A Dynamic Field Theory Based Pilot Model To Control Aircraft Pitch Attitudes Yasin Kaygusuz (ykaygusuz@tai.com.tr) TAI, Turkish Aerospace Industries, Fethiye Mah., Havacılık blv. No17, Akıncı, Kazan 06980, Ankara, Turkey METU Informatics Institute, Department of Cognitive Science, Dumlupınar Blv. No:1, Çankaya, 06800 Ankara, Turkey Murat Perit Çakır (perit@metu.edu.tr) METU Informatics Institute, Department of Cognitive Science, Dumlupınar Blv. No:1, Çankaya, 06800 Ankara, Turkey Abstract (Blakelock, 1991). The purpose of this study was to determine the VTOL specification for a future development In this study, a dynamic field theory (DFT) based cognitive aircraft with a focus on matching human performance model of a pilot performing pitch attitude control of a 3 degree of freedom aircraft model is presented. The cognitive characteristics obtained in conventional aircraft. Since no model is validated by comparing the pilot model’s pitch VTOL aircraft had yet to be built at the time, AFFDL did attitude hold performance with real flight test results of a not have any chance to use real flight test data, so human pilot on a real aircraft. A high degree of similarity was researchers preferred to use a simulated environment to observed between the behaviour of the human pilot and the obtain pilot performance parameters as rated by the Cooper- DFT model. The paper contains a brief summary of older Harper rating scale. This work led to the first control control theory based pilot models, describes the similarities between control theoretic and DFT approaches, and shows theoretic pilot model in 1960s, which is considered as the the DFT pilot’s flexibility to adapt to different temporal generic pilot model (Johnson & Pritchett, 2002). behaviours. The crossover model is one of the two well-known control theory based pilot models. The model takes its name from Keywords: Dynamic field theory, pilot cognitive model, cognitive modelling. the crossover frequency which is the frequency where the phase angle of a Bodé plot equals -180° or -π (Blakelock, Models of Pilot Cognition and Piloting Tasks 1991). The crossover model assumes a simple control loop of pilot-aircraft similar to the one given in Figure 1 below. 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 Figure 1. A representation of Crossover Model with a function to control some specific aspect of aircraft attitude. slight modification from Blakelock (1991). Such models treat the pilot as a set of control equations in the control loop of an aircraft function. Although these McRuer and Jex (1967) give a crossover model written in control models are great engineering efforts, they are frequency domain with parameters jw and Blakelock (1991) primarily geared towards controlling the aircraft as part of provides the same model in Laplace domain with variable s. an autopilot system, rather than providing tools for In the crossover model’s pilot-aircraft loop, we labelled the understanding human piloting behaviour. The second input as intention, which may refer to a navigation goal paradigm employs a cognitively more plausable approach, originating from the flight plan or a leg of a manoeuvre. In which will be discussed further after a review of control any case, the pilot is mostly interested with the deviation theory based pilot models. between the intended (or goal) state and the current One of the earliest control theory based pilot models situation. The crossover model aims to achieve humanly focused on determining the control parameters of vertical dynamical behaviour by adjusting the time constants to take-off and landing (VTOL) aircraft in the United States manage the deviation between the current situation and the Air Force Flight Dynamics Laboratory (AFFDL) goal, which is the main reason behind its stability. 152 However, the model neglects the spatiotemporal behaviour model. So paper pilot is a task dependent model that differs of the neural network underlying the decisions of the pilot. from a human pilot who can learn to fly any type of aircraft Therefore, one can conclude that such control theoretic with a performance depending on training hours. models of pilot behaviour are functional engineering The optimal pilot model is developed to overcome the task models that are not neurobiologically informed. McRuer dependency (i.e. dependency to aircraft dynamics) of the and Jex (1967) report that such a model holds only around paper pilot (Pollard, 1975). As it can be seen in Figure 3, in the crossover frequency of its Bodé plot, and this is where contrast to prior models the main improvement is the the name of the model arises. addition of the angular control element to the control loop, which is one of the primary controls performed by a human pilot. The optimal pilot goes one step further by adding a simulation of humanly behaviour in the form of an estimation-control loop. Therefore, the optimal pilot model can be considered as the first attempt in capturing the pilot’s cognitive abilities in a computational model, even though it is not biologically informed and it is still essentially a control model. Figure 2. A schematic representation of the paper pilot. The paper pilot differs from the crossover pilot by incorporating not only the position but also the angular situation of the aircraft into the control loops. 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 (Anderson, 1970; Anderson, Connors & Dillow, 1970). A schematic representation of the paper pilot model is provided in Figure Figure 3. A schematic of the optimal pilot model. 2. There are two control loops, one being inside and in contact with the aircraft dynamics, and one being outside Similar to the paper pilot, the optimal pilot also depends serving as an outer loop oriented towards position on a pilot rating function (PR), which is used to evaluate the behaviour. The use of such inner and outer control loops are model performance with current parameters like previously still commonly used in aircraft control modelling. cited gain or time constants. One major difference between The paper pilot model uses a performance-based approach the older model and the optimal pilot is that the noise due to for the determination of model parameters (Anderson, neuromuscular or perceptual factors is aimed to be included 1969). The use of the transfer function from the crossover in the model via noise input addition. White noise is model eased the development of the paper pilot. It is named typically employed to ensure that errors are distributed as paper pilot possibly because it depends on the evaluation equally around the target value (Blakelock, 1991). of pilot performance with questionnaires. In the model, the More recently, Johnson and Pritchett (2002) proposed a most important parameters are the gain and the lead time generic pilot model that can be both used as a simulated constants, which are selected to optimize the model pilot in engineering and scientific applications as well as an performance by minimizing attitude errors. autopilot controller. This model can be considered as one of The crossover model described above can control a single the newest and most generalized of all control theoretic parameter, and thus controlling multiple parameters models. Although this study is newer than the previously instantaneously requires the use of multiple crossover described approaches by three decades, Johnson and models. The paper pilot model has an advantage in Pritchett’s model is also based on McRuer and Jex (1967). comparison with the crossover model, as it uses both The generic pilot model is popularly employed as an position and angular parameters to control the displacement. autopilot system in modern aircraft systems. A human pilot This parallels to the real situation in an aircraft where the controls the aircraft with no direct contact with the position pilot generally controls the angular movements and the or attitude. The change in the position of an aircraft is the thrust level (i.e. speed for displacement). Therefore, the result of the speed, moments, inertia, current angles of the paper pilot is far more realistic as a model as compared to body etc. Similarly the angular control of the body is not the crossover model. directly performed, but rather the pilot controls the body The main weakness of the paper pilot is its performance movements via changing the positions of flight control dependency. Since the model parameters are adjusted using surfaces. The control parameters in an aircraft control the model performance iteratively, the model is very much system can be divided into two layers. A layer of dependent on the physical aircraft model. In other words, parameters is in direct contact with the aircraft body, and a the pilot model performance changes with the aircraft layer formed by higher-level parameters operates at a more 153 global level. In other words, this organisation is similar to concludes with our preliminary findings regarding the Marr’s (1982) three levels of analysis where the body of the model’s performance on an altitude hold task, which is aircraft resembles the biological layer, the direct parameters contrasted with real human pilot data. resemble the representation layer which are in direct contact with the biological layer, and finally the indirect parameters Dynamical Field Theory resemble the computational level which are shaped by the Neural field studies starting from late 1950s take the firing pilot’s intentions or mission parameters e.g. climb to a rates as the primary state variable with the assumption that specific altitude, go to a specific place etc. neuron populations are embedded in coarse-grained areas Researchers have been in search of an adaptive or dynamic (Meijer and Coombes, 2013). Beurle, Wilson, Cowan and aircraft attitude control capability for several decades due to Amari have laid the mathematical groundwork for neural the difficulty of predicting environmental effects in open field modelling. Beurle’s (1956) work on large scale neuron (uncontrolled) atmosphere. This necessity motivated the population excitation behaviour was extended with second paradigm in pilot modelling, which can be referred inhibitory capabilities contributed by Wilson and Cowan as neural or dynamic approaches. Such models are reported (1972) and Amari’s (1977) Mexican hat type kernels, which in various publications and are generally providing altogether provided a mathematical model for autopilot capabilities to control real or simulated aircraft characterizing neural population activity. dynamics. Some examples include Enns and Si’s (2004) Below is the Amari equation which is used to model the helicopter flight control with Neural Dynamic firing behaviour of a cortical area, nuclei or column on a Programming, Kaneshige and Burken’s (2008) neural functional basis (Amari, 1977). network based in-flight control model of a real F-15 aircraft, and neutrally informed intelligent models developed in NASA (Motter, 2008). Although these , , approaches offer very effective and successfully tested 1 , autopilot models, none of them are based on dynamic field theory In the equation above, the term w(Δx) is the interaction In this study, we opted for employing an intention layer to kernel and is convolved with a threshold function f (u(x’, t)) supply the pilot model with a goal. Such a layer can be which is used to supress the kernel’s excitory parts in case formed with a self-excitory dynamic neural field with a the system dynamics are below a preselected threshold. is very low decaying time constant so that the pilot never the time constant for the population dynamics. u(x, t) is the forgets his intention. Using a reference field or model to field activity function. The output of the U function create an intention is first proposed by Kaneshige, Bull and provides the activity value. H is the resting level of the Totah (2000), where 3 functions are used as reference model, whereas S(x, t) are the input(s). models for pitch, roll and yaw rates of the aircraft. Dividing ∆ is the interaction kernel representing the intention into 3 components as reference models of each neuron’s excitory or inhibitory relation from the behaviour in this way provides a useful and easy method to neuron at the origin with a distance x – x’. , is implement such a model. We have similarly used 3 different the threshold function. dynamic neural fields holding or memorizing the pilot’s Below is the equation defining a kernel example. intention patterns, which will be described further in subsequent sections. Note that the Kaneshige, Bull and Totah (2000) model uses neural networks with s-domain 2 transfer functions to control the aircraft, so dynamic neural fields are not used in this approach. While Kaneshige et al. Equation 2 provides a relation of neural interaction between continuously compare the reference models with current neural fields depending on their distal separation, i.e. it is a rates and form the next action based on their difference, this function of a spatial parameter. Notice that the activity loop can be assumed as a negative feedback line to achieve relation here is simply independent of time but it is a stability. function of the separation between the fields’ physical To sum up, existing pilot models in aviation industry are distances and forms a Gaussian with standard deviation σ. A predominantly control theoretic models that focus more on is the excitation constant which will vary with a Gaussian control dynamics than cognitive processes underlying a behaviour over distances between fields. winh is a constant human pilot’s performance. In this paper, we propose a value of inhibitory effect between neural fields. Dynamic Field Theory based approach to extend this line of work by incorporating biologically plausible layers that 1 , 3 modulate cognitive processes underlying pilot behaviour. 1 , The next section provides an overview of Dynamical Field Above given eq. 3 is the threshold function in form of a Theory. This is followed by a description of the physical sigmoid. aircraft model used in this study and the DFT based The DFT method allows model builders to implement architecture developed to model pilot behaviour. The paper networks of neural fields to create logical or spatiotemporal 154 decisions. One can adjust kernel parameters to modify a proportion of W with a coefficient of (1/cos( ). D: The spatiotemporal parameter. For example, the observation of Drag induced on the body of the aircraft due to the airspeed. the distance from an object can be represented by the : Angle of attack; i.e. the angle between the aircraft mean activity position of the field in the spatiotemporal axis and chord line (longitudinal axis of the aircraft) and the velocity the saliency of the activity amplitude of the same field. vector. Sideslip or skid effects are all neglected. The model described above is implemented in C++ and The Aircraft Model connected to our pilot model as a plugin which is A 3 degrees of freedom (3DoF) model was selected to implemented in the CEDAR framework (Lomp, 2013) model the aircraft in this study. The selected 3DoF model using a DFT approach. suits particularly well for understanding long-term navigation behaviour, and similar models have been used in The Architecture previous studies (e.g. Carretero, Nieto & Cordon, 2013). A The general architecture of our setup is the same as in 3DoF model neglects the moments inputs of the aircraft Figure 1. Unlike the crossover model that controls a single model, does not contain angular rates modelling and Euler parameter, the DFT pilot model is used to control multiple rates. Our model will include a point mass aircraft with a aircraft behaviours by using 2 control inputs (Figure 4). linear drag model. The mass of the aircraft is decreasing In this study, 3 axis behaviour of the aircraft model is proportional to the thrust used due to the fuel consumption. controlled via two inputs, namely the pitch and heading Below is the mathematical summary of the 3DoF aircraft correction. The model will focus on emulating the model. Since phugoids or dutch rolls are not aimed to be performance of a human pilot who intends to hold the captured in our application, a higher degree model is not pattern of flight stable. Only the pitch results will be considered. summarized in this paper. The roll control is left out of the scope of this paper. Figure 4 summarizes the control flow cos cos for each control parameter. sin cos sin cos sin sin 4 sin cos cos 0 Equation 4 contains the rate of change of the fundamental model parameters in time. The parameters used in Equation Figure 4. The architecture for the DFT Pilot Model. 4 are defined as follows. X: Longitudinal axis position of the aircraft (along body The intention layer, which is not shown in Figure 4, is used axis position). Y: Lateral axis position of the aircraft (cross to generate a constant behaviour to hold the aircraft at initial body axis position). h: Altitude of the aircraft upon flat attitude. The reason behind the use of the intention layer is earth Cartesian coordinate system (the normal axis to provide the pilot model a goal structure. In this position). V: The speed of the aircraft upon flat earth preliminary study we aimed to provide a DFT model that is Cartesian coordinate system. : Aircraft current heading deliberately oriented towards performing level flight. The angle. : Aircraft flight path angle. This angle is the angle architecture is used to control the aircraft on holding the between the flat earth surface and the aircraft velocity initial heading and altitude. Due to the unavailability of the vector. W: The weight of the aircraft plus the weight of the roll control channel, the aircraft roll attitude is not held fuel. In normal conditions, fuel is expected to decrease under control and left freely to oscillate due to the control proportional to the thrust applied by the engines to the behaviour. Since a 3DoF aircraft model is used, each aircraft. T: Constant aircraft thrust supplied by the engines. attitude channel can be assumed independent and harmless g: The gravitational acceleration. Flat earth model is used, g upon aircraft pitch performance. Since there is an intention can be assumed constant. wx, wy, wz: Components of wind layer to hold the aircraft in a selected path or pattern, our vector, i.e. the speed of wind in North and East direction DFT based architecture bears a strong similarity to the and finally the third one is in normal axis. : Aircraft pitch models proposed by Johnson and Pritchett (2002) and angle; the angle between the flat earth surface and the Kaneshige, Bull and Totah (2000). One major architectural aircraft nose. : Aircraft roll angle; i.e. the angle between difference between our approach and the existing models is the lateral axis of the aircraft and the flat earth surface. L: that our intention layer is formed by a neural field, whose The lift force. In this model L will be taken equal to a decaying time constant is adjusted to a numerically larger 155 value which is normally not used for decision fields, so that Another important consideration for pilot modelling is the activity of the field is almost non-decaying, even when that, whatever the controlled attitude (i.e. pitch or lateral), an input is not applied or an applied input is removed (see the pilot uses an angular parameter to control the Cartesian Appendix). Notice Amari equation is in an integro- behaviour of the aircraft. Thus, the pilot model should be differential form and time constants can be adjusted to able to make a transformation between coordinate systems shape the differential field produced by the equation. and compute the required angular correction to re-enter the Hence, the intention layer can be considered to function like flight path or hold the flight pattern. a working memory component. A block diagram of the pitch decision channel is given in Figure 5. Manual Altitude Hold Performance of a T‐38 Pilot at 20100 20 K ft 20092,5 Altitude, ft (Above Sea Level) 20050 20052,5 20000 19950 19942,5 19955 19952,5 19900 Figure 5. A representation of pitch decision channel. Figure 6. Manual altitude hold performance example from In the CEDAR implementation, the aircraft model’s flight tests output is connected to the perceptual neural fields (sensory fields used for observing the aircraft dynamics), which Results & Discussion transform the spatial parameters into neural field activations The DFT based pilot described above performed some so that they can be processed by the architecture. simulated flights completely autonomously and the results Figure 6 displays a graphical representation of the are qualitatively compared with actual flight test data performance of a T-38 Talon pilot trying to hold the aircraft obtained from T-38 flights. The behaviour of the human test at 20000 ft constant altitude manually for 2 minutes and 55 pilot exhibits an oscillatory behaviour around the targeted seconds. The plot indicates that there are various deviations flight pattern with plus or minus deviations. Some of these from the target altitude up to approximately 90 ft. Some of deviations are due to the dynamical behaviour of the T-38 these deviations may originate from the aircraft dynamics aircraft, which is expected. Especially in high altitudes the and some from the pilot. Accordingly, we deduce that a pilot was not able to follow the target altitude loss strictly. human pilot’s performance unified with the aircraft A similar behaviour is obtained with the DFT based pilot dynamics may result in up to 90 ft deviations at high model. Figure 7 shows the output obtained from a sample altitudes. The same Test Pilot showed a better performance run. with a maximum deviation of 53.2 ft when the holding task Figure 7 suggests that the DFT pilot is able to control was carried out at 8450 ft during the same flight. When the aircraft pitch attitude by limiting the aircraft altitude target altitude is 100 ft above ground, the same pilot made deviations. In the above example, the aircraft makes an error of maximum 7.5 ft. Therefore, we can deduce that constant decrease from 10.000 ft with a constant loss of as the aircraft is closer to the earth’s surface (i.e. as the altitude with 138 ft/step size (about 5 seconds). When the danger increases) during the holding task, the pilot naturally pilot model is started, it directly creates an input to stop the becomes more careful. decrease in altitude in an effort to protect the current flight A similar analysis may be performed for lateral hold path. As the plot indicates, the aircraft altitude oscillates performance. Our analysis on flight test data records have around the targeted altitude under the control of the pilot shown that the same pilot have a performance of pattern model, which is trying to keep the altitude constant. Notice holding on lateral navigation with a maximum error of the model reaction times and amplitudes can be adjusted via 29.504 ft. Lateral performance is hold out of scope for using the dynamic fields’ time constant (shown in equation current study. 1), sensor layer tolerances and excitory or inhibitory field In this study we tried to hold our 3 DoF aircraft model at parameters. level flight and our aim was to hold the deviations on or Overall, our preliminary results suggest that the pitch below the deviations observed in human pilot performance attitude performance of our DFT based pilot model is data. One important point is that the given deviations may comparable to the human pilot’s performance. Human pilots be dependent on the pilot’s experience. However, since the do not make any trigonometric computations to acquire the identity and the flight experience of the pilots were not cross track component of the distal deviation to obtain the available to the researchers, we cannot incorporate the required angle to hold the pitch attitude of the plane. The variability due to different expertise levels in our study. process of the computation happens naturally, embodied and embedded in a continuous way. The continuity in the 156 inner and outer loops of pilot control in the proposed DFT References architecture captures the dynamic and embodied nature of Amari S., (1977). “Dynamics of pattern formation in lateral the human pilot’s actions. Therefore, DFT seems to be a inhibition type neural fields”. 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