Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Adaptive Human Pilot Models for Aircraft Flight Control

  • Ronald A. HessEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_100123-1


Loss-of-control incidents in commercial and military aircraft have prompted a renewed interest in the manner in which the human pilot adapts to sudden changes or anomalies in the flight control system which augments the fundamental aircraft dynamics. A simplified control-theoretic model of the human pilot can be employed to describe adaptive pilot behavior in the so-called primary control loops and to shed light upon the limits of human control capabilities.


Control-theoretic pilot models Pilot crossover model Aircraft loss of control Single and multi-axis pilot control 

An Introduction to Control-Theoretic Models of the Human Pilot

A control-theoretic model of the human pilot refers to a representation in which the pilot is modeled as an element in a control system. Typically, this means that the dynamics of the pilot are represented by a transfer function, and this transfer function is placed in a block diagram where the pilot’s control inputs affect the aircraft’s responses. In its simplest form, such a representation is shown in Fig. 1.
Fig. 1

A block diagram of a control-theoretic model of the human pilot in a single-loop tracking task. Both Yp and Yc are represented by transfer functions

As a more concrete representation, “command” might indicate a command to the pilot/aircraft system in the form of a desired aircraft pitch attitude. “Control” might represent an aircraft elevator motion produced by the pilot, whose dynamics are represented by the linear, time-invariant transfer function Yp(s). “Controlled element” is the pertinent aircraft transfer function, Yc(s) representing the manner in which aircraft pitch attitude (“response”) is dependent upon the pilot’s control input.

Perhaps the most definitive representation of human pilot dynamics in tasks such as that shown in Fig. 1 is the “crossover” model of the combined human pilot and controlled element (McRuer and Krendel 1974), shown in Eq. 1.
$$\displaystyle \begin{aligned} \mathrm{Y}_p (s)\mathrm{Y}_c (s)\approx \omega_c \frac{e^{-\tau_e s}}{s} \end{aligned} $$
This is called the crossover model of the human pilot because it is a neighborhood of the frequency region where |Yp(jω)Yc(jω)| ≈ 1.0, where the model is valid. Figure 2 shows a typical measured YpYc(s) plotted on a Bode diagram and compared to the crossover model. The controlled element dynamics in this case were Yc = Kc/s (McRuer et al. 1965). The phase lags apparent for ω > ωc are attributable to the time delay τe in Eq. 1 and limit the magnitude of an open-loop crossover frequency for stable closed-loop operation of the pilot/aircraft system.
Fig. 2

A Bode diagram of the measured YpYc in a single-loop tracking task is shown. In this example, Yc = Kc/s

A more complete discussion of linear, time-invariant control-theoretic models of the human pilot can be found in Hess (1997).

A Simplified Pursuit Control Model of the Human Pilot

Pilot control behavior in command-following tracking tasks is often categorized as either compensatory or pursuit depending upon the type of visual information available to the pilot (Krendel and McRuer 1960; Hess 1981). Figure 3 compares two cockpit displays, one providing compensatory information (error only) and one providing pursuit information (command and error). Figure 4 is a block diagram representation of the pursuit tracking pilot model to be utilized herein (Hess 2006).
Fig. 3

Two cockpit displays can be created showing the difference between compensatory and pursuit tracking formats

Fig. 4

A pursuit tracking model of the human pilot from Hess (2006). In pursuit tracking behavior, vehicle output and output rate are assumed to be directly available to the pilot, here represented by Kp, Kr, and Gnm

It should be emphasized that the analysis procedure to be described utilizes a sequential loop closure formulation for piloted control. For example, in Fig. 1 the command or input may be an altitude command in which the pilot is using pitch attitude as a primary loop closure to control aircraft altitude. The element denoted Gnm in Fig. 4 represents the simplified dynamics of the neuromuscular system driving the cockpit inceptor. Further information on neuromuscular system models can be found in McRuer and Magdaleno (1966). In the model of Fig. 4, Gnm is given by
$$\displaystyle \begin{aligned} \mathrm{G}_{nm} =\frac{10^2}{s^2+2(.707)s+10^2} \end{aligned} $$
Figure 5 shows the manner in which Fig. 4 can be expanded to include such sequential closures. In Fig. 5, the “vehicle with primary loop closed” would simply be the M/C transfer function in Fig. 4. As discussed in Hess (2006), the adjustment rules for selecting Kro and Kpo are as follows: Kro is chosen as the gain value that results in a crossover frequency for the transfer function \(\mathrm {K}_{ro} \cdot \left [ {\dot {\mathrm {M}}_o /\mathrm {C}} \right ]\) equal to that for the adjacent inner loop and M/E in Fig. 4. Kpo is chosen to provide a desired open-loop crossover frequency in the outer-loop transfer function Mo/Eo. Nominally, this crossover frequency will be one-third the value for the crossover frequency in the inner loop of Fig. 4.
Fig. 5

A multi-loop extension of the pilot model of Fig. 4. The block “vehicle with primary loop closed” implies that the pilot model of Fig. 4 has been used in a primary-loop closure

A distinct advantage of the pilot model of Fig. 4 lies in the fact that only two parameters, the gains Kp and Kr, are necessary to implement the model in a primary control loop. Hess (2006) demonstrates the manner in which this is accomplished. Basically, Kr is chosen so that the Bode diagram of the transfer function \(\frac {\dot {\mathrm {M}}}{\mathrm {R}}(s)\) exhibits a 10 dB amplitude peaking near 10 rad/s. Kp is then chosen to yield a 2.0 rad/s crossover frequency in the Bode diagram of \(\frac {\mathrm {M}}{\mathrm {C}}(s)\). Hess (2006) demonstrates the ability of the two-parameter pilot model to reproduce pilot crossover model characteristics for a variety of vehicle dynamics in Fig. 4. The fact that only two gain values are necessary to create the pilot model suggests that extending the representation of Fig. 4 to encompass adaptive pilot behavior may be warranted.

A Rationale for Modeling the Adaptive Human Pilot

Loss of control is the leading cause of jet fatalities worldwide (Jacobson 2010). Aside from their frequency of occurrence, aviation accidents resulting from loss of control seize the public’s attention by yielding large number of fatalities in a single event. The rationale for modeling the human pilot in potential loss of control accidents can be best summarized as follows (McRuer and Jex 1967):
  1. (1)

    To summarize behavioral data

  2. (2)

    To provide a basis for rationalization and understanding of pilot control actions

  3. (3)

    To be used in conjunction with vehicle dynamics in forming predictions or in explaining the behavior of pilot-vehicle systems

To this list might be added: to be used in concert with human-in-the-loop flight simulation to offer a fundamental rationale for aircraft loss of control.

Modeling the Adaptive Human Pilot

Studies devoted to modeling the human pilot’s adaptive capabilities date from the mid-1960s. See, for example, Elkind and Miller (1966), Weir (1968), Young (1969), Niemela and Krendel (1974), and Hess (2016). As used herein, “adaptive behavior” will refer to the human pilot’s ability to adopt dynamic characteristics that allow control of sudden changes in the dynamics of the aircraft being controlled. This is in contrast to a human “learning” to control a dynamic system through a training process. Figure 6 from Hess (2016) shows the fundamental adaptive structure of the adaptive human pilot in a primary control loop.
Fig. 6

Modifying the model of Fig. 4 to enable modeling of pilot adaptive behavior

In Hess (2016) the adaptive logic governing changes in Kp and Kr are defined. The reader is referred to that document for specifics. The logic is based upon certain guidelines:
  1. (1)

    The adjustments to Kp and Kr must be predicated upon observations that can easily be made by the human pilot.

  2. (2)

    The logic driving the adjustments must be predicated on information available to the human pilot.

  3. (3)

    The post-adapted pilot models must follow the dictates of the crossover model of the human pilot (McRuer and Krendel 1974).

  4. (4)

    Performance improvement with adaptation must occur relatively quickly. This guideline is supported by the research reported by Hess (2009).

It should be noted that in Hess (2016), the adaptive pilot model is not limited to one axis of control. Examples in which the pilot is controlling two axes, e.g., aircraft pitch and roll, are presented.

An Example of Adaptive Pilot Modeling

The following example deals with piloted control of a hovering helicopter. The helicopter dynamics and flight control system are taken from Hall and Bryson (1973). Two vehicle axes are being controlled by the pilot, pitch attitude (θ), and roll attitude (φ). Random-appearing sums of sinusoids provided commands to the pitch and roll axes (θc and φc). Of particular importance is the fact that control response coupling was in evidence in the vehicle model, i.e. inputs to control pitch attitude also affected roll attitude and vice-versa. The vehicle “failures” were created by reducing the gain of the pitch and roll stability augmentation systems by a factor of 10 and reducing the sensitivity of the cockpit inceptors by a factor of 5. The failures were introduced at t = 50 s in a 120 s simulation conducted using MATLAB Simulink®. Details can be found in Hess (2016).

Figure 7 shows the pitch and roll attitude responses before and after the failure with the dashed line representing the pitch and roll command (θc, φc) and the solid lines representing the corresponding pilot/vehicle responses. Figure 8 shows the adaptive pilot model gains Kp and Kr for each loop.
Fig. 7

Simulink® simulation of helicopter pitch and roll responses before and after system “failure.” Note that, although there have been significant reductions in stability augmentation gains and control inceptor sensitivities, tracking performance remains reasonably constant

Fig. 8

Adaptive pilot model gains in the pitch and roll attitude control loops. As might be expected, the sharp reduction in control and inceptor sensitivities in the failure is accommodated by the adaptive model by increases in Kp and Kr in each control axis. Of equal importance is the fact that crossover model characteristics were in evidence when the Kp and Kr assumed their final values, as they were at the initiation of the adaptive changes

Recommended Reading

An excellent textbook aimed at advanced undergraduates and graduate student interested in manual control of dynamic systems has been authored by Jagacinski and Flach (2003).



  1. Elkind JI, Miller DC (1966) Process of adaptation by the human controller. In: Proceedings of the second annual NASA-university conference on manual controlCrossRefGoogle Scholar
  2. Hall WE Jr, Bryson AE Jr (1973) Inclusion of rotor dynamics in controller design for helicopters. J Aircr 10(4):200–206CrossRefGoogle Scholar
  3. Hess RA (1981) Pursuit tracking and higher levels of skill development in the human pilot. IEEE Trans Syst Man Cybern SMC-11(4):262–273CrossRefGoogle Scholar
  4. Hess RA (1997) Feedback control models – manual control and tracking. In: Salvendy G (ed) Handbook of human factors and ergonomics, 2nd edn, Chap. 38. Wiley, New YorkGoogle Scholar
  5. Hess RA (2006) Simplified approach for modelling pilot pursuit control behavior in multi-loop flight control tasks. In: Proc Inst Mech Eng J Aerosp Eng 220(G2):85–102Google Scholar
  6. Hess RA (2009) Modeling pilot control behavior with sudden changes in vehicle dynamics. J Aircr 46(5): 1584–1592CrossRefGoogle Scholar
  7. Hess RA (2016) Modeling human pilot adaptation to flight control anomalies and changing task demands. J Guid Control Dyn 39(3):655–666CrossRefGoogle Scholar
  8. Jacobson SR (2010) Aircraft loss of control causal factors and mitigation challenges. In: AIAA guidance navigation and control conference, 2–5 Aug 2010Google Scholar
  9. Jagacinski RJ, Flach JM (2003) Control theory for humans: quantitative approaches to modeling performance. Lawrence Erlbaum Associates, MahwahGoogle Scholar
  10. Krendel ES, McRuer DT (1960) A servomechanisms approach to skill development. J Frankl Inst 269(1): 24–42CrossRefGoogle Scholar
  11. McRuer DT, Jex HR (1967) Review of quasi-linear pilot models. IEEE Trans Hum Factors Electron HFE-8(3):231–249CrossRefGoogle Scholar
  12. McRuer DT, Krendel E (1974) Mathematical models of human pilot behavior, AGARDograph No. 188Google Scholar
  13. McRuer DT, Magdaleno RE (1966) Experimental validation and analytical elaboration for models of the pilot’s neuromuscular subsystem in tracking tasks, NASA CR-1757Google Scholar
  14. McRuer D, Graham D, Krendel E (1965) Human pilot dynamics in compensatory systems. Air Force Flight Dynamics Lab, report AFFDL-TR-65-15Google Scholar
  15. Niemela R, Krendel ES (1974) Detection of a change in plant dynamics in a man-machine system. In: Proceedings of the tenth annual NASA-university conference on manual controlCrossRefGoogle Scholar
  16. Weir DH (1968) Applications of the pilot transition response model to flight control system failure analysis. In: Proceedings of the fourth annual NASA-university conference on manual controlGoogle Scholar
  17. Young LR (1969) On adaptive manual control. Ergonomics 12(4):292–331CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.University of CaliforniaDavisUSA

Section editors and affiliations

  • Tariq Samad
    • 1
  1. 1.Technological Leadership InstituteUniversity of MinnesotaMinneapolisUSA