INTRODUCTIONThe earliest study of the human operator as a linear servomechanism is that of Tustin [2] who proposed that, despite amplitude nonlinearities, temporal discontinuities and haphazard fluctuations, there might be an "appropriate linear law" that would describe the main part of the operator's behavior.Insight from servomechanical design led McRuer and Krendel [3] to develop the ubiquitous human Crossover Model (CM), which within its framework accounts for how, and why, the human operator adapts to the controlled plant dynamics during compensatory tracking.With the crossover model, a variable pilot time delay can be used to explain phenomena such as increased highfrequency phase lag associated with increased amounts of error lead equalization.Similarly, ratchet (sustained high frequency, small amplitude pilot-vehicle system oscillations) can be ascribed to variable neuromuscular damping (first proposed by Johnston and McRuer in 1987 [4], and later investigated by Bachelder in 2003 [5] using wave-lets).In 1976 Smith [6] propounded that inner-loop rate feedback supported control of the error loop during compensatory tracking, whereby the rate of the controlled system's output was visually perceived by the operator.This manner of feedback was subject to two key constraints: 1) the bandwidth and noise associated with human visual sensing of rate, and 2) the requirement that the ratio of disturbance-to-system output is low, otherwise the error rate that the operator perceives will not correspond to system output rate.A realizable method for perceiving rate for use with inner-loop feedback was first posed by Hess in 1978 [7], whereby the operator employs kinesthetic perception of control rate and an internal model of system response to that rate.This approach was later incorporated into Hess' Structural Model of the human pilot [1,8].In 1969 Gaines [9] wrote "Models capable of representing behavior over large domains are particularly important in the study of learning systems where the mode of be-havior is expected to vary widely with experience.A variety of models is required, and within the modeling schemata there must be scope for a sufficient variety to provide adequate matches during all phases of learning."Building on Krendel and McRuer's [10] successive organization of perception (SOP) model for tracking skill development, Hess' pilot Structural Model provides a concise, integrated architecture for describing compensatory, pursuit, precognitive, and offnominal behavior.The work presented here extends Hess' Structural Model to account for and reproduce pilot compensatory behavior when different control styles are used.It lays the groundwork to explore how pilot control technique (i.e.pulsive versus continuous) influences the interplay between internal costing and the nominal values of a parameter set that defines pilot behavior. STRUCTURAL MODEL OF THE HUMAN PILOTIn 1978 Hess [7] proposed a model (see Fig. 1) for human compensatory tracking whose essential features included an outer loop operating on error (e), an inner loop feedback operating on stick position (δ), pilot elements that equalize the Y that transforms the physical system error to the visually displayed error being tracked.A disturbance d is added to the vehicle output m, and the negative of this is the error that the operator is attempting to null.According to McRuer and Krendel [3] the neuromuscular element can be approximated by Eqn (1), where n  and n  represent the natural fre- quency and damping ratio, respectively.()1) 2 2 ( 2 2 n n n n n s Yp       With the inner loop of Fig. 1 Fig. 1.Quasilinear dual-loop model of the human controller [7].Typically, the main function of the inner-loop is to provide vehicle output rate feedback and improve stability and precision.Hess proposed (see Fig. 1) that the neuromuscular force output is perceived and transformed into an estimate of vehicle output rate using an internal model of the manipulator and vehicle dynamics suite.For acceleration command dynamics, this process effectively requires the pilot to integrate the force output (in the dual-loop model shown the pilot first perceives the force rate, and integrates this twice).Hess hypothesized that proportional or derivative control in the feedback loop can be conducted using direct information from the muscle spindles and Golgi tendon organs [11], but integral control does not have analogous information and requires the operation to employ higher level cognitive processing [7].Thus when controlling acceleration command systems, the pilot will tend to generate a pulsive force output rather than a continuous one, since a pulse is the least difficult of all waveforms to integrate (an impulse is even easier, but is a variation of the pulse).While the pulse is held, the system response is the inverse Laplace transform (L -1 ) of the integral of the vehicle dynamics (for acceleration command system, this would be L -1 (K/s 3 )).Following the pulse, the system response is simply the inverse Laplace transform of the vehicle dynamics, L -1 (K/s 2 )."Ease of integrability" can be generally interpreted in a physiological sense as applying to those waveforms whose integration requires a minimum of higher-level activity in the central nervous system [12].As an operator becomes familiar (gains expertise) with the vehicle and manipulator, the transformation between force output and vehicle output rate should reduce to a one-step process.In his revised Structural Model [1], Hess reflects this simplification with a proprioceptive feedback element, PF Y , shown in Fig. 2.This element receives stick position (δM), and depending on the vehicle dynamics in the vicinity of the crossover frequency, PF Y will assume one of the forms shown in In manual control theory, proprioception refers to the monitoring of body's actionsexcluding the visual and vestibular systems.The kinesthetic system is a subsystem of the proprioceptive system, dedicated to the perception of position and movement.In this paper proprioceptive and kinesthetic input will be used interchangeably.A gain e K serves as the pilot element acting on error, and the neuromuscular and feel system elements are respectively denoted by Yp in Fig. 1.While the vari- ous other details of the Structural Model (Fig. 2) are described in [1], an element of key importance is the central processing time delay o  , which for a given pilot is approximated as vehicle-invariant.This represents a major simplification to the crossover model's effective time delay, which was used to explain (but could not predict) task and vehicle-dependent high frequency phase loss.[13].The vehicle dynamics used in the following example cases will either be acceleration or jerk command dynamics, consequently PF Y for both will be a first-order lag (see Table 1). Fig. 2. Structural Model of the Human Pilot WORKLOAD EXPERIMENTAn experiment was conducted that investigated the relationship between aircraft input/output states and pilot workload.Four command vehicle dynamics (proportional, rate, acceleration, jerk), vehicle gains (vehicle sensitivity to input), and display gains (display sensitivity to error) were used with a lateral station-keeping using a compensatory display, where a random forcing function continuously disturbed ownship's position.Fig. 4a shows a representation of the stationkeeping task and the display (KD), pilot (YP) and vehicle (YV) components of the closed-loop sys-tem.Fig. 4b gives the range of conditions within each component that were tested.The jerk condition for the vehicle dynamics (fourth condition listed for YV), contains a pole p whose location was varied.Twenty-three display configurations were tested with each subject using various combinations of the conditions shown in Fig. 4b.The configurations were selected to maximally span the Bedford rating over all vehicle command dynamics.Since pilot proficiency with any test condition was not a factor in this experiment, pilots were given two practice of each vehicle dynamic type (proportional, rate, acceleration, jerk) prior to testing. V Y , 2 s K V , s K V , V K 2 ) ( s p s K V      60 30, 10, , 5  V K   5 2, , 1  p   32 8, 4, 2, , 5 0.  D KOne may be tempted to think that the display gain and the vehicle gain are effectively interchangeable and the same gains from the pilot's vantage point.The following example will serve to disprove this common misnomer.If the pilot's input is zero, the disturbance is perceived through the display gainthe vehicle gain does not come into play at all.Based on his/her control activity and quiescence, a pilot learns to decouple the effects of the display gain from the vehicle gainthus decoupling aircraft motion due to disturbance from pilot-commanded vehicle motion.Four male participants took part in the study.Three were Experimental Test Pilots (graduates of Navy Test Pilot School) with 1,900, 1,900, and 2,450 rotary wing flight hours.The fourth participant had logged 800 hours of rotary wing flight time.Ownship error relative to the target location was displayed on a laptop monitor (see Fig. 5), and the pilot attempted to minimize the error using a gamepad joystick (Logitech Dual Action gamepad).The Bedford rating scale [14] was used to subjectively score each pilots spare capacity at the end of each 60-second tracking run.Dependent qualitative variables were: stick posi-tion, rate and acceleration, stick position reversals, display error, rate, and acceleration.The positional disturbances imposed on the helicopter were designed to be both realistic and a diagnostic probe for pilot control behavior.Composed of a sum of 11 non-harmonically-related sine waves, the disturbance was perceived by the pilot as a random processthe result, however, was that the pilot's control response power resided largely at the same frequencies contained in the input disturbances.Sum-of-sines (SOS) is a standard approach that has been employed by the manual control research community over many decades.The disturbance time history is shown in Fig. 5 (it ranged from approximately -1 to 3 feet, with a standard deviation of 1 foot).The results of the experiment are given in [15].The damped frequency of the gamepad joystick was approximately 200 rad/sec, well above the neuromuscular mode.Thus the feel system FS Y in Fig. 3 can be considered unity for this ex- periment. PULSIVE MODEL DEVELOPMENTIn the experiment two pilots were observed to use different pulse techniques when controlling the acceleration and jerk command dynamics.Fig. 6a shows the pulse width modulation (PWM) technique, where the gamepad joystick was rapidly deflected to the stops and released, so that pulse firing and pulse width were predominantly the only two control variables.In digital control PWM creates a square wave, a signal switched between on and off, to create analog results with digital means.Fig. 6b shows the pulse widthamplitude modulation (PWAM) technique (coined by the author), where stick motion consists of pulses for motion that reaches the stops, and amplitude-varying impulses otherwise.At the time that the pulse models were developed the CM was used to characterize the pilot element.Both the Structural Model and the CM yield equivalent frequency responses for the pilot (δ/e in Fig. 7a) in the region of crossover frequency ωc [7].The following describes the procedure that was employed to recognize and formulate the pulse logic for both the PWM and PWAM techniques.The open loop frequency response (y/e in Fig. 7a) was computed, from which the ωc and the effective time delay  were estimated.Assuming the pilot acts like a first-order lead with a time delay (see Yp in Fig. 7a), when crossover occurs K can be written in terms of known constants and the unknown lead term TL.This is substituted back into Yp so that the only unknown is TL, and a bestfit is performed (solid blue line in Fig. 7b) with pilot's magnitude and phase (filled circles in Fig. 7b) to yield TL, hence Yp.The output of Yp is termed the CM stick response, and this was computed in time over the run and compared with the actual stick pulses (Fig. 7c).It was observed that in general a pulse is triggered by zero-crossings and opening speed reversals (i.e.away from zero) in the CM stick response.Fig. 7c also shows a pulse that does not correlate with either a zero crossing or an opening speed reversal, and this kind of pulse occurred often enough to warrant examining its trigger source.In Fig. 8b the areas under actual and crossover stick signals are integrated in time, with integration starting and ending when the sticks change polarity.It is seen that the integrations approximately match when the stick polarities flip.By inspection pulses were observed to obey the logic shown at top of Fig. 8, where a pulse ceases if the area under the actual stick is greater than some fixed percentage of the area under the crossover model's signal.Pulses are triggered when the crossover model's stick encounters a zero crossing or opening speed reversal, or when the area under the actual stick is less than some fixed percentage of the area under the crossover model's signal.It was also observed that there is generally consistent a delay between when a zero crossing or opening speed reversal occurs, and when a pulse is actually triggered.This appears to be a safeguard against spurious triggering by requiring a certain amount of time to pass and for the amplitude to rise above some minimum threshold before the operator commits to a pulse.The logic governing PWAM was similar to PWM, except that the variable pulse amplitude was assigned to be the CM's stick amplitude at the time of pulse trigger, multiplied by a constant.Fig. 9 compares the modeled and actual stick outputs for the PWM and PWAM styles, and they subjectively appear to agree well.In the next section, modeled and actual behavior will be compared using frequency response, as well as probability distributions of the stick amplitude and periods of stick inactivity (quiescence). MODEL VERIFICATIONBachelder and Aponso [15] identified a nonlinear pilot control technique termed 'amplitude clipping,' whereby the pilot responds to error as predicted by the CM up to a certain stick amplitude and then holds that amplitude until the error signal reverses and returns, at which time the pilot re-sumes active continuous tracking.The amplitude at which the control input is capped can vary over time.Examples are now given where Structural Model was used to identify the pilot element for the PWM, PWAM, and amplitude clipping control techniques.Rather than iterate on the undamped natural frequency of the open loop neuromuscular system (ωNM) along with the other parameters of the Structural Model (Fig. 3) until a best-fit with the observed data is obtained (or fixing ωNM at some assumed value), the power spectrum of pilot's stick was examined.Fig. 10a shows the power spectrum density (PSD) of the stick when amplitude clipping was used to control acceleration command dynamics.The frequencies of the SOS forcing function are denoted with open circles, the highest frequency located approximately at 5 rad/sec.Fig. 10b is a close-up beyond 5 rad/sec, and power can be observed up to about 10 rad/sec, showing a concentration at around 7 rad/sec.When jerk-command dynamics are controlled (again using amplitude clipping), Fig. 10d shows the power to be more evenly distributed between 5 and 10 rad/sec.Based on these observations, ωNM was fixed at 8 rad/sec when amplitude clipping was used as the control style.This is lower than the value used by Hess in [8], which is likely due to the different inceptor and limb characteristics (the gamepad joystick is controlled by the thumb). Fig. 10. Spectral decomposition of stick response: a) Using acceleration-command vehicle dynamics (forcing function power denoted by open circles); b) Close-up beyond the forcing function power. c) Using jerk-command vehicle dynamics; b) Close-up beyond the forcing function power.Using the delay employed in [8], the pilot time delay was fixed at 0.20 seconds, and the five other parameters of the pilot Structural Model (Ke, TL, Kδ, TK, ϛNM) were iterated in a Simulink model of Fig. 3 to minimize the cost function J given in Eqn.phs mag J i Yp i i Yp i i YpYv i i YpYv i                            In Eqn 2, Δ( ) refers to the absolute difference between observed and simulated variable ( ). ) (  is the standard deviation of the stick, and PDF is the probability density function of the stick amplitude (see Fig. 13a).The elements in Eqn 2 are weighted by constants  .The time domain metrics (σ and PDF) were included since it is possible for a very different stick power distribution and σ to produce the same frequency response.Four runs from the workload experiment are used to examine the pilot models.Three runs use the same display, stick, and vehicle dynamics (vehicle is acceleration-command), and are flown by three different pilots: one employing the PWM technique, the second PWAM, and the third amplitude clipping (AC).The fourth run used AC and jerk-command dynamics, flown by the same pilot who employed AC with acceleration-command dynamics.These four runs were selected to highlight differences due to techniques and vehicle dynamics.The parameters minimizing the cost function for four simulation runs are given in Table 2, along with various metrics.The estimated Bedford rating (computed from the modeled response as described in [15]), Best, and the actual Bedford rating are given in Table 2. Also compared is the relative correlated output ρ 2 , defined as the portion of the power in the stick output which exists at the disturbance frequencies, divided by the total stick power.For instance, in Fig. 10a, summing the areas flanking each forcing frequency (out to the first local minimum in PSD) yields the correlated power, and this is divided by the total PSD area.Fig. 11 shows the identified open loop and pilot frequency responses (computed using cross spectral densities, [3]) from the observed pilot data and from the data generated by the nonlinear simulation (nonlinear due to the pilot technique element YTECH).This example employed acceleration-command dynamics, and the pilot technique was amplitude clipping.The solid line denotes the linear frequency response produced without the nonlinear pilot technique element.The nonlinear effects of clipping are minimal except at the lower frequencies, where magnitude is reduced.Looking at Table 2 the relative correlated output ρ 2 for the simulation is 0.93, also reflecting the technique's minimal impact on remnant.Note that the actual value of ρ 2 was 0.85, suggesting that the pilot's contribution to remnant due to internally generated noise is approximately 8% (0.93-0.85) of the total stick power.Without an accurate model of pilot technique, the 15% total remnant observed from the pilot data could not have been partitioned into technique and internal noise. Table 2. Pilot model parameter values used to generate describing functions, and comparison of simulated and actual measures.Fig. 12 shows good correspondence between the time histories of the actual and simulated stick amplitudes.Actual and simulated stick PDFs compare favorably in Fig. 13a, as does the distribution of quiescence time in Fig. 13b.Quiescence was defined as when the stick's rate fell below a threshold, when stick amplitudes were non-zero (i.e.time did not accrue towards quiescence when the stick was in the zero-force, zero-amplitude position).The metrics for this run in Table 2 (K/s 2 dynamics, AC denotes amplitude clipping), in combination with Fig. 11 -Fig.13, indicate that the integrated components of the model reproduced the pilot's response with high accuracy.Of note is that the pilot did not employ the kinesthetic feedback loop (Kδ was zero), instead equalizing the error channel with gain and lead. Fig. 11. Identified open loop and pilot frequency responses for the pilot data and nonlinear model data, with the linear model overlaid (acceleration-command dynamics, Amplitude-Clipping model). Note the difference in scale between OpenLoop and Pilot responses.Simulation of the control style PWAM in the Structural Model is now examined.The sharp edges and corners observed in the stick response for both PWM and PWAM control infer that their neuromuscular dynamics affected frequencies far higher than what was measured when amplitude clipping (pseudo-continuous) control is used.When the joystick stops are reached (+/-100%) the neuromuscular mode does not factor at all.The neuromuscular pilot element YNM was thus set to unity when modeling PWM and PWAM, eliminating ωNM and ζNM from the identification process.Fig. 14 shows good model agreement with the actual frequency and time responses.The linear response (i.e. when the pilot technique element is left out) in Fig. 14b illustrates how highfidelity modeling can expose observed measurements as artifacts of technique rather than the result of internal processing.McRuer [3] describes the phenomenon of low frequency 'droop' observed in pilots, which was not accounted for by the basic CM.This low frequency phase loss increased with the order of the system being controlled, and in [7] was attributed to and reproduced using the inner kinesthetic feedback loop.However, in this run the marked difference in phase (and magnitude) between the linear response and the nonlinear response at the lowest frequency is due entirely due to the PWAM technique.If the kines-thetic feedback were contributing to the phase and magnitude droop this would have caused the linear response to move toward the modeled nonlinear response.The actual measured phase agrees with the nonlinear model, including at the higher frequencies where the pilot phase also departs from the linear response.Phase droop also occurs with rate and position command dynamics [3], where continuous control would certainly be employed and technique would not be a factor, but this example highlights the potential importance of including pilot technique when assigning causality.Looking at Table 2, the pilot made substantial use of inner-loop proprioceptive feedback (Kδ = 0.25), and remnant due to technique (1-ρ 2 sim = 24%) was considerably larger than when amplitude clipping was employed by the other pilot (where 1-ρ 2 sim = 7%).Despite the seemingly stochastic nature of PWAM, the pilot's internal remnant (4%) was half the internal noise associated with the amplitude clipping technique.This is quite remarkable given that the pilot appears to be simultaneously integrating both the physical stick position as well as the internally-generated stick position to generate the pulse commands (see Fig. 8).The frequency and time domain results in Fig. 15 show excellent correspondence between modeled and pilot data for PWM control.The simulated PWM control technique produced 33% remnant, and since this coincided with the remnant observed in the experimental data then the pilot apparently generated almost no internal noise (given the model's accuracy).The technique also appears to be responsible for the leveling of magnitude at the higher frequencies (note the observed and nonlinear model magnitudes match, departing from the linear response in Fig. 15).Kinesthetic feedback was activated (Kδ =0.10), but to a lesser extent than with PWAM.The last example examines a run that employed amplitude clipping to control jerk dynamics -dynamics which are extremely challenging to stabilize and to conduct tracking with.In Fig. 16 the model produced a good match with the pilot data in frequency response and stick amplitude distribution, and a fair match in the time response and quiescence distribution.The internal noise (ρ 2 sim -ρ 2 act) of the pilot is the highest (11%) out of the four runs presented, and in contrast to when this pilot was controlling acceleration command dynamics, he now employed proprioceptive feedback (Kδ = 0.10) and generated the largest lag time constant (TK=1.13,more than double what the other two pilots operated at).With the evidence suggesting that both PWM and PWAM integrate the internal stick signal and the physical stick position (Fig. 8b), the Structural Model has been modified (Fig. 17) with techniquedependent switches that can enable the integration paths to the pilot technique element when needed.Since the two pulsive techniques required pure kinesthetic integration of the stick, it seems reasonable to assume that this same information would be employed by the first-order lag in the kinesthetic feedback loop (see YPF in Fig. 3).Coincidentally PWM and PWAM were both observed to employ this loop. CONCLUSIONSTwo models representing two types of observed pilot pulsive behaviorpulse width modulation (PWM), and pulse width amplitude modulation (PWAM)were developed.These two pulsive models and a third nonlinear model (amplitude-clipped continuous control) were analyzed using pilot data Hess' pilot Structural Model.Preliminary results suggest:1) The pulsive models used in conjunction with the pilot Structural Model closely reproduced the pilot data both in the frequency and time domains during closedloop simulation.This suggests that for the range of tasks and control styles encountered, the models captured the fundamental mechanisms governing pulsive and control processes.2) Pulsing can produce artifacts such as low frequency droop that may appear as characteristics internal to the pilot when they are the result of control technique.Accurate modeling can identify such artifacts.3) The pulse models developed give important insight for the amount of remnant (stick output uncorrelated with the forcing function) that arises from nonlinear pilot technique, and for the remaining remnant arising from different sources unrelated to tracking control (i.e.neuromuscular tremor, etc.).4) In addition to emulating observed pilot behavior, the pilot Structural Model provides a method of economy for modeling higher frequency response.By assuming an invariant pilot time delay and neuromuscular damping, and using the stick power spectrum to estimate the neuromuscular natural frequency, kinesthetic feedback systematically emulated high frequency phase loss.In contrast, the single-loop CM accounts for this phase loss using an effective time delay, which is roughly attributed to increased level of difficulty.5) During pulsive control of K/s 2 (acceleration command) vehicle dynamics, it appears that skilled pilots: 1) produce a continuous, internally-generated stick signal that they integrated in time; 2) integrate the actual stick position; and 3) compare the two integrations to issue or cease a pulse command.Since the two pulsive techniques (PWM and PWAM) required pure kinesthetic integration of the stick, it seems reasonable to assume that this same information could be employed by the firstorder lag in the kinesthetic feedback loop.Both pulsive techniques were observed to use this loop.6) The pilot employing PWM rapidly deflected the gamepad's joystick to the stops (i.e.maximum deflection), producing sharplyedged and cornered pulses.The PWAM style employed both this technique and a train of spikes, where the stick impulsively rose to some peak amplitude and rapidly return to zero when released.The best matching between the modeled and observed behavior (PWM and PWAM) was obtained by setting the neuromuscular pilot element YNM to unity, implying that those techniques were largely unaffected by the neuromuscular constraints typically associated with manual tracking.Thus pulsing can present a method for ameliorating unfavorable stick characteristics.The cases explored in this study are too few to offer statistically significant results, rather they are intended to provide insight and guidance for future research.error and stick signals (respectively e Yp , m Yp  ), a pilot element n Yp generating the neuromuscular force of the particular limb which drives the manipulator, the manipulator dynamics  Y that pro- duces the control system input (usually stick displacement) from the force command, a controlled element c Y representing the vehicle dynamics, and the display element d closed, the simple quadratic form for n Yp can exhibit the key fea- tures of measured high-frequency human control-ler dynamics, namely, a typically subcritical damping ratio CL n  , and a minimum second-order am- plitude fall-off beyond the undamped natural frequency CL n  .The injected remnant signal ne is included to account for nonlinearities and/or time variations in quasilinear fashion. Fig. 33Fig. 3 reduces the Structural Model to the components relevant for fixed-base compensatory control (hence the vestibular paths are removed), with two modifications.The pilot element operating on the error channel is now represented by e Y , Fig. 3 .3Fig. 3. Pilot Structural Model simplified for fixed-base tracking. Fig. 4 .4Fig. 4. Station-keeping task.a) Pilot, display, and vehicle elements; b) Range of conditions for display and vehicle elements. Fig. 5 .5Fig. 5. Simulation environment. Fig. 6 .6Fig. 6.Pilot control techniques used in tracking task.a) Pulse width modulation; b) Pulse width-amplitude modulation. Fig. 7 .7Fig. 7. CM employment for PWM logic identification.a) Basic CM elements; b) Identified pilot frequency response for PWM technique; c) CM stick signal overlaid on actual stick history showing correspondence between pulsing and CM's stick signal. Fig. 8 .8Fig. 8. PWM Crossover Model and stick integration.a) CM stick signal overlaid on actual stick; b) Comparison CM integration and actual stick integration (they are roughly equal at each zero crossing of the CM output).Pulse logic shown at top, governing pulse width and pulses not associated with zero crossing and opening speed reversal. Fig. 9 .9Fig. 9. Comparison of pulse models with actual data: a) Pulse Width Modulation; b) Pulse Width Amplitude Modulation. difference in the open loop magnitudes (YpYv , in dB) between observed and simulated at each frequency i of the forcing function, and phase of the pilot element, respectively. Fig. 12 .12Fig. 12.Comparison of actual and simulated stick (acceleration-command dynamics, Amplitude-Clipping model). Fig. 13 .13Fig. 13.Distributions for stick associated with Fig. 12 comparing actual and model: a) Stick amplitude distribution; b) Stick quiescence distribution. Fig. 14 .14Fig. 14.Pulse Width Amplitude Modulation (acceleration command dynamics): a) Comparison of actual and simulated stick; b) Frequency response comparison of open-loop; c) Stick amplitude distribution; d) Stick quiescence distribution. Fig. 15 .15Fig. 15.Pulse Width Modulation (acceleration command dynamics): a) Comparison of actual and simulated stick; b) Frequency response comparison of open-loop; c) Stick amplitude distribution; d) Stick quiescence distribution. Fig. 16 .16Fig. 16.Amplitude Clipping (jerk command dynamics): a) Comparison of actual and simulated stick; b) Frequency response comparison of open-loop; c) Stick amplitude distribution; d) Stick quiescence distribution. Fig. 17 .17Fig. 17.Pilot Structural Model showing integration of internal stick and physical stick signals as technique-dependent inputs to the pilot technique element. Table 1 (to approximately generate1M  , the rate ofthe output). The vehicle dynamics in Table 1 areposition, rate, and acceleration command, respec-tively, and the correspondingY is a first-orderPFlead, proportional, and first-order lag, respectively. Table 1 .1Proprioceptive feedback element YPF form. AcknowledgmentsThis work was supported by cooperative agreement NNX16AJ91A between the U.S. Army Aviation Development Directorate and San Jose State University.This paper has been approved for public release: unlimited distribution. Unified Theory for Aircraft Handling Qualities and Adverse Aircraft-Pilot Coupling RAHess 10.2514/2.4169 Journal of Guidance, Control, and Dynamics Journal of Guidance, Control, and Dynamics 0731-5090 1533-3884 20 6 1997 American Institute of Aeronautics and Astronautics (AIAA) Hess, R. A., "Unified Theory for Aircraft Handling Qualities and Adverse Aircraft-Pilot Coupling", Journal of Guid- ance, Control, and Dynamics, Vol. 20, No. 6, 1997. The nature of the operator's response in manual control, and its implications for controller design ATustin 10.1049/ji-2a.1947.0025 Journal of the Institution of Electrical Engineers - Part IIA: Automatic Regulators and Servo Mechanisms 2054-0728 94 2 1947 Institution of Engineering and Technology (IET) Tustin, A., "The nature of the human operators response in manual control and its implication for controller design," J. Instn. Elect. Engrs, 94, 190, 1947. DYNAMIC RESPONSE OF HUMAN OPERATORS DuaneTMcruer EzraSKrendel 10.21236/ad0110693 November 1973 Defense Technical Information Center 188 McRuer, D. T. and Krendel, E. S., "Mathematical Models of Human Pilot Behavior," No. AGARDograph No. 188, November 1973. Investigation of limb-side stick dynamic interaction with roll controll DonaldEJohnston DuaneTMcruer 10.2514/3.20200 Journal of Guidance, Control, and Dynamics Journal of Guidance, Control, and Dynamics 0731-5090 1533-3884 10 2 March-April 1987 American Institute of Aeronautics and Astronautics (AIAA) Johnston, D.E., and McRuer, D. T., "Investigation of Limb-Side Stick Dynamic Interaction with Roll Control," Journal of Guidance, Control, and Dynamics, Vol 10, No 2, March-April 1987, pp 178-186. Wavelet-Based Analysis of Roll Ratchet Using a Flight Test Database EdBachelder DavidKlyde 10.2514/6.2003-5692 AIAA Atmospheric Flight Mechanics Conference and Exhibit Austin, TX American Institute of Aeronautics and Astronautics August 11-14, 2003 Bachelder, E. N., and Klyde, D. H., "Wavelet-Based Analysis of Roll Ratchet Using a Flight Test Database," AIAA 2003-5692 presented at AIAA Atmospheric Flight Mechanics Conference, Austin, TX, August 11-14, 2003. A unified theory for pilot opinion rating RalphHSmith 10.1037/e506152009-039 Proceedings of the Twelfth Annual Conference on Manual Control the Twelfth Annual Conference on Manual Control American Psychological Association (APA) May 1976 Smith, R. H., "A Unified Theory for Pilot Opinion Rating, "Proceedings of the Twelfth Annual Conference on Manual Control, May 1976, pp. 542-558. Dual-Loop Model of the Human Controller RAHess 10.2514/3.55773 Journal of Guidance, Control, and Dynamics Journal of Guidance, Control, and Dynamics 0731-5090 1533-3884 1 4 July-Aug. 1978 American Institute of Aeronautics and Astronautics (AIAA) R. A. Hess, "A Dual-Loop Model of the Human Controller," Journal of Guidance, Control, and Dynamics, vol. 1, pp. 254-260, July-Aug. 1978. Pursuit Tracking and Higher Levels of Skill Development in the Human Pilot RonaldAHess 10.1109/tsmc.1981.4308673 IEEE Transactions on Systems, Man, and Cybernetics IEEE Trans. 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