Aircraft controllability and stability

Controllability and observability are leading factors that need to be considered when designing
a system, and that is applicable for each and every type. In an aircraft system point of view, these
facts can be explicitly described. In an aircraft point of view, controllability and maneuverability
are interrelated, and one can be increased with the expense of their parameter. Accuracy and
precision are the other two factors that can be found in each system and those can be considered
as the main component that can be used to analyze the performance.

1. Aircraft Controllability and Stability
in Control Systems’ Perspective

2. 1


Abstract
Controllability and observability are leading factors that need to be considered when designing
a system, and that is applicable for each and every type. In an aircraft system point of view, these
facts can be explicitly described. In an aircraft point of view, controllability and maneuverability
are interrelated, and one can be increased with the expense of their parameter. Accuracy and
precision are the other two factors that can be found in each system and those can be considered
as the main component that can be used to analyze the performance.
This report is dedicated to addressing how controllability and observability are used in system
point of view and how the accuracy and precision are essential to the systems. In the later part,
that discusses the relationship between controllability and observability and how these concepts
are used in different aircraft designs and how they are improved in the various aircraft categories.

3. 2


Table of Contents
Abstract ............................................................................................................................................ 1
Table of Contents ............................................................................................................................. 2
Introduction...................................................................................................................................... 3
Controllability and Observability .................................................................................................... 4
Accuracy and Precision ................................................................................................................... 5
Controlled Flight .............................................................................................................................. 7
Conclusion ....................................................................................................................................... 9
References...................................................................................................................................... 10

4. 3


Introduction
Controllability, stability, observability, and maneuverability are different nomenclatures used
in the control system's point of view. Understanding of those terminologies is more critical to
develop more complex systems without considering the type.
Controllability is the response of an aircraft in a steady flight on the pilot control input.
Stability can be described as the tendency of an airplane to return to a trimmed position after
disturbance in an air stream. Maneuverability can be defined as the ability for the aircraft to
commence and sustain maneuvers, its responsiveness, and its performance rate of roll or turn and
pitch rate. But the observability is developed within the control system designing method, and
there are several technical methodologies for that. These factors work in an interrelated and
correlated manner, not as individual and unique features.
When considering the accuracy and precision, these are also correlated facts that need to be
understood and should implement in each system. When the accuracy is high, but the precision is
low or vice versa, the reliability of the system gets low. So, there should be high accuracy and
precision in most of the arrangements. Several technics can follow to increase accuracy and
precision, but there are limitations. In aircraft systems especially control systems, these factors
should be highly considered and clearly identified.

5. 4


Controllability and Observability
The state variable approach is a powerful method to analyze and design of control system.
The state-space analysis is a modern approach that uses in digital computers. Analyze and
designing of systems can be carried out in a linear system, non-linear system, time-invariant
system, varying time system, and multiple inputs and output systems. That state variable approach
is different from the transfer function model as there are several drawbacks such as, the transfer
function is defined under zero initial condition, the transfer function applies to linear time-invariant
systems, transfer function analysis is restricted to a single input and single-output systems. Also,
that does not provide information regarding the internal state of the system. So that controllability
and observability concept has developed.
Controllability concept proved the usefulness of the state variable approach. Mainly, that
indicates, state variable can be controlled to achieve the desired output. In a system, if each state
variable can be found such that those variables can take from a desired initial state to a desired
final stage, that system is said to be a controllable system. Otherwise, the system is uncontrollable.
In other words, a system is said to completely state controllable if it is possible to transfer the state
from an initial state to any other desired state in specified finite time by a control vector.
A system is said to be utterly observable if every state can be identified entirely by the
measurements of the output over a finite time interval. Using the observability test can be used to
find the state variable is observable or measurable. Also, that can be used to solve the problem of
reconstructing unmeasurable state variables from measurable ones in the minimum possible length
of time.
Simply, controllability is concerned with whether one can design control input to steer to
arbitrary values and observability is concerned with whether without knowing the initial state, one
can determine the state of a system given the input and the output.

6. 5


Accuracy and Precision
In a simple definition, accuracy means the closeness of a measured value to a standard or
known value. Accuracy describes systematic errors, a measure of statistical bias. Also, that can be
used to express a combination of both types of observational error.
Precision refers to the closeness of two or more measurements to each other. In other words,
the data set is said to be precise if the values are close to each other when it measures the same
condition. Precision is a description of random errors, a measure of statistical variability.

Figure 1 - Accuracy and Precision

a. Accuracy b. Precision
Figure 2 - Accuracy and Precision - the difference

7. 6

In the scientific world, the accuracy of a measurement is the degree of a quantity to the actual
value of the measurement. Precision relates to reproducibility and repeatability. Precision and
accuracy are two independent properties in measurements. A measurement system can be accurate
or precise or both. Otherwise, those can be not accurate and precise, as well. The measurement
system is said to be valid if both accurate and precise. The comparison between accuracy and
precision is given in Table 1.
Table 1 - Accuracy and Precision - comparison
Basis for comparison Accuracy Precision
Meaning Relates to the level of
difference between the
actual measured value
and absolute value
This refers to the level of
variation that lies in the values
of several measurements under
the same conditions.
Represents Results close to the
standard values
Results how close with one
another
Degree Degree of conformity Degree of reproducibility
Factor Single-factor Multiple factors
Measure of Statistical bias Statistical variability
Concerned with Systematic error Random error
By controlling all the other variables in the system is the primary method to improve accuracy
and precision. Taking measurement multiple times and increasing the number of samples will
remove the random error in the measurements and increase the precision of the results.

8. 7

Controlled Flight
When considering the controlling of an aircraft, the stability and the controllability are vital
concepts. The stability can be categorized into two as static and dynamic. Furthermore, these can
be classified as positive, negative, and neutral stability.
Static stability is the initial tendency of an object to return to its original position after being
disturbed. When the controls are changed and release, the airplane initially moves back to the
original position is the positive static stability. When the aircraft stays where it is after changing
the controls, that shows neutral stability, and when it tends to move further away from the original
position, that means negative stability.
Dynamic stability is there if the aircraft is positively stable. Dynamic stability is the overall
response of an object to its static stability. When an aircraft is disturbed, the overall pattern of
movement becomes progressively smaller, that will be the positive dynamic stability. When it is
in the neutral dynamic stability, the overall pattern of movements is continuously unchanged, if
the airplane is disturbed. If the overall pattern of movements become progressively larger when
the aircraft is disturbed, that shows the negative dynamic stability.
As an aircraft has 3 axes, longitudinal, lateral, and vertical, each axis has its own stability.
Pitch control is responsible for longitudinal stability. The center of gravity and center of lift and
horizontal stabilizer downforce are the facts that need to concern in longitudinal stability, and that
will mostly affect the aircraft loading.
Lateral stability is interrelated with the rolling movement around the longitudinal axis. If
excellent lateral stability will tend to bring the wings to a level flight altitude when one wing is
lower than the other. In general, cases, positive dihedral wings, and high wings provide more
lateral stability. Directional stability is related to the yaw movements, around its vertical axis, and
the airplane’s ability to not be adversely affected by force, creating a yaw type motion. Generally,
sweptback wings, double taper wing arrangements, to a lesser extent, will provide more directional
stability than other wing configurations.
Controllability of an aircraft is the capability of an aircraft to respond to the pilots' control
inputs, and the maneuverability is the quality of the aircraft that can be easily controlled in the
given space region. Also, the airplanes are designed such that, dynamically more stable than the
rotorcrafts because of the sudden maneuverability should be there.
If something is very stable, it is more difficult to change the altitude of that. If an aircraft is
unstable, it’s easier to change its altitude. Based on that, civilian aircraft tend to be very stable,
and fighter jets are more volatile. Commercial aircrafts are easier to control, safe in operation and

9. 8

more comfortable because of the task mentioned above. On the other hand, fighter jets are more
unstable, so most of such aircraft are difficult to handle by pilots. Thus, artificial stability methods
such as computerized controlling are used.
A more suitable example of the fact that discussed above is the BE.2 aircraft. That aircraft
was designed as a two-seater trainer aircraft in 1912. As the purpose is the training pilots, designers
tend to design is a highly stable state. So that the maneuverability is drastically reduced and
controlling response is lagged. Because of that situation, that aircraft was easily outmaneuvered
by the pilots. So, it had to be withdrawn from the frontline service in the war zone because that is
not fit for the air-to-air battles. But that was used in artillery observations and aerial photography
duties.

Like previous sections, controllability is the response of an aircraft in steady flight, on pilot
control inputs. For instance, when the pilot deflects the ailerons, a high resulting roll rate means a
fast response. The stability can be described in the level flight as the tendency of an aircraft
airframe to return to a trimmed position after a disturbance in the air stream. So, there is no need
for interaction from the pilot to get the aircraft to its initial position from the deflected position.
For that, both control deflection and aerodynamic stability should be preserved. As an example, if
the center of gravity (CG) is far aft position, that may not recover the stability whether the inputs
are given. So that there is an issue in slow flights to get back to the stable situation when the CG
is positioned far aft. So that, less stability makes the less controllability of the aircraft at slow
speeds.

10. 9

Conclusion
Controllability, Stability, Maneuverability, and observability are several factors that need to
be considered in the aircraft system design. Those factors need to be considered not only in the
aircraft systems but also in the other control system design. By changing the parameters of the
system, those can be controlled.
Stability and controllability have an inverse relationship as stability can be increased by
expensing the controllability. So that military aircraft are more controllable and less stable. On the
contrary, commercial aircrafts are more stable to ensure comfortability and less controllable.
Accuracy and precision are the other two factors need to be considered when designing the
control system. These two parameters should be in the system together. Otherwise, there will be
several errors, and remedies should be introduced.

11. 10


References
[1] “Stability and Control (Part Two),” 2017. [Online] Available: https://www.fligh-
mechanic.com/stability-and-control/.
[2] “Aircraft Stability (Part One),” 2017. [Online] Available: https://www.fligh-
mechanic.com/aircraft-stability-part-one/.
[3] “Aircraft Stability (Part Two),” 2017. [Online] Available: https://www.fligh-
mechanic.com/aircraft-stability-part-two/.
[4] D.A. Caughey, “Introduction to Aircraft Stability and Control Course Notes,” Sibley School of
Mechanical and Aerospace Engineering, New York, 2011
[5] Surbhi. S. “Difference Between Accuracy and Precision”, Key Differences, 5 January 2018.
[Online] Available: https://keydifferences.com/difference-between-accuracy-and-precision.html.
[Accessed 26 September 2019]
[6] “What is the Difference Between Accuracy and Precision?”, ThoughCo. [Online] Available:
https://www.thoughtco.com/difference-between-accuracy-and-precision-609328. [Accessed 26
September 2019]
[7] Skiba R. “Stability, Controllability and Maneuverability”, volume 16 No 3. 1999