly to the heading autopilot, or
(b) a step heading error to the roll orientation autopilot through a  feedback outer loop.
○Different aspects of the two automatic turn approaches:
(a) The automatic turn maneuver which is executed through the heading autopilot may result in
excessive yaw rate and thus necessitate a yaw rate limiter. On the other hand, the automatic
turn maneuver performed with the roll orientation autopilot may result in excessive roll angle
and thus necessitate a limitation of the roll angle.
.
(b) In a coordinated level turn (right figure), the lateral
L
av= g
r

.
acceleration of the A/C will be
ah= U0
  U 0 r cos  U 0 r
Y
. ah  U 0 

Equivalently, we also have ah  g tan .

--- In an automatic turn with the heading autopilot,
Z
where the maximum yaw rate is fixed by the
limiter, the lateral acceleration of the turn will depend on the flight speed.
--- In an automatic turn with the roll orientation autopilot, where the maximum roll angle is
fixed by the limiter, the lateral acceleration of the turn is independent of the flight speed.
102
◎Second task: Compensation for the turn on the pitch motion◎
○About the turn compensation on the pitch motion:
 Compensation on the AOA of the A/C:
L
W
=
mg
--- In a level turn, the aircraft banked to a roll angle
.
.
 and thus necessitate an increase in A.O.A.
.

mU0

to maintain the lift: L  W cot   W =====>
r
--- This need to increase the AOA is real, and can
q
be automatically compensated by an altitude Y

hold autopilot, or be manually adjusted by the

pilot through a step pitch angle command to the
Z
pitch orientation autopilot.
 Compensation in the pitching rate due to the turn:
--- It is seen from the figure above that, in a steady level turn, a component of the heading rate,
 sin   r tan  , will be picked up by the pitching rate gyro.
q
--- This pitching rate signal due to a steady turn is superficial, it exists only because the gyro
is installed in a non-inertial frame.
--- Nevertheless, because this signal will be picked up by the pitching rate gyro and be feed
back to the pitch orientation autopilot, an erroneous pitch motion will result, unless when
proper counter action is taken.
--- A proper counter action to remedy the problem is to issue a superficial pitch rate command
to neutralize the superficial pitching rate signal picked up by the pitching rate gyro.
--- The required superficial pitch rate command is in the amount of qref  r tan which
can be computed when the roll angle  and the yaw rate r are known.
--- Then, as the inertial reference frame is concerned, q remains zero during the turn.
103
《Integrated Controller for Lateral Beam Guidance》
◎Geometry of lateral beam guidance◎
○ Preliminaries on lateral beam guidance:
 Generally, an A/C is guided by pencil shaped directional RF transmission as heading reference
 Two kinds of transmission are generally employed:
--- See Appendix A for detail
(a) VOF or Omni ==> For mid way course guidance.
(b) Localizer beam ==> For landing glide path guidance.
○Typical geometry of lateral beam guidance:
Typical geometry of a
N
---  : angular error;  0 as shown
lateral beam guidance
--- d : distance off course;  0 as shown

---   ref : interception angle (will be
beam boundary
negative when  and d are  0 .)
--- Geometrical relations:
d
(1) tan  
R
d
   57.3
R
(2) d  U 0 sin(   ref )  U 0

 ref-
  ref
U0
d
C
L
 ref
beam boundary
R
57.3
○Control objective: Nullify the angular error  .
---  will be measured in real-time
 Problem: We have no direct control over  .
--- But we have direct control over the heading angle  .
57.3  1
d  U o (   ref )
--- And from the above relations:  
R
R
 Modify control objective: Eliminate  through control of  .
104
◎Lateral beam follower – Some design guidelines◎
○Generalized block diagram of a lateral beam follower:
 com= 0
 ref
The
Coordinated A/C
coupler com with lateral autopilot   
  1
1U
Rs 0

Geometry
  will be measured in real-time by means of the proper navigational instrument..
 The intermediate lateral autopilot employed will determine the structure of the coupler.
--- In general, any of the three intermediate lateral autopilots can be used for this design.
--- However, since a control of  is the theme of the game here, a heading autopilot will be
the primary candidate for the lateral beam following design.
==> Use of any other intermediate lateral autopilots for the design will require an additional
 feedback inner-loop to provide the heading control capability to the system.
○Coupler structure:
 The coupler must maintain the A/C on course even under the presence of a steady crosswind.
--- A good disturbance rejection capability of the coupler is sought.
--- This will imply an integrator feedback design.
 However, inclusion of an integrator in the coupler will lead to a double pole at s  0 , and causes
these branches of the locus to move into the RHP, leaving no allowable solution.
 Feasible coupler structure:  com ( s )  K 
sv
 ( s), v  1
s
--- A zero at s  v  0 is placed to pull the locus back into the LHP.
--- The value of v will be determined through root locus analysis.
105
◎Lateral beam follower –A design example◎
○Conditions of the example design:
 Assume that a heading autopilot is used for the lateral beam following design
 The coordinated A/C dynamics identified in P.90 of this note is used here.
○ The A/C model – the closed-loop system of the heading autopilot:
 The coordinated A/C (see P.90 of this note):
1.76(s  8.41)( s  0.767)( s  1.97)
 10
 a ( s ),  a ( s ) 
e a ( s )
s( s  4.427)( s  3.179)[ s  1.516  1.086i ]( s  0.017)
s  10
s  0.1


 The heading autopilot design: e ( s )  0.2781.49
[

(
s
)


(
s
)]


(
s
)

com
a
s


 The following relation between  and  is obtained from the dynamics of the coordinated A/C:
 ( s) /  ( s)  4.126s( s  4.49)[ s  1.73  0.745i] /[( s  8.41)( s  0.767)( s  1.97)] ,
 ( s) 
As a result, the closed-loop system thus becomes:
 ( s)
 7.29( s  0.1)( s  8.406)( s  1.967)
 com ( s ) ( s  0.175)( s  4.69)( s  10.26)[ s  0.34  0.34i ][ s  2.02  1.44i ]
--- We have omitted a cancelled pole and zero pair at s  0.767 .

○Block diagram for the lateral beam follower design:
U0
K
R
 7.29( s  v )( s  0.1)( s  8.406)( s  1.967)
s 2 ( s  0.175)( s  4.69)( s  10.26)[ s  0.34  0.34i ][ s  2.02  1.44i ]
--- This diagram is for root locus analysis only; its input and output have been omitted.
106
○Closed-loop system analysis:
 Often, a yaw limiter is installed in the heading autopilot, and the system is nonlinear in nature.
--- However, a root locus analysis for linear systems is still adopted here
--- Because of the non-linearity of the yaw command limiter, the final value of K  can only
be determined through trial on error simulation on the closed-loop system.
3
j
2
Solution at v = 0.13
and K = 0.085 R/U0
1

-10
-9
-8
-7
-6
-5
-4
-3
-2
1
-1
max K = 0.182 R/U0
-1
A 0 locus still applies
-2
2
3
-3
 A cluster of slow CL pole pairs, s  -0.114  0.155i and s  -0.109  0.125i , result; the CL
response will be sluggish.
--- The zeros at s  -0.1 and at s  -v can only suppress one pair of the slow CL poles.
 Because some branches of the locus (colored in pink) destabilizes so fast, we can not increase
K  to improve the solution ==>Note: K  is expressed in terms of the multiple of R /U 0
107
○Closed-loop system for simulations:
 Configurations of the lateral beam guidance systems for closed-loop simulation:
com Limiter
-
s+v
s  e
Coupler
com
rcom Limiter
s+z
- es
z
Equivalent yaw orientation aitopilot
rcom
Coordinated r
1K
K e
A/C with
 e
s

a
x
aileron servo 
Heading autopilot loop
--- Two limiting circuits have been incorporated.
--- The  com (or com ) limiter is used to limit the value of  .
 We have used the geometry:
d  U 0 sin( ref   )  (ref  )  U 0 / 57.3
 This relation is valid, only if ref    0.6 rad .
--- System will not converge when  goes beyond 1 rad
 The pilot must fly the A/C so that the lateral beam follower
is activated when ref    0.6 rad . Then,
    ref    0.6 rad .
.
--- The rcom limiter is installed to limit the peak value of  .
 The yaw rate of the motion will be limited as a result.
 Limiting the yaw rate then reduces the bank angle.
 ref
1U
Rs 0
1 
s
Geometry
  1, so that   
Assuming
com Limiter
0.6
com
e
Slope =1
-0.6
rcom Limiter
0.1
rcom
es
Slope =1
-0.1
108

○Result of the closed-loop system simulations:
250U0
Beam boundary
Station

 (t )
2.5
Initial 
Crosswind
 ref
Case 1

Case 2

Case 3

Case 4

2
2
1
2
0.2U0
0
0
0
Crosswind

0
10
0
0
 In all cases, where the coupler was engaged at a distance equals 250 .times the flight speed ,
the A/C was back on course beyond a range of 150 .times the flight speed.
--- Because the coupler gain is a function of R /U 0 , all distances in relation to this simulation
were expressed in terms of the multiple of the flight speed.
 Because the beam intercept geometry is nonlinear, convergence of the simulation will depend
on the starting values of  and R .
--- For a  that starts from 2 , a converging result exists only if R  300U0 from the t  0 .
 A large R /U 0 implies a large K  , hence a sensitive beam intercept feedback loop.
 If compounded with a large  , the initial drive on  will be large, thereby enhancing
the nonlinear geometry, and prohibits the convergence of the system.
--- The use of  com limiter does allow us to start from R  600U 0 , for the same initial  .
However, the rcom limiter must be turned off, and the bank angle becomes unacceptable.
 For a early engagement of the coupler, the pilot must maneuver the A/C to reduce the initial 
109
◎ More on the simulation result ◎
○The role of the two nonlinear limiting circuits:
 Because of the  com limiter, a  (t )  0.6, t ;
resulted, and a linear beam intercept geometry is
maintained. (The top right figure shows the worst
case of the four cases simulated.)
--- Because the controllability of the system,
 d    U 0 cos( ref   ) ,
will become small for   1 rad .
0.6
0.4
Data from Case 2
(t)
0.2
0
-0.2
-0.4
-0.6
0
0.6
0.4
50
100
150
200
Data from Case 2
0.2
0
(t)
 The rcom limiter, however, limits the bank angle -0.4
-0.6
0
50
100
150
200
within a  30 degree range. (The lower figure)
○ The problem of the varying loop gain with a changing flight distance R :
:
 From the root locus analysis, we have set a design point at KU0 / R  0.085 .
--- If we fix K  at K  0.085R / U0 for a particular speed U 0 and a particular initial
distance R0 ,, then the loop gain of the system, KU0 / R , will vary as R decreases.
--- Because the locus may turn unstable for K U 0 / R  0.182 , the coupler may not work
properly when R  R0  0.085 / 0.182 . We will either reduce K  or turn off the coupler.
 In a landing condition, the localizer station is located at the far end of the run way such that
the A/C would always maintain a safe distance to the station and no instability problem exists.
 During mid course guidance, we may need to disengage the coupler when the A/C is too close
to the Omni station.
-0.2
110