In this study, a dynamic field theory (DFT) based cognitive model of a pilot performing pitch attitude control of a 3 degree of freedom aircraft model is presented. The cognitive model is validated by comparing the pilot model's pitch attitude hold performance with real flight test results of a human pilot on a real aircraft. A high degree of similarity was observed between the behaviour of the human pilot and the DFT model. The paper contains a brief summary of older control theory based pilot models, describes the similarities between control theoretic and DFT approaches, and shows the DFT pilot's flexibility to adapt to different temporal behaviours.
Several mathematical models that emulate a human pilot’s abilities to control an aircraft have been proposed in aerospace engineering since 1950s. Most of these are functional models that simply provide a transfer function constructed upon control theoretic principles such as root loci and Bodé plots, which are primarily based on data obtained from questionnaires filled by the pilots or flight test instrumentation. In particular, these models belong to the first among two main modeling paradigms, which focus on performing a specific task by using a pilot transfer function to control some specific aspect of aircraft attitude. Such models treat the pilot as a set of control equations in the control loop of an aircraft function. Although these control models are great engineering efforts, they are primarily geared towards controlling the aircraft as part of an autopilot system, rather than providing tools for understanding human piloting behaviour. The second paradigm employs a cognitively more plausable approach, which will be discussed further after a review of control theory based pilot models.
One of the earliest control theory based pilot models
focused on determining the control parameters of vertical
take-off and landing (VTOL) aircraft in the United States
Air Force Flight Dynamics Laboratory (AFFDL)
The crossover model is one of the two well-known control
theory based pilot models. The model takes its name from
the crossover frequency which is the frequency where the
phase angle of a Bodé plot equals -180° or -π
The Paper Pilot is another seminal model like the
crossover model, which employs the McRuer and Jex
model as an inner loop. Hence, it is a far more complex
model in comparison with the crossover model
The paper pilot model uses a performance-based approach for the determination of model parameters (Anderson, 1969). The use of the transfer function from the crossover model eased the development of the paper pilot. It is named as paper pilot possibly because it depends on the evaluation of pilot performance with questionnaires. In the model, the most important parameters are the gain and the lead time constants, which are selected to optimize the model performance by minimizing attitude errors.
The crossover model described above can control a single parameter, and thus controlling multiple parameters instantaneously requires the use of multiple crossover models. The paper pilot model has an advantage in comparison with the crossover model, as it uses both position and angular parameters to control the displacement. This parallels to the real situation in an aircraft where the pilot generally controls the angular movements and the thrust level (i.e. speed for displacement). Therefore, the paper pilot is far more realistic as a model as compared to the crossover model.
The main weakness of the paper pilot is its performance dependency. Since the model parameters are adjusted using the model performance iteratively, the model is very much dependent on the physical aircraft model. In other words, the pilot model performance changes with the aircraft model. So paper pilot is a task dependent model that differs from a human pilot who can learn to fly any type of aircraft with a performance depending on training hours.
The optimal pilot model is developed to overcome the task
dependency (i.e. dependency to aircraft dynamics) of the
paper pilot
Researchers have been in search of an adaptive or dynamic
aircraft attitude control capability for several decades due to
the difficulty of predicting environmental effects in open
(uncontrolled) atmosphere. This necessity motivated the
second paradigm in pilot modelling, which can be referred
as neural or dynamic approaches. Such models are reported
in various publications and are generally providing
autopilot capabilities to control real or simulated aircraft
dynamics. Some examples include
To sum up, existing pilot models in aviation industry are predominantly control theoretic models that focus more on control dynamics than cognitive processes underlying a human pilot’s performance. In this paper, we propose a Dynamic Field Theory based approach to extend this line of work by incorporating biologically plausible layers that modulate cognitive processes underlying pilot behaviour. The next section provides an overview of Dynamical Field Theory. This is followed by a description of the physical aircraft model used in this study and the DFT based architecture developed to model pilot behaviour. The paper
Equation 2 provides a relation of neural interaction between neural fields depending on their distal separation, i.e. it is a function of a spatial parameter. Notice that the activity relation here is simply independent of time but it is a function of the separation between the fields’ physical distances and forms a Gaussian with standard deviation σ. A is the excitation constant which will vary with a Gaussian behaviour over distances between fields. winh is a constant value of inhibitory effect between neural fields.
1 ,
Above given eq. 3 is the threshold function in form of a sigmoid.
The DFT method allows model builders to implement networks of neural fields to create logical or spatiotemporal concludes with our preliminary findings regarding the model’s performance on an altitude hold task, which is contrasted with real human pilot data.
Neural field studies starting from late 1950s take the firing
rates as the primary state variable with the assumption that
neuron populations are embedded in coarse-grained areas
Below is the Amari equation which is used to model the
firing behaviour of a cortical area, nuclei or column on a
functional basis
In the equation above, the term w(Δx) is the interaction kernel and is convolved with a threshold function f (u(x’, t)) which is used to supress the kernel’s excitory parts in case the system dynamics are below a preselected threshold. is the time constant for the population dynamics. u(x, t) is the field activity function. The output of the U function provides the activity value. H is the resting level of the model, whereas S(x, t) are the input(s).
∆ is the interaction kernel representing each neuron’s excitory or inhibitory relation from the neuron at the origin with a distance x – x’. , is the threshold function.
Below is the equation defining a kernel example. proportion of W with a coefficient of (1/cos( ). D: The Drag induced on the body of the aircraft due to the airspeed.
: Angle of attack; i.e. the angle between the aircraft mean chord line (longitudinal axis of the aircraft) and the velocity vector. Sideslip or skid effects are all neglected.
The model described above is implemented in C++ and
connected to our pilot model as a plugin which is
implemented in the CEDAR framework
The general architecture of our setup is the same as in Figure 1. Unlike the crossover model that controls a single parameter, the DFT pilot model is used to control multiple aircraft behaviours by using 2 control inputs (Figure 4).
In this study, 3 axis behaviour of the aircraft model is controlled via two inputs, namely the pitch and heading correction. The model will focus on emulating the performance of a human pilot who intends to hold the pattern of flight stable. Only the pitch results will be summarized in this paper. The roll control is left out of the scope of this paper. Figure 4 summarizes the control flow for each control parameter. decisions. One can adjust kernel parameters to modify a spatiotemporal parameter. For example, the observation of the distance from an object can be represented by the activity position of the field in the spatiotemporal axis and the saliency of the activity amplitude of the same field.
A 3 degrees of freedom (3DoF) model was selected to
model the aircraft in this study. The selected 3DoF model
suits particularly well for understanding long-term
navigation behaviour, and similar models have been used in
previous studies
cos sin sin cos cos cos
sin sin 0
sin cos cos
Equation 4 contains the rate of change of the fundamental model parameters in time. The parameters used in Equation 4 are defined as follows.
X: Longitudinal axis position of the aircraft (along body
axis position). Y: Lateral axis position of the aircraft (cross
body axis position). h: Altitude of the aircraft upon flat
earth Cartesian coordinate system (the normal axis
position). V: The speed of the aircraft upon flat earth
Cartesian coordinate system. : Aircraft current heading
angle. : Aircraft flight path angle. This angle is the angle
between the flat earth surface and the aircraft velocity
vector. W: The weight of the aircraft plus the weight of the
fuel. In normal conditions, fuel is expected to decrease
proportional to the thrust applied by the engines to the
aircraft. T: Constant aircraft thrust supplied by the engines.
g: The gravitational acceleration. Flat earth model is used, g
can be assumed constant. wx, wy, wz: Components of wind
vector, i.e. the speed of wind in North and East direction
and finally the third one is in normal axis. : Aircraft pitch
angle; the angle between the flat earth surface and the
aircraft nose. : Aircraft roll angle; i.e. the angle between
the lateral axis of the aircraft and the flat earth surface. L:
The lift force. In this model L will be taken equal to a
The intention layer, which is not shown in Figure 4, is used
to generate a constant behaviour to hold the aircraft at initial
attitude. The reason behind the use of the intention layer is
to provide the pilot model a goal structure. In this
preliminary study we aimed to provide a DFT model that is
deliberately oriented towards performing level flight. The
architecture is used to control the aircraft on holding the
initial heading and altitude. Due to the unavailability of the
roll control channel, the aircraft roll attitude is not held
under control and left freely to oscillate due to the control
behaviour. Since a 3DoF aircraft model is used, each
attitude channel can be assumed independent and harmless
upon aircraft pitch performance. Since there is an intention
layer to hold the aircraft in a selected path or pattern, our
DFT based architecture bears a strong similarity to the
models proposed by
In the CEDAR implementation, the aircraft model’s output is connected to the perceptual neural fields (sensory fields used for observing the aircraft dynamics), which transform the spatial parameters into neural field activations so that they can be processed by the architecture.
Figure 6 displays a graphical representation of the performance of a T-38 Talon pilot trying to hold the aircraft at 20000 ft constant altitude manually for 2 minutes and 55 seconds. The plot indicates that there are various deviations from the target altitude up to approximately 90 ft. Some of these deviations may originate from the aircraft dynamics and some from the pilot. Accordingly, we deduce that a human pilot’s performance unified with the aircraft dynamics may result in up to 90 ft deviations at high altitudes. The same Test Pilot showed a better performance with a maximum deviation of 53.2 ft when the holding task was carried out at 8450 ft during the same flight. When the target altitude is 100 ft above ground, the same pilot made an error of maximum 7.5 ft. Therefore, we can deduce that as the aircraft is closer to the earth’s surface (i.e. as the danger increases) during the holding task, the pilot naturally becomes more careful.
A similar analysis may be performed for lateral hold performance. Our analysis on flight test data records have shown that the same pilot have a performance of pattern holding on lateral navigation with a maximum error of 29.504 ft. Lateral performance is hold out of scope for current study.
In this study we tried to hold our 3 DoF aircraft model at level flight and our aim was to hold the deviations on or below the deviations observed in human pilot performance data. One important point is that the given deviations may be dependent on the pilot’s experience. However, since the identity and the flight experience of the pilots were not available to the researchers, we cannot incorporate the variability due to different expertise levels in our study.
Another important consideration for pilot modelling is that, whatever the controlled attitude (i.e. pitch or lateral), the pilot uses an angular parameter to control the Cartesian behaviour of the aircraft. Thus, the pilot model should be able to make a transformation between coordinate systems and compute the required angular correction to re-enter the flight path or hold the flight pattern.
20100 l) e v Le20050 a e S e vo20000 b A ( t ,fe19950 d u t li t A19900
Manual Altitude Hold Performance of a T‐38 Pilot at 20 K ft
20092,5 20052,5 19942,5 19955 19952,5
The DFT based pilot described above performed some simulated flights completely autonomously and the results are qualitatively compared with actual flight test data obtained from T-38 flights. The behaviour of the human test pilot exhibits an oscillatory behaviour around the targeted flight pattern with plus or minus deviations. Some of these deviations are due to the dynamical behaviour of the T-38 aircraft, which is expected. Especially in high altitudes the pilot was not able to follow the target altitude loss strictly. A similar behaviour is obtained with the DFT based pilot model. Figure 7 shows the output obtained from a sample run.
Figure 7 suggests that the DFT pilot is able to control aircraft pitch attitude by limiting the aircraft altitude deviations. In the above example, the aircraft makes constant decrease from 10.000 ft with a constant loss of altitude with 138 ft/step size (about 5 seconds). When the pilot model is started, it directly creates an input to stop the decrease in altitude in an effort to protect the current flight path. As the plot indicates, the aircraft altitude oscillates around the targeted altitude under the control of the pilot model, which is trying to keep the altitude constant. Notice the model reaction times and amplitudes can be adjusted via using the dynamic fields’ time constant (shown in equation 1), sensor layer tolerances and excitory or inhibitory field parameters.
Overall, our preliminary results suggest that the pitch attitude performance of our DFT based pilot model is comparable to the human pilot’s performance. Human pilots do not make any trigonometric computations to acquire the cross track component of the distal deviation to obtain the required angle to hold the pitch attitude of the plane. The process of the computation happens naturally, embodied and embedded in a continuous way. The continuity in the inner and outer loops of pilot control in the proposed DFT architecture captures the dynamic and embodied nature of the human pilot’s actions. Therefore, DFT seems to be a promising approach for modelling dynamic, embodied and embedded aspects of pilots’ cognitive and behavioural performance.
1 11 21
31 Simulation Step Number
In future work, the aircraft model will be improved with 6 DoF dynamics to be able to discriminate between the behaviour of the aircraft and the behaviour of the pilot model. In the next step, the control of the attitude will be improved with lateral navigation, roll control and obstacle avoidance hierarchy.
This study is supported by Turkish Aerospace Industries (TAI) and is part of a thesis study in METU Cognitive Science Department with the support provided by TAI.
A working set of parameters is given below. This set of parameters is used with two interacting fields to obtain dynamical control behaviour. Static gains are also used in the architecture to adjust motor behaviour but they are not considered here since the reader can easily adjust its own parameters to create the temporal behaviour of the pilot. This is similar to the neuromuscular delays and transfer functions used in the optimal pilot model.
Initial Mass: 5000 lbs, Constant Trust: 6000 lbfs, Initial X Position: 0, Initial X Position: 0, Initial Altitude: 10000 ft, Initial Airspeed: 298 Knots, Fuel Burn Rate: 5 lbs/min.
Pitch Decision Neural Field 1; Resting level: -1, Time scale: 100, Global inhibition: -0.001, Dimensionality: 1, Sizes: 90, Input noise gain: 0.1, Sigmoid Kernel Threshold: Threshold: 0, Beta: 100, Lateral kernels, Gaussian: Dimensionality: 1, Amplitude: 2, Sigmas:3,
Pitch Decision Neural Field 2; Resting level: -1, Time scale: 500, Global inhibition: -0.01, Dimensionality: 1, Sizes: 90, Input noise gain: 0.1, Sigmoid Kernel Threshold: Threshold is 0, Beta: 100,
Wind Mean (ft/s): 5, Standard deviation: 0,
Memory Trace as Intention Layer Sizes: 90; Time scale build up: 10, Time scale decay: 109.
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