Keywords

Introduction

Modern flight control and navigation systems are characterized by two features: (1) they employ fly-by-wire controls and (2) they introduce extensive automation support into the cockpit, ranging from complex augmented flight control systems in manual control modes to powerful flight management computers and autopilots that assume responsibility for most flight control tasks (and which may operate the aircraft in ways that are difficult for pilots to monitor and understand). These modern systems leave the pilot in a supervisory control mode most of the time. Consequently, crew members monitor, supervise, plan, and, in essence, serve as information managers. The level of supervisory control tasks can be different from conventional command control in which the operator issues auto-pilot commands (“set altitude”, “set airspeed,” etc.) and task-level control in which the operator issues commands such as “line formation,” “trail formation,” etc. Although civilian pilots have experience flying their aircraft manually, they are seldom in active, direct control of the aircraft. However, if a failure or unexpected upset occurs, they are required to assume control immediately. As for military pilots, they (especially fighter pilots) use manual control in the majority of piloting tasks.

The effective use of manned flight vehicles has always required a satisfactory match of vehicle characteristics (which include vehicle dynamics, control manipulators, displays) with the human pilot’s characteristics as a flight controller. The provision of proper vehicle handling qualities by the flight control system and display and manipulator design has often posed serious problems which the vehicle system engineer must solve.

Their solutions require the knowledge of mutual interactions between the pilot and the vehicle. The understanding of such interactions requires a mathematical theory which can be used to explain known findings and to predict new ones. For handling qualities, such theory is based on the methods of control engineering and treats the pilot-vehicle system as a closed-loop (in general, a multiloop) entity. The sine qua non of the theory is a model of pilot dynamic characteristics in a form suitable for application using relatively conventional control engineering techniques. An adequate description of a pilot’s dynamics response characteristics is not easily obtained because of the pilot’s inherent adaptability and capacity for learning.

Main Variables of the Pilot-Aircraft System

The pilot-aircraft manual control system, shown in Fig. 1, is characterized by a number of variables. The main group of these variables is the so-called task variables which comprise all the system inputs (command inputs i(t), disturbances d(t)) and control system elements (display, manipulators, and controlled element dynamics, which is defined by the aircraft frame and flight control system dynamics).

Pilot-Vehicle System Modeling, Fig. 1
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Pilot-aircraft system

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A specific feature of pilot-aircraft systems is the dependence of the piloting task on the task variables. For different piloting tasks, these variables or their parameters differ too. Stability of the closed-loop system is always a necessary, though not sufficient, criterion for the control strategy. Consequently, the pilot’s dynamics are profoundly affected by the display and controlled element dynamics, because his response must be adapted to provide the necessary loop stability and accuracy. The characteristics of the other task variables (i(t), d(t)), related to the mission and control strategy, also exert direct influence on the pilot dynamics, although their effects are more in the nature of adjustment and emphasis than of changes in fundamental form.

These variables constitute an enormous range of possible conditions and piloting tasks. In addition to the task variables, the other groups of variables–procedural (p–instructions, training schedule order of presentation of trials etc.), environmental (\(\epsilon\)–illumination, vibration, temperature, and so forth), pilot centered (σ–physical condition, motivation etc.)—have less influence on pilot-aircraft system features.

Types of Pilot-Aircraft Systems

The structure of the pilot-aircraft system depends on the piloting task. Some tasks (for example, the pitch tracking task) can be interpreted with the help of the single loop compensatory block diagram. In that case the pilot perceives only the error signal, \(y(t) = e(t) = i(t) - x(t)\), and control c(t). Figure 1 is the pilot pitch control command. The other tasks require more complicated descriptions. For example, the landing task is a multiloop compensatory task, where the inner loop closed by the pilot is the pitch control loop. Some piloting tasks are multichannel control tasks, in which the pilot perceives several visual stimuli (for example pitch angle and bank angle) and generates commands in several channels too. Pilots also perceive stimuli of different sensing modalities (visual, vestibular, kinesthetic). In cases where these influence his actions, the multimodality of the pilot-aircraft system has to be analyzed.

A great many past experiments in which human dynamic measurements were taken have been conducted for investigation of compensatory tracking tasks. Some practical piloting tasks (e.g., aim-to-aim tracking in case when the target flies against a background of clouds) correspond to pursuit conditions. In that case, the pilot perceives the information about the error signal e(t) and the input signal i(t).

In many piloting tasks the single loop compensation system defines the main features of more complicated types of pilot-aircraft systems and its flying qualities. Therefore, this type of the system has been investigated in more depth.

Pilot Control Response Characteristics

The most obvious aspect of human dynamic behavior in a manual control task is the pilot’s control actions within that task. When the key variables are fixed and the signals in the control loop are approximately time stationary over an interval of interest, the pilot-vehicle system can be presented as a quasi-linear system. In that case, the pilot response can be presented by two components: the pilot-describing function, W p (j ω), taking into account the linear portion of pilot response on the stimulus e(t), and remnant n e (t), which takes into account all nonlinear, nonstationary effects of pilot behavior (Fig. 2).

Pilot-Vehicle System Modeling, Fig. 2
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Quasi-linear paradigm for the human pilot

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In the majority of piloting tasks n e (t) is a stationary process characterizing the remnant spectral density \(S_{n_{e}n_{e}}(\omega )\) (McRuer and Krendel 1974). The pilot control response characteristics W p (j ω) and \(S_{n_{e}n_{e}}(\omega )\) depend explicitly on the task variables (McRuer and Jex 1967; McRuer et al. 1968). In much experimental research, the technique for identification of these characteristics was based on the use of an input signal consisting of the sum of non-harmonically-related sine waves with cut off frequency ω i at 1.5, 2.5, and 4 rad/s and different controlled element dynamics (Allen and Jex 1972; Magdaleno 1972; Shirley 1969).

In addition to control response, other types of pilot’s responses also characterize his behavior: physiological (F) and psychophysiological ψ responses (Fig. 1). For one of the psychophysiological response characteristics, the pilot opinion rating (PR) is widely used in experimental investigations as well as for the measurement of pilot control response. Pilot opinion ratings are defined by specialized scales (e.g., the Cooper-Harper scale (Cooper and Harper 1969)).

Modeling Pilot Behavior in Manual Control

Experimental investigations have demonstrated a specific regularity: for a variety of forcing functions and controlled elements the slope of the open-loop describing function \(\left \vert W_{\mathrm{OL}}(j\omega )\right \vert\) vs frequency was unity, i.e., −20 dB/dec in the region of the crossover frequency ω c (McRuer and Jex 1967). This observation has led to the conclusion that near ω c , WOL(j ω) can be presented by the “crossover model” (McRuer and Jex 1967)

$$\displaystyle{W_{\mathrm{OL}}(j\omega ) = W_{p}(j\omega ) \cdot W_{C} = \frac{\omega _{c}} {j\omega }e^{-j\omega \tau _{e} }}$$

This model has two parameters:

$$\displaystyle\begin{array}{rcl} & \omega _{c} =\omega _{co}(\omega _{c}) + \Delta \omega (\omega _{i})& {}\\ & \tau _{e} =\tau _{o}(\omega _{c}) + \Delta \tau (\omega _{i}) & {}\\ \end{array}$$

For the controlled element dynamics \(W_{C} = \frac{K} {s(Ts+1)}\), the increase of constant T leads to an increase of τ0 and a decrease of ωC0. The empirical dependences of \(\Delta \omega _{c}\) and \(\Delta \tau _{e}\) on ω i obtained for the rectangular form of input spectrum are the following: \(\Delta \omega = 0.18\omega _{i}\), \(\Delta \tau = -0.07\omega _{i}\).

McRuer proposed several modifications of the open-loop system crossover and pilot describing function models (McRuer and Krendel 1974). One of the simplest ones (used widely in many researches) which might be recommended for description of pilot-aircraft system characteristics in the crossover frequency range is the following

$$\displaystyle{W_{p}(j\omega ) = K_{p}\frac{T_{L}j\omega + 1} {T_{1}j\omega + 1} e^{-j\omega \tau _{e} }}$$

The selection of the parameters K p , T L , and T I is carried out by using “adjustment rules” so that the closed-loop system conforms to experimental frequency response characteristics. These adjustment rules reflect the main features of pilot behavior – adaptation and optimization.

A more complicated model of pilot describing function (“structural model”) was offered by R. Hess (1979, 1984). It takes into account the additional inner loop generated by the pilot as a result of his response to the kinesthetic cue (Fig. 3). The modification of this model (Efremov and Tjaglik 2011) demonstrated good agreement with the pilot describing function as measured in experiments. One of the features of this modified model is the criterion used for the parameter optimization: or \(I =\min [\sigma _{e}^{2} +\beta \sigma _{ n}^{2}]\). This procedure requires the knowledge of the pilot remnant spectral density. For the single loop system, such a model was developed by Levison et al. (1969).

$$\displaystyle{S_{n_{e}n_{e}}(\omega ) = 0.01\pi \frac{\sigma _{e}^{2} +\sigma _{ \dot{e}}^{2}T_{L}^{2}} {1 + T_{L}^{2}\omega ^{2}} }$$

In the limited number of researches, the classic approach to pilot modeling considered above was used for more complicated types of the pilot-aircraft system, when the pilot perception of motion cues was taken into account (multimodality system (Hess 1990)) or for a case of the multiloop pilot-aircraft system (Stapleford et al. 1967).

Pilot-Vehicle System Modeling, Fig. 3
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Pilot structural model

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A different approach to pilot behavior modeling was developed by Kleiman et al. (1970). It is based on the modern optimal control theory and assumes that the pilot’s goal is to minimize the cost function:

$$\displaystyle{I =\mathop{ \lim }\limits _{T} \frac{1} {T}\int _{0}^{T}(xQx^{T} + uQ_{ c}u^{T} +\dot{ u}G_{ c}\dot{u}^{T})dt}$$

The model takes into account the main pilot limitation parameters: time delay in perception, the observation and motor noises, and the neuromuscular dynamics.

The predictive part of the model consists of the optimal controller (\(-L^\ast\)), Kalman filter and predictor (Fig. 4). The software for definition of these elements allows the use of this model for the different types of the pilot-aircraft systems.

Pilot-Vehicle System Modeling, Fig. 4
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Optimal pilot model

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The classical and optimal pilot behavior models have been applied widely for different manual control tasks: the development of alternative criteria for flying qualities (Efremov et al. 1998; Neal and Smith 1971), the flight control system (Schmidt 1979) and display design (Klein and Clement 1973), the analysis of reasons for pilot-induced oscillation (McRuer 1997) and the development of means for its suppression (Efremov 1995), and many others.

In some of the researches, attempts have been made to find the relationship between the parameters of the closed-loop system, pilot control response characteristics, and pilot opinion ratings. The technique developed in these researches is called the “paper pilot technique” (Anderson 1970). The following modification of this technique has enabled a close match between the results of mathematical modeling (PR, T L , accuracy, etc.) of the different types of the pilot-aircraft system and the results of experimental investigations (Efremov and Ogloblin 2006).

Summary and Future Directions

Pilot behavior has been studied extensively for single-loop stationary manual control tasks. Two approaches to the mathematical modeling of the pilot behavior have been developed: classical and optimal control. Both of them have produced good agreement with experimental results. The discussed models describe one of the main features of the pilot adaptation – “parameter adaptation”, when a change of any task variable causes a change of human operator control response characteristics. Only a limited number of experimental investigations have been carried out for more complicated cases: multiloop and multimodality pilot-aircraft closed-loop systems. Broader investigations are necessary in the future to obtain accurate pilot mathematical models for these cases. Future investigation in pilot behavior modeling area is also necessary for better formulations of other aspects of pilot adaptation:

  • “Structural adaptation”, when the pilot selects the loops and the best type of behavior (compensatory, pursuit, etc.) appropriate for the different task variables and, in the case of the flight control system, changes in dynamics.

  • “Goal adaptation”, when a change of the piloting task or a failure in the controlled element dynamics is accompanied by a change of the goals.

Other future directions in pilot modeling are the development of models to predict the results in the case of sharp changes of controlled element dynamics, to optimize the controlled element dynamics, to define the relationship between the pilot control response characteristics and his opinion rating in different piloting tasks, to get new criteria for the handling qualities, prediction of pilot-induced oscillations, and to solve many other manual control problems.

Cross-References