# Adaptive Human Pilot Models for Aircraft Flight Control

**DOI:**https://doi.org/10.1007/978-1-4471-5102-9_100123-1

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## Abstract

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.

## Keywords

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

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 Y_{p}(s). “Controlled element” is the pertinent aircraft transfer function, Y_{c}(s) representing the manner in which aircraft pitch attitude (“response”) is dependent upon the pilot’s control input.

*crossover model*of the human pilot because it is a neighborhood of the frequency region where |Y

_{p}(j

*ω*)Y

_{c}(j

*ω*)| ≈ 1.0, where the model is valid. Figure 2 shows a typical measured Y

_{p}Y

_{c}(s) plotted on a Bode diagram and compared to the crossover model. The controlled element dynamics in this case were Y

_{c}= K

_{c}/s (McRuer et al. 1965). The phase lags apparent for

*ω*>

*ω*

_{c}are attributable to the time delay

*τ*

_{e}in Eq. 1 and limit the magnitude of an open-loop crossover frequency for stable closed-loop operation of the pilot/aircraft system.

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

*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).

_{nm}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, G

_{nm}is given by

_{ro}and K

_{po}are as follows: K

_{ro}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. K

_{po}is chosen to provide a desired open-loop crossover frequency in the outer-loop transfer function M

_{o}/E

_{o}. Nominally, this crossover frequency will be one-third the value for the crossover frequency in the inner loop of Fig. 4.

A distinct advantage of the pilot model of Fig. 4 lies in the fact that only two parameters, the gains K_{p} and K_{r}, are necessary to implement the model in a primary control loop. Hess (2006) demonstrates the manner in which this is accomplished. Basically, K_{r} 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. K_{p} 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

- (1)
To summarize behavioral data

- (2)
To provide a basis for rationalization and understanding of pilot control actions

- (3)
To be used in conjunction with vehicle dynamics in forming predictions or in explaining the behavior of pilot-vehicle systems

## Modeling the Adaptive Human Pilot

_{p}and K

_{r}are defined. The reader is referred to that document for specifics. The logic is based upon certain guidelines:

- (1)
The adjustments to K

_{p}and K_{r}must be predicated upon observations that can easily be made by the human pilot. - (2)
The logic driving the adjustments must be predicated on information available to the human pilot.

- (3)
The post-adapted pilot models must follow the dictates of the crossover model of the human pilot (McRuer and Krendel 1974).

- (4)
Performance improvement with adaptation must occur relatively quickly. This guideline is supported by the research reported by Hess (2009).

## 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 (*θ*_{c} and *φ*_{c}). 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).

*θ*

_{c},

*φ*

_{c}) and the solid lines representing the corresponding pilot/vehicle responses. Figure 8 shows the adaptive pilot model gains K

_{p}and K

_{r}for each loop.

## 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).

## Cross-References

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