Flight Control Systems and Autopilots
Brian Jewell
Department of Engineering, Calvin College
Engineering 315 Final Paper
Professor Ribeiro
Abstract: Autopilot systems have been crucial to
flight control for decades and have been making
flight easier, safer, and more efficient. However,
these autopilot systems are complex devices that
require precise control and stability. These
systems usually include a form of digital control
systems to allow for easier implementation. One
example, the Beaver Autopilot system, uses an
inner, outer loop system to maintain control while
simpler systems often only require something as
simple as a PID controller to keep the aircraft
stable.
1. Introduction
Since the creation of the first aircraft, the
ability for people to travel large distances in
relatively short periods of time has drastically
increased. However, in the beginning of the
airplane age, traveling on these craft was difficult
as there are many components of air travel and
controlling these components can be an extremely
difficult task for a pilot. In modern aircraft, there
are simply too many things for the pilot to control
them all so some form of automation must be
done. Also, long air trips can cause problems for
the pilots. While the plane is traveling along the
same trajectory, flying can and does become a
rather monotonous job for the pilot and the pilot
runs a higher risk of falling asleep or suffering
from a reduced response time. For these reasons,
autopilot systems have become a blessing to the
aerospace industry.
However, these autopilot systems are not
simple systems. They require complex control
systems with robust measuring equipment. The
scope of this paper is to give an overview of
autopilot systems (with a description of digital
controls), to examine the Beaver Autopilot System,
and to explore a simple flight control example.
2. History
The earliest form of autopilots have been
in existence for decades. The first systems were
created an implemented about ten years after the
Wright Brothers flew the very first airplane: the
Kitty Hawk. These earlier systems were simply a
gyroscope that gave the plane a smoother flight
path. The only control that these systems gave was
in the altitude and pitch. They kept the plane from
flying with its nose pointed down and from flying
crooked.
Around the time of Second World War,
the very first fully functional autopilot systems
were designed and tested. These earlier systems
had the capability to keep the flight path level as
well as launch and land the aircraft. This
revolutionary system, however, was not a simple
task and it was prone to failure. The systems
would often break down and crash the plane (by
making the plane point straight down as opposed
to straight forward. To keep the systems operating
properly, the plane required a crew that was more
than twice as large as the original autopilot-less
planes. This caused problems because it took far
more work to keep the autopilot working than it
did to actually fly the plane without such a device.
For this reason, the autopilot was not used very
often for many years. It wasn’t until the 1960’s
that the device really took off (to use an atrocious
pun). At this point, more sophisticated systems
were being introduced and a new form of flight
control was in the works: a computer controlled
flight. This technique called “fly by wire” didn’t
become a standard until closer to the 80s but it had
its beginnings in the late 60s.
The basic concept of the “fly by wire”
systems is digital control systems. To understand
this form of autopilot a brief description of digital
control systems must be discussed.
3. Digital Control Systems
In a typical control system, the equipment
to measure and control signals can be extremely
complicated and can require enormous levels of
sophistication. However, if it were possible to use
a computer to control the systems, a simple “off
the counter” processor could be able to handle
complex control systems. For example, a system
that requires complicated mathematical algorithms
for control could simply digitize the signal and
send it to a processor to take care of the
calculations. The processor (usually called a
“minicomputer”) is usually inexpensive and
relatively easy to implement. The control system
using these sorts of devices is shown below in
Figure 1: Digital Control System Block Diagram.
Figure 1: Digital Control System Block Diagram
In this system, the digital computer reads in the
digital signals from the feedback loop and the
input and it sends them to the D/A converter. This
converter takes the digital values from the
computer and converts the signals into a usable
value for the actuator and process. The signals are
then sent via the feedback loop through the
measurement sensors until it reaches the analog to
digital convert. This portion takes the measured
value and converts it into a binary digital signal
that can be read by the computer.
This digitizing is where the real challenge
enters into the picture. Since computers cannot
read the same kind of signals that an analog device
can, some method of transforming the analog data
to readable digital data must be introduced. This is
done through a method called sampling. A simple
circuit is set up with a switch (shown below in
Figure 2: Switch Digitizer). The switch samples
the value of the signal at regular intervals.
like function. An example of this is shown below
in Figure 3: Discrete Signal.
Figure 3: Discrete Signal
As can be seen, the resulting function is no longer
a smooth signal but it is a series of step functions
that represent the original signal.
To deal with these functions, the zTransform must be used. The z-Transform is an
extension of the LaPlace transform and is of the
following form: Z = esT where s is the value from
the LaPlace transform and T is the period of the
sampler (how many seconds between samples). In
the z-Plane, there are several methods of stability
analysis. For example, a sampled system is stable
if all of the poles of the closed loop transfer
function T(z) lie within the unit circuit of the zplane.
These systems can readily be constructed
in MATLAB. The function can be defined as it
would in any transfer function however the
sampling time is also included (so the definition is
as follows: sys=tf(num,den,Ts) where Ts is the
sampling time). The systems can be converted
from continuous to digital and back again using the
c2d and d2c commands. Below, in Figure 4:
Discrete Step Response the following MATLAB
code was entered:
>> num=[1];den=[1 1 0];
>> sysc=tf(num,den);
>> sysd=c2d(sysc,1,'zoh');
>> sys=feedback(sysd,[1]);
>> T=[0:1:20];step(sys,T)
This code yields the following graph:
Figure 2: Switch Digitizer
These samples must be at a high enough frequency
to accurately represent the input signal. This
process takes the signal and breaks it up into a step
Figure 4: Discrete Step Response
As can be seen by the above plot, the digital signal
is no longer a smooth curve. Depending on the
sampling rate (in this case, once every second) the
value is measured and then held constant until the
next value is measured. For a digital control
system, this value is converted into a binary
number that is then fed into the minicomputer for
analysis.
This sort of system is extremely beneficial
to the aviation industry. With a digital control
system, the autopilots can have a much more
precise control of the flight path of the aircraft.
Rather than feed the controlled signal (such as
altitude or yaw) through a complex process (which
would be extremely difficult to design), the signal
can be converted to a digital signal and sent to the
minicomputer. In the minicomputer, the signal can
be operated on with a higher level of ease because
the computer can directly run the algorithms on the
digital numbers. This method can yield a higher
quality control system for the aircraft. Although it
does require more circuitry (the minicomputer) it
is usually smaller and easier to implement backup
systems.
With this general understanding of digital
control systems, the Beaver Autopilot System is
the focus of the rest of this paper. This digital
control system overview will help understand
some of the mystery of the proprietary (and
therefore undisclosed) portions of the Beaver
system.
guidance and control. The guidance function of an
auto-pilot determines the speed and the course to
be followed by the craft. This is done by
measuring the current actual values and comparing
them to some reference system. The control
function is the function that takes the data from the
guidance system and applies the proper
corrections. For example, if the guidance says that
the altitude of the aircraft is 200m too high, the
control function would move the wing flaps to
bring the craft back down to the appropriate level.
The control does not usually contain any sort of
measuring devices as this function is delegated
entirely to the guidance function. The guidance
loop acts as a commander to the control loop and
the control loop commands the physical movement
and response of the aircraft. As is evident, it is
desirable for these control systems to have a fast
and stable response. They must also be able to
withstand any disturbances from the surrounding
environment. This is extremely important because,
if a disturbance caused a critical control system to
become unstable, the autopilot would cease to
function and possibly put the lives of the
passengers at risk.
The best way to describe the two functions
is to think of them as two interrelated loops. The
control loop is the inner loop as it is controlled by
the outer loop guidance system. This is best
shown in Figure 5: Basic Block Diagram of
Autopilot.
4. Beaver Autopilot System
The Beaver autopilot document that is
used for this report entitled “A Simulink Toolbox
for Flight Dynamics and Control Analysis” and is
written by Marc Rauw. This document describes
the Beaver system in great detail and discusses its
implementation in the Flight Dynamic Control
toolbox for SIMULINK. However, since this
toolbox was not written by the SIMULINK people,
the standard SIMULINK package does not contain
this toolbox.
Therefore, for any attempted
simulations, regular SIMULINK will be utilized
and any unknown functions will be estimated as
best as is capable by this author.
4.1 Functions
The functions of an autopilot system can
be broken down into two major categories:
Figure 1: Basic Block Diagram of Beaver Autopilot
These two controllers (guidance and control)
control two major areas of the flight path of the
aircraft: Longitudinal and Latitudinal direction.
The Longitudinal Mode is discussed below. The
Latitudinal mode is of a similar format with
slightly different constants and different control
blocks.
Figure 6: Block Diagram of Longitudinal Mode
4.1.1 Longitudinal Mode Overview
This portion of the auto-pilot controls the
pitch angle and the altitude of the aircraft. The
complete block diagram for this portion of the
autopilot is shown above in Figure 6: Block
Diagram of Longitudinal Mode. As can be seen by
the above diagram, there are several components
that make up this portion. The main three blocks
of the system are the controllers of this function.
They take the values from the outer loops which
pass through constants and integrators and output
the appropriate controls for the aircraft. The input
signal Href is the current altitude as measured from
the guidance systems. This value then is taken
with the control’s new altitude as well as the pitch
angle (θ) and fed into the control blocks of the
diagram. It should be noted that the gains shown
in the feedback loops of the system are all variable
and depend on the velocity of the aircraft. This
happens because the control to the aircraft will
change as the speed does. Wind resistance and
other factors contribute to this.
The final portion of the longitudinal mode
of the aircraft is the Approach mode. It should be
noted that the Glideslope device is a unique device
to the Beaver autopilot mode. This portion of the
control system is a feedback loop from the Hdot
output (from Figure 6) to the input Hdotref signal.
The glideslope receiver is an on-board
measurement device that interacts with a
transmitter on the airport runway. This system is
an extra feedback loop that has more control over
the descent of the aircraft. To properly operate,
the distance to the runway is calculated using
Distance Measurement Equipment (DME).
However, this equipment doesn’t often work well
with autopilot modules because of hardware
limitations. Therefore, a different approach must
be used. The three dimensional distance to the
runway is calculated using the following equation.
In this equation, R is the three dimensional
distance to the runway, Href is the height above
the runway, and γgs is the reference flight path
angle or, the angle the plane makes when flying
along the nominal path. Generally, a radio
altimeter is used to determine the value of Href.
During a glideslope approach, there are
two different modes of operation. The first is the
“glideslope armed mode. As the authors of the
Beaver document say: “This phase is engaged as
the approach mode is selected by the pilot. The
longitudinal autopilot mode in which the aircraft
flew before selecting the approach mode, usually
ALH, will be maintained until the aircraft has
reached the glideslope reference plane” (Rauw,
177). This mode simply tells the aircraft that it is
going to be landing soon and that it needs to get
ready for landing. It does not affect any of the
current flight paths.
The second mode is the glideslope
coupled mode. The author describes this mode by
saying that “This phase is initiated as soon as the
aircraft passes the glideslope reference plane for
the first time. In this phase the control laws of the
GS mode take over the longitudinal guidance task
of the autopilot” (Rauw, 177). In this mode, the
GS actually takes over the rest of the autopilot. It
does this by adding its own signals with the Hdotref
input signal. When the GS is not engaged, the
signal that is the output of the GS is zero allowing
the aircraft to operate as it normally would. The
timing of the coupling of the GS is extremely
important. If the GS is coupled too earlier, the
aircraft will follow the path as shown below in
Figure 7: Result of Early GS Coupling
block. This block is assumed to be a simple signal
delay and is set to delay the signal by one second.
The next block is the Actuator and Cable
Dynamics block. This block, for the sake of the
simulation is assumed to be a simple transfer
function (a second order is used). At the heart of
the block diagram is the Beaver Dynamics. This
block is the portion of the control system that reads
in the measured values and operates on them. For
the sake of simulation, the block was assumed to
be three transfer functions: one of which is a
simple constant value, the second is an integrator
function, and the third is a derivative function.
After the system was constructed, the outputs were
examined. The θ plot is shown below in Figure 8:
θ Simulink Plot.
Figure 7: Result of Early GS Coupling
As can be seen by the above figure, the timing is
important because, if the GS is coupled too early,
the aircraft tries to approach the reference line (the
slanted dotted line in the figure) before it is
supposed to. The result of this is that the plane
will rise to the reference line and then have to
suddenly shift down after the line is crossed. To
properly couple the GS, the mode controller is
constantly examining the state of the aircraft.
When the aircraft reaches the correct point, the
mode controller immediately switches to coupled
mode and the aircraft can land. This system is not
perfect and it does yield a slight overshoot but the
resulting overshoot is far more desirable than the
overshoot shown in Figure 7.
4.1.2 Longitudinal Mode Simulation
To get a better picture of how exactly this
autopilot system works, it became desirable to
simulate the system in MATLAB. All of the K
values (as seen in Figure 6) are given in the Beaver
document and can be constructed in Simulink.
However, there are still a few different blocks that
are not explained in the Beaver document. This is
due to the fact that the autopilot system is
proprietary information (or if it isn’t, the authors of
the document don’t disclose the information).
Because of this, the following assumptions are
made. The first is in the Computational Delay
Figure 8: θ Simulink Plot
As can be seen, this is invalid data. The plot
shows nothing and every one of the outputs looks
about the same. Changes made in the functions of
the control system yielded no results either. The
system would either be zero and then drop off to
negative infinity or the signal would be zero and
rise to positive infinity. The system did not
compensate for anything. The reason that these
simulations did not yield valid results is because of
the fact that the setup of the Beaver Dynamics is
unavailable for research. The actual system for the
Beaver Dynamics I probably not actually a simple
transfer function. If it was a simple transfer
function, changes to the simulated system would
have had a larger effect. The Beaver Dynamics is
probably a control system in and of itself. Since
the system is a moderately complex system, it can
probably be assumed that the Beaver Dynamics is
a digital control system. There is probably a
minicomputer (as discussed earlier) at the heart of
the system that does all of the actual control for the
aircraft. For this reason, it cannot be adequately
simulated for this paper. For that to happen, more
information about the Beaver Dynamic would have
to be available for study. To make up for this lack
of simulation, a simple aircraft flight control
system is examined in the final portion of this
paper.
4.2 Beaver Conclusion
The Beaver Autopilot system is a complex
system that cannot be readily simulated due to its
complexity and a lack of information concerning
its primary controllers (the Beaver Dynamics to be
precise).
However, that aside, it is still a
fascinating system. The document by Marc Rauw
gives a solid and detailed description of the system
and makes it simple for people with basic
experience in control systems to understand the
peripherals. While it does not go into detail on the
heart of the system, it at least gives a general
overview of how the system works. The Beaver
autopilot system is a unique system that does not
follow all of the same rules that its brethren follow.
For example, the GS as discussed is a unique
feature to the Beaver Autopilot System in that it is
not how the landing mode is implemented. Most
other systems use the distance measurement
equipment (DME). It should be noted that the
description given in this paper only gives a brief
overview of the system. Many of the details of the
system (as well as the lateral and turn
compensation modes) were not discussed. To
better understand those modes, or to understand
the system in greater detail, see the paper by Marc
Rauw.
5. MATLAB Simulation
5.1 Purpose
The purpose of the following simulation is
the better understand a particular example of a
flight control system. Since the Beaver Autopilot
could not be simulated in this paper, a simpler
example is necessary. The following sections give
a description of a particular simple system. They
then run through some simulations to examine how
the system responds.
5.2 The Problem
This example comes from page 624 of
Modern Control Systems by Richard Dorf and
Robert Bishop. The control system of the problem
is that of a bi-wing aircraft. The control system is
shown below in Figure 9: Bi-Wing Flight
Controller
Figure 9: Bi-Wing Flight Controller
As can be seen in Figure 9, the aircraft consists of
an engine, a controller and Aircraft Dynamics.
There is also a little disturbance in the system
caused by wind. The goal of this exploration is to
determine the best way to control a step input
signal (simulating some variable of flight that
needs to be rectified). Because this control system
is controlling the flight of an aircraft, the percent
overshoot and steady-state errors must be as small
as possible (less than 5% for steady state error).
5.3 Analysis
For this example, the Aircraft Dynamics
and the Engine blocks are considered
unchangeable and that it is the controller than must
be modified to meet the appropriate requirements.
The simplest approach is to simply use a constant
gain function to control the system. The gain
largely has control over the stability of the system.
For certain gains, the system is stable, and for
others, it is not. After setting the system up in
SIMULINK, the value of the gain (K) was varied
and the results examined. It was found that values
of K greater than approximately 1.5 caused the
system to become unstable. However, gains of les
than 1.5 caused stability but the steady state error
was extremely high. As is shown in Figure 10:
Steady State Error of Pure Gain System, the steady
state error for the system ranges from 20% for
gains closer to 1.0 and up to 50% for smaller gains.
As can be seen, this response is already better than
any of the constant gain system responses. The
steady state error is eliminated and the percent
overshoot is less (although it is still about 30%).
However, as can be seen, the response of the
system is relatively slow. This would not be
acceptable for an aircraft as it is imperative that the
system respond quickly to changes in its state. To
speed up the response time, the proportional
portion of the PID controller is increased until the
desired response time is met. If the response time
is defined to be the time needed to rise from 10%
to 90%, a good response time would be 0.5
seconds. This is achieved when the proportional
component is set to 5. It yields the result shown
below in Figure 12: PID Controlled System (P=5,
I=1, D=1).
Figure 10: Steady State Error of Pure Gain System
As can be seen by the above plots, the system that
has the faster and smoother response also has a
completely unacceptable steady state error. The
system that has a slower response and a large
amount of overshoot has a better stead state error
but it is still around 15% which is unacceptable.
If a better result is to be attained, a
different approach becomes necessary.
To
eliminate this error and overshoot, implementing
some other kind of controller will be beneficial.
The usual approach is to implement a PID
controller. The components in this kind of
controller can take sensitive control systems and
give them a more stable, smoother, faster, and less
oscillatory response. A PID controller was added
and the system was tested in SIMULINK. The
first step in setting up a PID controller is to set all
of the values to 1. The results of this test are
shown below in Figure 11: PID Controlled System
(P=1, I=1, D=1).
Figure 11: PID Controlled System (P=1, I=1, D=1)
Figure 12: PID Controlled System (P=5, I=1, D=1)
As can be seen, this is a fairly good response. The
steady state error is very close to zero, the percent
overshoot is 2% and the response time is less than
0.5 seconds. However, this system is not perfect.
Although it may not be initially evident by the
above plot, there is oscillation in the signal and the
oscillations last for more than 10 seconds. While
some systems may not have serious problems with
these oscillations, flight control systems may have
complications. For example, if this system was the
altitude controller, the aircraft may see these
oscillations as vibrations of the aircraft. These
vibrations would add to the vibrations that are
already present and could increase the natural wear
and tear of the aircraft devices. Also, if the
vibrations occurred at the exact right (or wrong)
frequency, some systems that use this signal could
become unstable. Therefore, the system must be
modified again to accommodate for these
oscillations. The best results that could be attained
in the time span allowed for the experiment ended
up not yielding a much better response. The
oscillations were eliminated but the percent
overshoot is substantially higher as is shown below
in Figure 13: PID Controlled System (P=1, I=3,
D=0.2)
example of a flight control system was explored to
see the effects of various controllers on the system.
Autopilot systems and, more broadly, flight control
systems are complex systems that generally are
sensitive systems. However, in order for flight to
be smooth, the systems must be robust and able to
handle disturbances.
If a disturbance could
potentially cause instability, the flight would
become dangerous. However, to combat these
unexpected instabilities, most flight systems are 2
and 3 times redundant: they have several backup
systems that can step in and take over in the event
of a failure. These emergency systems can mean
the difference between flight and a crash in the
event of a sudden disturbance. However, it is still
up the control systems on the aircraft to insure that
the plane will make it from point A to point B and
back again.
Figure 13: PID Controlled System (P=1, I=3, D=0.2)
As can be seen by the above plot, if the system can
handle a 25% overshoot, this response is better
because of the fact that the oscillations are not
present here. However, if the system can handle
oscillations, the first PID controller is much more
desirable because of its high response time, low
overshoot, and low steady state error.
Bibliography
Rauw, Marc. A Simulink Toolbox for Flight
Dynamics
and
Control
Analysis.
Published by Marc Rauw, 1994 – 2001
Richard Dorf and Robert Bishop. Modern Control
Systems. New Jersey: Prentice Hall, 2001
5.4 Summary
The system presented in the previous
example, shows how an aircraft responds to
changes in the system. For all of the explorations,
the system was given a step input which could be
equated to a change in altitude ordered by the pilot.
The pilot would change the altitude and the system
would have to respond quickly and smoothly.
Because the system presented in the problem is
inherently sensitive to changes, a PID controller is
necessary to aid the system in responding
effectively. It was found that a larger proportional
controller as well as a unit integrator and derivator
were necessary to keep the system stable and
responding quickly. However, as were discovered,
there were tiny oscillations present that could
potentially cause problems for the aircraft.
6. Conclusion
Through this paper, a brief overview of
Digital Control systems was given to show how
they relate to autopilot systems, the Beaver
Autopilot system was analyzed and studied, and an
Flight Dynamic and Control Toolbox page.
< http://home.wanadoo.nl/dutchroll/>
Hughes, Arthur. History of Air Navigation. Great
Britain: Unwin Bothers Limited Working,
1946
Shevell, Richard. Fundamentals of Flight. NJ:
Prentice Hall, 1983